YES H-Termination proof of ../tpdb/FP/full_haskell/FiniteMap_keysFM_GE_9.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ LR

mainModule Main
  ((FiniteMap.keysFM_GE :: Ord a => FiniteMap.FiniteMap (Maybe a) b  ->  Maybe a  ->  [Maybe a]) :: Ord a => FiniteMap.FiniteMap (Maybe a) b  ->  Maybe a  ->  [Maybe a])

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

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

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

  foldFM_GE :: Ord 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

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

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


module Main where
  import qualified FiniteMap
import qualified Maybe
import qualified Prelude

module Maybe where
  import qualified FiniteMap
import qualified Main
import qualified Prelude


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

is transformed to
keysFM_GE0 key elt rest = key : rest

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

mainModule Main
  ((FiniteMap.keysFM_GE :: Ord b => FiniteMap.FiniteMap (Maybe b) a  ->  Maybe b  ->  [Maybe b]) :: Ord b => FiniteMap.FiniteMap (Maybe b) a  ->  Maybe b  ->  [Maybe b])

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

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

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

  foldFM :: (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

  keysFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 key elt rest = key : rest

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


module Main where
  import qualified FiniteMap
import qualified Maybe
import qualified Prelude

module Maybe where
  import qualified FiniteMap
import qualified Main
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 Main
  ((FiniteMap.keysFM_GE :: Ord b => FiniteMap.FiniteMap (Maybe b) a  ->  Maybe b  ->  [Maybe b]) :: Ord b => FiniteMap.FiniteMap (Maybe b) a  ->  Maybe b  ->  [Maybe b])

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

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

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

  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 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

  keysFM_GE :: Ord b => FiniteMap b a  ->  b  ->  [b]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 key elt rest = key : rest

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


module Main where
  import qualified FiniteMap
import qualified Maybe
import qualified Prelude

module Maybe where
  import qualified FiniteMap
import qualified Main
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 Main
  ((FiniteMap.keysFM_GE :: Ord b => FiniteMap.FiniteMap (Maybe b) a  ->  Maybe b  ->  [Maybe b]) :: Ord b => FiniteMap.FiniteMap (Maybe b) a  ->  Maybe b  ->  [Maybe b])

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

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

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

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

  foldFM_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

  keysFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 key elt rest = key : rest

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


module Main where
  import qualified FiniteMap
import qualified Maybe
import qualified Prelude

module Maybe where
  import qualified FiniteMap
import qualified Main
import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

mainModule Main
  ((FiniteMap.keysFM_GE :: Ord a => FiniteMap.FiniteMap (Maybe a) b  ->  Maybe a  ->  [Maybe a]) :: Ord a => FiniteMap.FiniteMap (Maybe a) b  ->  Maybe a  ->  [Maybe a])

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

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

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

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

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

  keysFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 key elt rest = key : rest

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


module Main where
  import qualified FiniteMap
import qualified Maybe
import qualified Prelude

module Maybe where
  import qualified FiniteMap
import qualified Main
import qualified Prelude


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

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

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

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

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

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

The following Function with conditions
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

absReal0 x True = `negate` x

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

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

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

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

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

compare3 x y = compare2 x y (x == y)



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

mainModule Main
  ((FiniteMap.keysFM_GE :: Ord a => FiniteMap.FiniteMap (Maybe a) b  ->  Maybe a  ->  [Maybe a]) :: Ord a => FiniteMap.FiniteMap (Maybe a) b  ->  Maybe a  ->  [Maybe a])

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

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

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

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

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

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

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

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

  keysFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 key elt rest = key : rest

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


module Main where
  import qualified FiniteMap
import qualified Maybe
import qualified Prelude

module Maybe where
  import qualified FiniteMap
import qualified Main
import qualified Prelude


Let/Where Reductions:
The bindings of the following Let/Where expression
reduce1 x y (y == 0)
where 
d  = gcd x y
reduce0 x y True = x `quot` d :% (y `quot` d)
reduce1 x y True = error []
reduce1 x y False = reduce0 x y otherwise

are unpacked to the following functions on top level
reduce2Reduce1 vyw vyx x y True = error []
reduce2Reduce1 vyw vyx x y False = reduce2Reduce0 vyw vyx x y otherwise

reduce2D vyw vyx = gcd vyw vyx

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

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

are unpacked to the following functions on top level
gcd0Gcd' x vvy = gcd0Gcd'2 x vvy
gcd0Gcd' x y = gcd0Gcd'0 x y

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

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

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



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

mainModule Main
  ((FiniteMap.keysFM_GE :: Ord b => FiniteMap.FiniteMap (Maybe b) a  ->  Maybe b  ->  [Maybe b]) :: Ord b => FiniteMap.FiniteMap (Maybe b) a  ->  Maybe b  ->  [Maybe b])

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

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

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

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

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

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

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

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

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

  keysFM_GE :: Ord b => FiniteMap b a  ->  b  ->  [b]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 key elt rest = key : rest

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


module Main where
  import qualified FiniteMap
import qualified Maybe
import qualified Prelude

module Maybe where
  import qualified FiniteMap
import qualified Main
import qualified Prelude


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

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

mainModule Main
  (FiniteMap.keysFM_GE :: Ord b => FiniteMap.FiniteMap (Maybe b) a  ->  Maybe b  ->  [Maybe b])

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

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

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

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

  foldFM_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

  keysFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [a]
keysFM_GE fm fr = foldFM_GE keysFM_GE0 [] fr fm

  
keysFM_GE0 key elt rest = key : rest

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


module Main where
  import qualified FiniteMap
import qualified Maybe
import qualified Prelude

module Maybe where
  import qualified FiniteMap
import qualified Main
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_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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primPlusNat(Succ(vyy10300), Succ(vyy401000)) → new_primPlusNat(vyy10300, 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_primCmpNat(Succ(vyy65000), Succ(vyy66000)) → new_primCmpNat(vyy65000, vyy66000)

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_foldFM_GE11(vyy49, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE21(vyy330, vyy331, new_foldFM_GE5(vyy49, vyy334, h, ba), vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba)
new_foldFM_GE21(vyy330, vyy331, vyy69, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba) → new_foldFM_GE11(new_keysFM_GE0(vyy330, vyy331, vyy69, h, ba), vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs0(vyy3330, h), h, ba)
new_foldFM_GE11(vyy49, vyy330, vyy331, vyy332, vyy333, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), False, h, ba) → new_foldFM_GE11(vyy49, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs0(vyy3340, h), h, ba)
new_foldFM_GE4(vyy49, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba) → new_foldFM_GE11(vyy49, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs0(vyy3340, h), h, ba)
new_foldFM_GE11(vyy49, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba) → new_foldFM_GE4(vyy49, vyy334, h, ba)
new_foldFM_GE11(vyy49, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE4(vyy49, vyy334, h, ba)

The TRS R consists of the following rules:

new_lt14(vyy650, vyy660, ge, gf) → new_esEs8(new_compare12(vyy650, vyy660, ge, gf), LT)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, hd)) → new_esEs4(vyy3000, vyy400, hd)
new_esEs12(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, baa)) → new_esEs20(vyy3000, vyy400, baa)
new_esEs25(vyy3001, vyy401, ty_Int) → new_esEs19(vyy3001, vyy401)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt4(vyy650, vyy660) → new_esEs8(new_compare5(vyy650, vyy660), LT)
new_esEs21(vyy650, vyy660, app(app(ty_@2, bb), bc)) → new_esEs6(vyy650, vyy660, bb, bc)
new_primCmpNat2(Zero, vyy6500) → LT
new_lt19(vyy651, vyy661, app(app(ty_Either, dab), dac)) → new_lt14(vyy651, vyy661, dab, dac)
new_ltEs4(EQ, GT) → True
new_compare29(vyy650, vyy660, False, ga, gb, gc) → new_compare111(vyy650, vyy660, new_ltEs15(vyy650, vyy660, ga, gb, gc), ga, gb, gc)
new_esEs28(vyy650, vyy660, ty_Char) → new_esEs13(vyy650, vyy660)
new_compare24(vyy650, vyy660, False) → new_compare110(vyy650, vyy660, new_ltEs4(vyy650, vyy660))
new_compare([], :(vyy660, vyy661), bff) → LT
new_compare10(vyy650, vyy660, True, bb, bc) → LT
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Nothing, gg) → False
new_esEs4(Nothing, Just(vyy400), gg) → False
new_ltEs10(vyy65, vyy66, ceg) → new_not(new_esEs8(new_compare8(vyy65, vyy66, ceg), GT))
new_lt7(vyy650, vyy660, gd) → new_esEs8(new_compare(vyy650, vyy660, gd), LT)
new_lt20(vyy650, vyy660, app(app(ty_Either, dbd), dbe)) → new_lt14(vyy650, vyy660, dbd, dbe)
new_ltEs6(Nothing, Just(vyy6600), fg) → True
new_esEs27(vyy651, vyy661, ty_Bool) → new_esEs17(vyy651, vyy661)
new_lt19(vyy651, vyy661, ty_Int) → new_lt4(vyy651, vyy661)
new_ltEs9(vyy65, vyy66) → new_not(new_esEs8(new_compare13(vyy65, vyy66), GT))
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(vyy650), Right(vyy660), bbe, bab) → True
new_compare32(vyy650, vyy660, ty_Bool) → new_compare30(vyy650, vyy660)
new_lt20(vyy650, vyy660, ty_@0) → new_lt18(vyy650, vyy660)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs15(vyy3000, vyy400)
new_compare(:(vyy650, vyy651), [], bff) → GT
new_lt8(vyy650, vyy660, app(app(app(ty_@3, ga), gb), gc)) → new_lt6(vyy650, vyy660, ga, gb, gc)
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs21(vyy650, vyy660, ty_Bool) → new_esEs17(vyy650, vyy660)
new_lt19(vyy651, vyy661, ty_Integer) → new_lt11(vyy651, vyy661)
new_esEs12(vyy3000, vyy400, app(ty_[], fd)) → new_esEs18(vyy3000, vyy400, fd)
new_lt20(vyy650, vyy660, app(ty_Maybe, dbb)) → new_lt13(vyy650, vyy660, dbb)
new_foldFM_GE22(vyy330, vyy331, vyy69, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba) → new_foldFM_GE12(new_keysFM_GE0(vyy330, vyy331, vyy69, h, ba), vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs0(vyy3330, h), h, ba)
new_lt8(vyy650, vyy660, ty_Bool) → new_lt10(vyy650, vyy660)
new_lt8(vyy650, vyy660, ty_@0) → new_lt18(vyy650, vyy660)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_foldFM_GE12(vyy49, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba) → new_foldFM_GE30(vyy330, vyy331, new_foldFM_GE5(vyy49, vyy334, h, ba), h, ba)
new_esEs11(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_compare16(@0, @0) → EQ
new_esEs17(True, True) → True
new_lt8(vyy650, vyy660, app(app(ty_@2, bb), bc)) → new_lt16(vyy650, vyy660, bb, bc)
new_lt10(vyy650, vyy660) → new_esEs8(new_compare30(vyy650, vyy660), LT)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Ratio, beb), bch) → new_esEs20(vyy3000, vyy400, beb)
new_esEs21(vyy650, vyy660, app(app(app(ty_@3, ga), gb), gc)) → new_esEs7(vyy650, vyy660, ga, gb, gc)
new_lt20(vyy650, vyy660, ty_Float) → new_lt12(vyy650, vyy660)
new_esEs25(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_esEs12(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs7(Left(vyy650), Left(vyy660), app(app(app(ty_@3, bbb), bbc), bbd), bab) → new_ltEs15(vyy650, vyy660, bbb, bbc, bbd)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs28(vyy650, vyy660, ty_Double) → new_esEs14(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, app(app(app(ty_@3, dg), dh), ea)) → new_esEs7(vyy3001, vyy401, dg, dh, ea)
new_esEs11(vyy3001, vyy401, app(ty_Ratio, ec)) → new_esEs20(vyy3001, vyy401, ec)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, cea)) → new_esEs4(vyy3000, vyy400, cea)
new_primCmpNat1(vyy6500, Succ(vyy6600)) → new_primCmpNat0(vyy6500, vyy6600)
new_esEs27(vyy651, vyy661, ty_Double) → new_esEs14(vyy651, vyy661)
new_compare30(vyy650, vyy660) → new_compare25(vyy650, vyy660, new_esEs17(vyy650, vyy660))
new_ltEs6(Just(vyy6500), Just(vyy6600), app(ty_Ratio, bhc)) → new_ltEs10(vyy6500, vyy6600, bhc)
new_compare32(vyy650, vyy660, app(app(ty_@2, cfe), cff)) → new_compare15(vyy650, vyy660, cfe, cff)
new_ltEs6(Just(vyy6500), Just(vyy6600), app(app(ty_@2, bhh), caa)) → new_ltEs13(vyy6500, vyy6600, bhh, caa)
new_esEs10(vyy3002, vyy402, app(ty_Ratio, da)) → new_esEs20(vyy3002, vyy402, da)
new_pePe(False, vyy127) → vyy127
new_lt13(vyy650, vyy660, fg) → new_esEs8(new_compare7(vyy650, vyy660, fg), LT)
new_esEs18([], :(vyy400, vyy401), cae) → False
new_esEs18(:(vyy3000, vyy3001), [], cae) → False
new_primCmpNat1(vyy6500, Zero) → GT
new_ltEs7(Right(vyy650), Right(vyy660), bbe, app(app(ty_@2, bcc), bcd)) → new_ltEs13(vyy650, vyy660, bcc, bcd)
new_lt19(vyy651, vyy661, ty_Ordering) → new_lt9(vyy651, vyy661)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Bool) → new_ltEs5(vyy6500, vyy6600)
new_ltEs19(vyy652, vyy662, app(ty_[], cgg)) → new_ltEs11(vyy652, vyy662, cgg)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Char, bab) → new_ltEs12(vyy650, vyy660)
new_esEs22(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare26(vyy650, vyy660, False, fg) → new_compare14(vyy650, vyy660, new_ltEs6(vyy650, vyy660, fg), fg)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_@2, bdc), bdd), bch) → new_esEs6(vyy3000, vyy400, bdc, bdd)
new_esEs20(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cbh) → new_asAs(new_esEs24(vyy3000, vyy400, cbh), new_esEs23(vyy3001, vyy401, cbh))
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Maybe, bde), bch) → new_esEs4(vyy3000, vyy400, bde)
new_ltEs14(vyy65, vyy66) → new_not(new_esEs8(new_compare18(vyy65, vyy66), GT))
new_esEs10(vyy3002, vyy402, app(app(ty_@2, ca), cb)) → new_esEs6(vyy3002, vyy402, ca, cb)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Ordering, bch) → new_esEs8(vyy3000, vyy400)
new_esEs27(vyy651, vyy661, ty_Int) → new_esEs19(vyy651, vyy661)
new_primCmpNat0(Zero, Succ(vyy66000)) → LT
new_esEs22(vyy3000, vyy400, ty_Float) → new_esEs15(vyy3000, vyy400)
new_esEs27(vyy651, vyy661, app(app(app(ty_@3, daf), dag), dah)) → new_esEs7(vyy651, vyy661, daf, dag, dah)
new_esEs21(vyy650, vyy660, ty_Char) → new_esEs13(vyy650, vyy660)
new_esEs25(vyy3001, vyy401, app(app(ty_Either, ccc), ccd)) → new_esEs5(vyy3001, vyy401, ccc, ccd)
new_esEs10(vyy3002, vyy402, ty_Char) → new_esEs13(vyy3002, vyy402)
new_esEs25(vyy3001, vyy401, app(app(ty_@2, cce), ccf)) → new_esEs6(vyy3001, vyy401, cce, ccf)
new_esEs8(LT, LT) → True
new_esEs5(Left(vyy3000), Left(vyy400), ty_@0, bch) → new_esEs9(vyy3000, vyy400)
new_lt5(vyy650, vyy660, fh) → new_esEs8(new_compare8(vyy650, vyy660, fh), LT)
new_ltEs6(Just(vyy6500), Just(vyy6600), app(app(ty_Either, bhf), bhg)) → new_ltEs7(vyy6500, vyy6600, bhf, bhg)
new_ltEs8(vyy65, vyy66) → new_not(new_esEs8(new_compare19(vyy65, vyy66), GT))
new_lt19(vyy651, vyy661, app(app(ty_@2, dad), dae)) → new_lt16(vyy651, vyy661, dad, dae)
new_esEs25(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Bool) → new_ltEs5(vyy650, vyy660)
new_esEs28(vyy650, vyy660, ty_Integer) → new_esEs16(vyy650, vyy660)
new_lt11(vyy650, vyy660) → new_esEs8(new_compare19(vyy650, vyy660), LT)
new_ltEs5(True, False) → False
new_pePe(True, vyy127) → True
new_primEqNat0(Zero, Zero) → True
new_esEs5(Right(vyy3000), Right(vyy400), bec, app(app(ty_@2, bef), beg)) → new_esEs6(vyy3000, vyy400, bef, beg)
new_ltEs12(vyy65, vyy66) → new_not(new_esEs8(new_compare31(vyy65, vyy66), GT))
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_@0) → new_ltEs16(vyy650, vyy660)
new_esEs25(vyy3001, vyy401, app(ty_[], cdc)) → new_esEs18(vyy3001, vyy401, cdc)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Double) → new_ltEs14(vyy650, vyy660)
new_esEs12(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_lt8(vyy650, vyy660, ty_Integer) → new_lt11(vyy650, vyy660)
new_esEs27(vyy651, vyy661, ty_Char) → new_esEs13(vyy651, vyy661)
new_esEs14(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs19(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs5(True, True) → True
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_esEs13(Char(vyy3000), Char(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs13(vyy3000, vyy400)
new_compare(:(vyy650, vyy651), :(vyy660, vyy661), bff) → new_primCompAux1(vyy650, vyy660, new_compare(vyy651, vyy661, bff), bff)
new_foldFM_GE12(vyy49, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE22(vyy330, vyy331, new_foldFM_GE5(vyy49, vyy334, h, ba), vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, ty_@0) → new_esEs9(vyy3001, vyy401)
new_keysFM_GE0(vyy330, vyy331, vyy68, h, ba) → :(vyy330, vyy68)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, app(app(app(ty_@3, bce), bcf), bcg)) → new_ltEs15(vyy650, vyy660, bce, bcf, bcg)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(vyy1030), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1030, vyy40100)))
new_primCmpInt(Pos(Succ(vyy6500)), Pos(vyy660)) → new_primCmpNat1(vyy6500, vyy660)
new_esEs11(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_lt20(vyy650, vyy660, ty_Double) → new_lt17(vyy650, vyy660)
new_esEs5(Right(vyy3000), Right(vyy400), bec, app(ty_[], bfd)) → new_esEs18(vyy3000, vyy400, bfd)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs22(vyy3000, vyy400, app(ty_[], cbf)) → new_esEs18(vyy3000, vyy400, cbf)
new_ltEs19(vyy652, vyy662, app(app(app(ty_@3, chd), che), chf)) → new_ltEs15(vyy652, vyy662, chd, che, chf)
new_compare32(vyy650, vyy660, ty_Integer) → new_compare19(vyy650, vyy660)
new_compare9(vyy650, vyy660, ga, gb, gc) → new_compare29(vyy650, vyy660, new_esEs7(vyy650, vyy660, ga, gb, gc), ga, gb, gc)
new_compare17(vyy650, vyy660, True, ge, gf) → LT
new_compare29(vyy650, vyy660, True, ga, gb, gc) → EQ
new_lt20(vyy650, vyy660, ty_Ordering) → new_lt9(vyy650, vyy660)
new_compare25(vyy650, vyy660, True) → EQ
new_esEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bd, be, bf) → new_asAs(new_esEs12(vyy3000, vyy400, bd), new_asAs(new_esEs11(vyy3001, vyy401, be), new_esEs10(vyy3002, vyy402, bf)))
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Integer, bch) → new_esEs16(vyy3000, vyy400)
new_ltEs18(vyy651, vyy661, app(ty_Ratio, bga)) → new_ltEs10(vyy651, vyy661, bga)
new_ltEs19(vyy652, vyy662, ty_Integer) → new_ltEs8(vyy652, vyy662)
new_ltEs5(False, False) → True
new_ltEs18(vyy651, vyy661, app(app(ty_Either, bgd), bge)) → new_ltEs7(vyy651, vyy661, bgd, bge)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy10300), Zero) → Succ(vyy10300)
new_esEs10(vyy3002, vyy402, app(ty_[], cg)) → new_esEs18(vyy3002, vyy402, cg)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Bool, bab) → new_ltEs5(vyy650, vyy660)
new_compare28(vyy650, vyy660, False, bb, bc) → new_compare10(vyy650, vyy660, new_ltEs13(vyy650, vyy660, bb, bc), bb, bc)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, ceb), cec), ced)) → new_esEs7(vyy3000, vyy400, ceb, cec, ced)
new_esEs10(vyy3002, vyy402, ty_@0) → new_esEs9(vyy3002, vyy402)
new_esEs28(vyy650, vyy660, app(ty_Maybe, dbb)) → new_esEs4(vyy650, vyy660, dbb)
new_lt20(vyy650, vyy660, ty_Int) → new_lt4(vyy650, vyy660)
new_compare18(Double(vyy650, vyy651), Double(vyy660, vyy661)) → new_compare5(new_sr(vyy650, vyy660), new_sr(vyy651, vyy661))
new_ltEs19(vyy652, vyy662, ty_Float) → new_ltEs9(vyy652, vyy662)
new_esEs21(vyy650, vyy660, ty_Double) → new_esEs14(vyy650, vyy660)
new_esEs21(vyy650, vyy660, app(ty_[], gd)) → new_esEs18(vyy650, vyy660, gd)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bdf), bdg), bdh), bch) → new_esEs7(vyy3000, vyy400, bdf, bdg, bdh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(vyy650), Left(vyy660), bbe, bab) → False
new_ltEs19(vyy652, vyy662, ty_Ordering) → new_ltEs4(vyy652, vyy662)
new_esEs27(vyy651, vyy661, app(app(ty_Either, dab), dac)) → new_esEs5(vyy651, vyy661, dab, dac)
new_primCmpNat2(Succ(vyy6600), vyy6500) → new_primCmpNat0(vyy6600, vyy6500)
new_esEs11(vyy3001, vyy401, ty_Float) → new_esEs15(vyy3001, vyy401)
new_esEs10(vyy3002, vyy402, ty_Float) → new_esEs15(vyy3002, vyy402)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primCompAux0(vyy132, GT) → GT
new_ltEs19(vyy652, vyy662, ty_Char) → new_ltEs12(vyy652, vyy662)
new_lt20(vyy650, vyy660, ty_Integer) → new_lt11(vyy650, vyy660)
new_esEs8(EQ, EQ) → True
new_esEs11(vyy3001, vyy401, ty_Int) → new_esEs19(vyy3001, vyy401)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Double, bch) → new_esEs14(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_esEs12(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs10(vyy3002, vyy402, app(app(app(ty_@3, cd), ce), cf)) → new_esEs7(vyy3002, vyy402, cd, ce, cf)
new_ltEs7(Left(vyy650), Left(vyy660), ty_@0, bab) → new_ltEs16(vyy650, vyy660)
new_lt19(vyy651, vyy661, app(app(app(ty_@3, daf), dag), dah)) → new_lt6(vyy651, vyy661, daf, dag, dah)
new_compare32(vyy650, vyy660, app(ty_Ratio, ceh)) → new_compare8(vyy650, vyy660, ceh)
new_esEs26(vyy3000, vyy400, app(ty_[], cee)) → new_esEs18(vyy3000, vyy400, cee)
new_compare([], [], bff) → EQ
new_ltEs18(vyy651, vyy661, ty_Ordering) → new_ltEs4(vyy651, vyy661)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs4(EQ, LT) → False
new_esEs22(vyy3000, vyy400, app(ty_Ratio, cbg)) → new_esEs20(vyy3000, vyy400, cbg)
new_esEs27(vyy651, vyy661, ty_Float) → new_esEs15(vyy651, vyy661)
new_esEs21(vyy650, vyy660, app(ty_Ratio, fh)) → new_esEs20(vyy650, vyy660, fh)
new_lt8(vyy650, vyy660, ty_Float) → new_lt12(vyy650, vyy660)
new_esEs28(vyy650, vyy660, ty_Int) → new_esEs19(vyy650, vyy660)
new_esEs15(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs19(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt20(vyy650, vyy660, app(app(app(ty_@3, dbh), dca), dcb)) → new_lt6(vyy650, vyy660, dbh, dca, dcb)
new_primCmpNat0(Succ(vyy65000), Succ(vyy66000)) → new_primCmpNat0(vyy65000, vyy66000)
new_esEs22(vyy3000, vyy400, app(ty_Maybe, cbb)) → new_esEs4(vyy3000, vyy400, cbb)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, app(ty_Maybe, ccg)) → new_esEs4(vyy3001, vyy401, ccg)
new_ltEs18(vyy651, vyy661, ty_Bool) → new_ltEs5(vyy651, vyy661)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare10(vyy650, vyy660, False, bb, bc) → GT
new_compare27(vyy650, vyy660, True, ge, gf) → EQ
new_lt8(vyy650, vyy660, ty_Char) → new_lt15(vyy650, vyy660)
new_esEs21(vyy650, vyy660, ty_Int) → new_esEs19(vyy650, vyy660)
new_ltEs18(vyy651, vyy661, app(app(app(ty_@3, bgh), bha), bhb)) → new_ltEs15(vyy651, vyy661, bgh, bha, bhb)
new_compare14(vyy650, vyy660, False, fg) → GT
new_esEs5(Right(vyy3000), Right(vyy400), bec, app(app(ty_Either, bed), bee)) → new_esEs5(vyy3000, vyy400, bed, bee)
new_ltEs19(vyy652, vyy662, app(ty_Ratio, cge)) → new_ltEs10(vyy652, vyy662, cge)
new_primEqNat0(Succ(vyy300000), Succ(vyy40000)) → new_primEqNat0(vyy300000, vyy40000)
new_esEs27(vyy651, vyy661, ty_Ordering) → new_esEs8(vyy651, vyy661)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Integer) → new_ltEs8(vyy6500, vyy6600)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Int) → new_ltEs17(vyy6500, vyy6600)
new_primCompAux1(vyy650, vyy660, vyy128, bff) → new_primCompAux0(vyy128, new_compare32(vyy650, vyy660, bff))
new_ltEs19(vyy652, vyy662, ty_Double) → new_ltEs14(vyy652, vyy662)
new_esEs9(@0, @0) → True
new_compare111(vyy650, vyy660, True, ga, gb, gc) → LT
new_ltEs4(GT, EQ) → False
new_ltEs18(vyy651, vyy661, ty_@0) → new_ltEs16(vyy651, vyy661)
new_esEs11(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_ltEs19(vyy652, vyy662, app(app(ty_Either, cgh), cha)) → new_ltEs7(vyy652, vyy662, cgh, cha)
new_compare8(:%(vyy650, vyy651), :%(vyy660, vyy661), ty_Integer) → new_compare19(new_sr0(vyy650, vyy661), new_sr0(vyy660, vyy651))
new_esEs5(Left(vyy3000), Left(vyy400), ty_Int, bch) → new_esEs19(vyy3000, vyy400)
new_compare32(vyy650, vyy660, app(app(ty_Either, cfc), cfd)) → new_compare12(vyy650, vyy660, cfc, cfd)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Char) → new_ltEs12(vyy6500, vyy6600)
new_ltEs19(vyy652, vyy662, ty_Int) → new_ltEs17(vyy652, vyy662)
new_ltEs7(Left(vyy650), Left(vyy660), app(ty_[], bae), bab) → new_ltEs11(vyy650, vyy660, bae)
new_esEs11(vyy3001, vyy401, app(ty_Maybe, df)) → new_esEs4(vyy3001, vyy401, df)
new_esEs28(vyy650, vyy660, ty_Ordering) → new_esEs8(vyy650, vyy660)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_lt20(vyy650, vyy660, app(ty_Ratio, dba)) → new_lt5(vyy650, vyy660, dba)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_esEs11(vyy3001, vyy401, app(ty_[], eb)) → new_esEs18(vyy3001, vyy401, eb)
new_ltEs4(EQ, EQ) → True
new_ltEs19(vyy652, vyy662, app(ty_Maybe, cgf)) → new_ltEs6(vyy652, vyy662, cgf)
new_esEs12(vyy3000, vyy400, app(app(app(ty_@3, fa), fb), fc)) → new_esEs7(vyy3000, vyy400, fa, fb, fc)
new_ltEs6(Just(vyy6500), Nothing, fg) → False
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy65000), Zero) → GT
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Ordering) → new_ltEs4(vyy650, vyy660)
new_ltEs18(vyy651, vyy661, app(ty_[], bgc)) → new_ltEs11(vyy651, vyy661, bgc)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy6600))) → LT
new_compare32(vyy650, vyy660, ty_Ordering) → new_compare6(vyy650, vyy660)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, gh), ha)) → new_esEs5(vyy3000, vyy400, gh, ha)
new_esEs21(vyy650, vyy660, ty_Float) → new_esEs15(vyy650, vyy660)
new_ltEs4(GT, LT) → False
new_sr0(Integer(vyy6600), Integer(vyy6510)) → Integer(new_primMulInt(vyy6600, vyy6510))
new_lt8(vyy650, vyy660, app(app(ty_Either, ge), gf)) → new_lt14(vyy650, vyy660, ge, gf)
new_primPlusNat1(Succ(vyy10300), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy10300, vyy401000)))
new_esEs12(vyy3000, vyy400, ty_Float) → new_esEs15(vyy3000, vyy400)
new_compare28(vyy650, vyy660, True, bb, bc) → EQ
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_esEs28(vyy650, vyy660, app(app(ty_Either, dbd), dbe)) → new_esEs5(vyy650, vyy660, dbd, dbe)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, hb), hc)) → new_esEs6(vyy3000, vyy400, hb, hc)
new_ltEs5(False, True) → True
new_compare32(vyy650, vyy660, app(ty_[], cfb)) → new_compare(vyy650, vyy660, cfb)
new_ltEs6(Just(vyy6500), Just(vyy6600), app(ty_Maybe, bhd)) → new_ltEs6(vyy6500, vyy6600, bhd)
new_esEs22(vyy3000, vyy400, app(app(ty_@2, cah), cba)) → new_esEs6(vyy3000, vyy400, cah, cba)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Ordering, bab) → new_ltEs4(vyy650, vyy660)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_compare24(vyy650, vyy660, True) → EQ
new_ltEs7(Right(vyy650), Right(vyy660), bbe, app(ty_[], bbh)) → new_ltEs11(vyy650, vyy660, bbh)
new_foldFM_GE5(vyy49, EmptyFM, h, ba) → vyy49
new_foldFM_GE5(vyy49, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba) → new_foldFM_GE12(vyy49, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs0(vyy3340, h), h, ba)
new_esEs27(vyy651, vyy661, ty_@0) → new_esEs9(vyy651, vyy661)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Char) → new_ltEs12(vyy650, vyy660)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Float) → new_esEs15(vyy3001, vyy401)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs15(vyy3000, vyy400)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, app(ty_Ratio, bbf)) → new_ltEs10(vyy650, vyy660, bbf)
new_lt15(vyy650, vyy660) → new_esEs8(new_compare31(vyy650, vyy660), LT)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Float) → new_ltEs9(vyy6500, vyy6600)
new_compare17(vyy650, vyy660, False, ge, gf) → GT
new_compare26(vyy650, vyy660, True, fg) → EQ
new_primCompAux0(vyy132, LT) → LT
new_esEs23(vyy3001, vyy401, ty_Int) → new_esEs19(vyy3001, vyy401)
new_ltEs19(vyy652, vyy662, app(app(ty_@2, chb), chc)) → new_ltEs13(vyy652, vyy662, chb, chc)
new_compare32(vyy650, vyy660, ty_Int) → new_compare5(vyy650, vyy660)
new_not(False) → True
new_esEs28(vyy650, vyy660, ty_@0) → new_esEs9(vyy650, vyy660)
new_lt18(vyy650, vyy660) → new_esEs8(new_compare16(vyy650, vyy660), LT)
new_compare32(vyy650, vyy660, app(app(app(ty_@3, cfg), cfh), cga)) → new_compare9(vyy650, vyy660, cfg, cfh, cga)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs12(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_ltEs7(Left(vyy650), Left(vyy660), app(ty_Ratio, bac), bab) → new_ltEs10(vyy650, vyy660, bac)
new_ltEs7(Left(vyy650), Left(vyy660), app(ty_Maybe, bad), bab) → new_ltEs6(vyy650, vyy660, bad)
new_esEs22(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, ty_@0) → new_esEs9(vyy3001, vyy401)
new_foldFM_GE30(vyy330, vyy331, vyy68, h, ba) → new_keysFM_GE0(vyy330, vyy331, vyy68, h, ba)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Float, bch) → new_esEs15(vyy3000, vyy400)
new_esEs27(vyy651, vyy661, app(ty_[], daa)) → new_esEs18(vyy651, vyy661, daa)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, cde), cdf)) → new_esEs5(vyy3000, vyy400, cde, cdf)
new_esEs22(vyy3000, vyy400, app(app(app(ty_@3, cbc), cbd), cbe)) → new_esEs7(vyy3000, vyy400, cbc, cbd, cbe)
new_primCmpInt(Pos(Succ(vyy6500)), Neg(vyy660)) → GT
new_esEs21(vyy650, vyy660, ty_Integer) → new_esEs16(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_lt6(vyy650, vyy660, ga, gb, gc) → new_esEs8(new_compare9(vyy650, vyy660, ga, gb, gc), LT)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare27(vyy650, vyy660, False, ge, gf) → new_compare17(vyy650, vyy660, new_ltEs7(vyy650, vyy660, ge, gf), ge, gf)
new_compare19(Integer(vyy650), Integer(vyy660)) → new_primCmpInt(vyy650, vyy660)
new_ltEs18(vyy651, vyy661, ty_Float) → new_ltEs9(vyy651, vyy661)
new_esEs24(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs28(vyy650, vyy660, app(app(app(ty_@3, dbh), dca), dcb)) → new_esEs7(vyy650, vyy660, dbh, dca, dcb)
new_compare32(vyy650, vyy660, ty_@0) → new_compare16(vyy650, vyy660)
new_esEs5(Left(vyy3000), Right(vyy400), bec, bch) → False
new_esEs5(Right(vyy3000), Left(vyy400), bec, bch) → False
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs27(vyy651, vyy661, app(app(ty_@2, dad), dae)) → new_esEs6(vyy651, vyy661, dad, dae)
new_compare110(vyy650, vyy660, True) → LT
new_esEs11(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), bec, app(ty_Ratio, bfe)) → new_esEs20(vyy3000, vyy400, bfe)
new_primEqNat0(Zero, Succ(vyy40000)) → False
new_primEqNat0(Succ(vyy300000), Zero) → False
new_ltEs7(Left(vyy650), Left(vyy660), app(app(ty_Either, baf), bag), bab) → new_ltEs7(vyy650, vyy660, baf, bag)
new_compare110(vyy650, vyy660, False) → GT
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Double) → new_ltEs14(vyy6500, vyy6600)
new_esEs22(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, gg) → True
new_lt19(vyy651, vyy661, ty_Double) → new_lt17(vyy651, vyy661)
new_compare111(vyy650, vyy660, False, ga, gb, gc) → GT
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_[], bea), bch) → new_esEs18(vyy3000, vyy400, bea)
new_compare32(vyy650, vyy660, ty_Char) → new_compare31(vyy650, vyy660)
new_esEs12(vyy3000, vyy400, app(app(ty_Either, ed), ee)) → new_esEs5(vyy3000, vyy400, ed, ee)
new_lt19(vyy651, vyy661, app(ty_Ratio, chg)) → new_lt5(vyy651, vyy661, chg)
new_esEs27(vyy651, vyy661, ty_Integer) → new_esEs16(vyy651, vyy661)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Float) → new_ltEs9(vyy650, vyy660)
new_ltEs15(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cgb, cgc, cgd) → new_pePe(new_lt20(vyy650, vyy660, cgb), new_asAs(new_esEs28(vyy650, vyy660, cgb), new_pePe(new_lt19(vyy651, vyy661, cgc), new_asAs(new_esEs27(vyy651, vyy661, cgc), new_ltEs19(vyy652, vyy662, cgd)))))
new_esEs27(vyy651, vyy661, app(ty_Maybe, chh)) → new_esEs4(vyy651, vyy661, chh)
new_ltEs4(LT, GT) → True
new_compare6(vyy650, vyy660) → new_compare24(vyy650, vyy660, new_esEs8(vyy650, vyy660))
new_esEs27(vyy651, vyy661, app(ty_Ratio, chg)) → new_esEs20(vyy651, vyy661, chg)
new_esEs25(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_lt8(vyy650, vyy660, ty_Ordering) → new_lt9(vyy650, vyy660)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy6600))) → GT
new_compare5(vyy65, vyy66) → new_primCmpInt(vyy65, vyy66)
new_esEs12(vyy3000, vyy400, ty_Int) → new_esEs19(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Double) → new_esEs14(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), bec, app(app(app(ty_@3, bfa), bfb), bfc)) → new_esEs7(vyy3000, vyy400, bfa, bfb, bfc)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Integer, bab) → new_ltEs8(vyy650, vyy660)
new_lt8(vyy650, vyy660, ty_Int) → new_lt4(vyy650, vyy660)
new_esEs28(vyy650, vyy660, app(app(ty_@2, dbf), dbg)) → new_esEs6(vyy650, vyy660, dbf, dbg)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs16(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_compare25(vyy650, vyy660, False) → new_compare11(vyy650, vyy660, new_ltEs5(vyy650, vyy660))
new_esEs12(vyy3000, vyy400, app(ty_Ratio, ff)) → new_esEs20(vyy3000, vyy400, ff)
new_esEs21(vyy650, vyy660, app(ty_Maybe, fg)) → new_esEs4(vyy650, vyy660, fg)
new_ltEs17(vyy65, vyy66) → new_not(new_esEs8(new_compare5(vyy65, vyy66), GT))
new_lt12(vyy650, vyy660) → new_esEs8(new_compare13(vyy650, vyy660), LT)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Char, bch) → new_esEs13(vyy3000, vyy400)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Float, bab) → new_ltEs9(vyy650, vyy660)
new_esEs19(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_lt8(vyy650, vyy660, app(ty_Ratio, fh)) → new_lt5(vyy650, vyy660, fh)
new_esEs11(vyy3001, vyy401, app(app(ty_@2, dd), de)) → new_esEs6(vyy3001, vyy401, dd, de)
new_esEs28(vyy650, vyy660, app(ty_[], dbc)) → new_esEs18(vyy650, vyy660, dbc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs4(LT, EQ) → True
new_compare32(vyy650, vyy660, ty_Float) → new_compare13(vyy650, vyy660)
new_esEs10(vyy3002, vyy402, app(app(ty_Either, bg), bh)) → new_esEs5(vyy3002, vyy402, bg, bh)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Integer) → new_ltEs8(vyy650, vyy660)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs14(vyy3000, vyy400)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, app(app(ty_Either, bca), bcb)) → new_ltEs7(vyy650, vyy660, bca, bcb)
new_lt19(vyy651, vyy661, ty_@0) → new_lt18(vyy651, vyy661)
new_esEs12(vyy3000, vyy400, app(ty_Maybe, eh)) → new_esEs4(vyy3000, vyy400, eh)
new_ltEs16(vyy65, vyy66) → new_not(new_esEs8(new_compare16(vyy65, vyy66), GT))
new_asAs(False, vyy91) → False
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs16(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_lt16(vyy650, vyy660, bb, bc) → new_esEs8(new_compare15(vyy650, vyy660, bb, bc), LT)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Char) → new_esEs13(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy6500)), Neg(vyy660)) → new_primCmpNat2(vyy660, vyy6500)
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_ltEs7(Left(vyy650), Left(vyy660), ty_Double, bab) → new_ltEs14(vyy650, vyy660)
new_lt19(vyy651, vyy661, ty_Float) → new_lt12(vyy651, vyy661)
new_compare32(vyy650, vyy660, ty_Double) → new_compare18(vyy650, vyy660)
new_esEs18([], [], cae) → True
new_ltEs6(Just(vyy6500), Just(vyy6600), app(app(app(ty_@3, cab), cac), cad)) → new_ltEs15(vyy6500, vyy6600, cab, cac, cad)
new_esEs21(vyy650, vyy660, app(app(ty_Either, ge), gf)) → new_esEs5(vyy650, vyy660, ge, gf)
new_esEs21(vyy650, vyy660, ty_Ordering) → new_esEs8(vyy650, vyy660)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], hh)) → new_esEs18(vyy3000, vyy400, hh)
new_compare32(vyy650, vyy660, app(ty_Maybe, cfa)) → new_compare7(vyy650, vyy660, cfa)
new_gtEs0(vyy3330, h) → new_not(new_esEs8(new_compare26(vyy3330, Nothing, new_esEs4(vyy3330, Nothing, h), h), LT))
new_lt20(vyy650, vyy660, app(app(ty_@2, dbf), dbg)) → new_lt16(vyy650, vyy660, dbf, dbg)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Int) → new_esEs19(vyy3000, vyy400)
new_compare14(vyy650, vyy660, True, fg) → LT
new_ltEs18(vyy651, vyy661, ty_Char) → new_ltEs12(vyy651, vyy661)
new_ltEs11(vyy65, vyy66, bff) → new_not(new_esEs8(new_compare(vyy65, vyy66, bff), GT))
new_primCmpInt(Pos(Zero), Pos(Succ(vyy6600))) → new_primCmpNat2(Zero, vyy6600)
new_ltEs18(vyy651, vyy661, ty_Int) → new_ltEs17(vyy651, vyy661)
new_ltEs18(vyy651, vyy661, app(app(ty_@2, bgf), bgg)) → new_ltEs13(vyy651, vyy661, bgf, bgg)
new_lt8(vyy650, vyy660, app(ty_Maybe, fg)) → new_lt13(vyy650, vyy660, fg)
new_esEs18(:(vyy3000, vyy3001), :(vyy400, vyy401), cae) → new_asAs(new_esEs22(vyy3000, vyy400, cae), new_esEs18(vyy3001, vyy401, cae))
new_lt19(vyy651, vyy661, ty_Bool) → new_lt10(vyy651, vyy661)
new_foldFM_GE12(vyy49, vyy330, vyy331, vyy332, vyy333, vyy334, False, h, ba) → new_foldFM_GE5(vyy49, vyy334, h, ba)
new_compare7(vyy650, vyy660, fg) → new_compare26(vyy650, vyy660, new_esEs4(vyy650, vyy660, fg), fg)
new_compare31(Char(vyy650), Char(vyy660)) → new_primCmpInt(vyy650, vyy660)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_@0) → new_ltEs16(vyy6500, vyy6600)
new_esEs10(vyy3002, vyy402, ty_Int) → new_esEs19(vyy3002, vyy402)
new_ltEs6(Nothing, Nothing, fg) → True
new_ltEs19(vyy652, vyy662, ty_Bool) → new_ltEs5(vyy652, vyy662)
new_esEs25(vyy3001, vyy401, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs7(vyy3001, vyy401, cch, cda, cdb)
new_ltEs7(Left(vyy650), Left(vyy660), app(app(ty_@2, bah), bba), bab) → new_ltEs13(vyy650, vyy660, bah, bba)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Bool, bch) → new_esEs17(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), bec, app(ty_Maybe, beh)) → new_esEs4(vyy3000, vyy400, beh)
new_esEs28(vyy650, vyy660, ty_Bool) → new_esEs17(vyy650, vyy660)
new_esEs28(vyy650, vyy660, app(ty_Ratio, dba)) → new_esEs20(vyy650, vyy660, dba)
new_esEs22(vyy3000, vyy400, ty_Int) → new_esEs19(vyy3000, vyy400)
new_ltEs4(LT, LT) → True
new_compare11(vyy650, vyy660, False) → GT
new_esEs22(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs19(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, app(app(ty_Either, db), dc)) → new_esEs5(vyy3001, vyy401, db, dc)
new_ltEs18(vyy651, vyy661, ty_Double) → new_ltEs14(vyy651, vyy661)
new_esEs21(vyy650, vyy660, ty_@0) → new_esEs9(vyy650, vyy660)
new_esEs10(vyy3002, vyy402, ty_Integer) → new_esEs16(vyy3002, vyy402)
new_compare11(vyy650, vyy660, True) → LT
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs19(vyy3000, vyy400)
new_lt8(vyy650, vyy660, ty_Double) → new_lt17(vyy650, vyy660)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_Either, bda), bdb), bch) → new_esEs5(vyy3000, vyy400, bda, bdb)
new_ltEs18(vyy651, vyy661, app(ty_Maybe, bgb)) → new_ltEs6(vyy651, vyy661, bgb)
new_lt17(vyy650, vyy660) → new_esEs8(new_compare18(vyy650, vyy660), LT)
new_esEs22(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy6600))) → new_primCmpNat1(vyy6600, Zero)
new_lt9(vyy650, vyy660) → new_esEs8(new_compare6(vyy650, vyy660), LT)
new_esEs10(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Int) → new_ltEs17(vyy650, vyy660)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Float) → new_esEs15(vyy3000, vyy400)
new_esEs28(vyy650, vyy660, ty_Float) → new_esEs15(vyy650, vyy660)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare8(:%(vyy650, vyy651), :%(vyy660, vyy661), ty_Int) → new_compare5(new_sr(vyy650, vyy661), new_sr(vyy660, vyy651))
new_compare12(vyy650, vyy660, ge, gf) → new_compare27(vyy650, vyy660, new_esEs5(vyy650, vyy660, ge, gf), ge, gf)
new_asAs(True, vyy91) → vyy91
new_lt19(vyy651, vyy661, app(ty_Maybe, chh)) → new_lt13(vyy651, vyy661, chh)
new_esEs22(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_lt20(vyy650, vyy660, app(ty_[], dbc)) → new_lt7(vyy650, vyy660, dbc)
new_esEs24(vyy3000, vyy400, ty_Int) → new_esEs19(vyy3000, vyy400)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Ordering) → new_ltEs4(vyy6500, vyy6600)
new_lt20(vyy650, vyy660, ty_Char) → new_lt15(vyy650, vyy660)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, cdg), cdh)) → new_esEs6(vyy3000, vyy400, cdg, cdh)
new_ltEs6(Just(vyy6500), Just(vyy6600), app(ty_[], bhe)) → new_ltEs11(vyy6500, vyy6600, bhe)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, he), hf), hg)) → new_esEs7(vyy3000, vyy400, he, hf, hg)
new_compare15(vyy650, vyy660, bb, bc) → new_compare28(vyy650, vyy660, new_esEs6(vyy650, vyy660, bb, bc), bb, bc)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, app(ty_Maybe, bbg)) → new_ltEs6(vyy650, vyy660, bbg)
new_ltEs4(GT, GT) → True
new_ltEs13(@2(vyy650, vyy651), @2(vyy660, vyy661), bfg, bfh) → new_pePe(new_lt8(vyy650, vyy660, bfg), new_asAs(new_esEs21(vyy650, vyy660, bfg), new_ltEs18(vyy651, vyy661, bfh)))
new_esEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cca, ccb) → new_asAs(new_esEs26(vyy3000, vyy400, cca), new_esEs25(vyy3001, vyy401, ccb))
new_esEs22(vyy3000, vyy400, app(app(ty_Either, caf), cag)) → new_esEs5(vyy3000, vyy400, caf, cag)
new_compare13(Float(vyy650, vyy651), Float(vyy660, vyy661)) → new_compare5(new_sr(vyy650, vyy660), new_sr(vyy651, vyy661))
new_lt8(vyy650, vyy660, app(ty_[], gd)) → new_lt7(vyy650, vyy660, gd)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(vyy132, EQ) → vyy132
new_lt19(vyy651, vyy661, ty_Char) → new_lt15(vyy651, vyy661)
new_ltEs18(vyy651, vyy661, ty_Integer) → new_ltEs8(vyy651, vyy661)
new_ltEs19(vyy652, vyy662, ty_@0) → new_ltEs16(vyy652, vyy662)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Int, bab) → new_ltEs17(vyy650, vyy660)
new_esEs10(vyy3002, vyy402, app(ty_Maybe, cc)) → new_esEs4(vyy3002, vyy402, cc)
new_esEs25(vyy3001, vyy401, app(ty_Ratio, cdd)) → new_esEs20(vyy3001, vyy401, cdd)
new_esEs10(vyy3002, vyy402, ty_Bool) → new_esEs17(vyy3002, vyy402)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_lt20(vyy650, vyy660, ty_Bool) → new_lt10(vyy650, vyy660)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, cef)) → new_esEs20(vyy3000, vyy400, cef)
new_esEs12(vyy3000, vyy400, app(app(ty_@2, ef), eg)) → new_esEs6(vyy3000, vyy400, ef, eg)
new_esEs25(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_primCmpInt(Neg(Succ(vyy6500)), Pos(vyy660)) → LT
new_esEs10(vyy3002, vyy402, ty_Double) → new_esEs14(vyy3002, vyy402)
new_not(True) → False
new_lt19(vyy651, vyy661, app(ty_[], daa)) → new_lt7(vyy651, vyy661, daa)

The set Q consists of the following terms:

new_ltEs19(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Ordering)
new_compare(:(x0, x1), [], x2)
new_esEs10(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Ordering)
new_lt6(x0, x1, x2, x3, x4)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_gtEs0(x0, x1)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, ty_Integer)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs21(x0, x1, app(ty_[], x2))
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs4(Nothing, Just(x0), x1)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_Ordering)
new_lt14(x0, x1, x2, x3)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqNat0(Zero, Succ(x0))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat2(Zero, x0)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_compare32(x0, x1, ty_@0)
new_compare13(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs16(Integer(x0), Integer(x1))
new_compare17(x0, x1, True, x2, x3)
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_foldFM_GE12(x0, x1, x2, x3, EmptyFM, x4, True, x5, x6)
new_compare14(x0, x1, False, x2)
new_keysFM_GE0(x0, x1, x2, x3, x4)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs21(x0, x1, ty_Bool)
new_lt8(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Ordering)
new_esEs8(GT, GT)
new_compare32(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, ty_Float)
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Bool)
new_esEs8(LT, LT)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs18(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs17(False, False)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_compare15(x0, x1, x2, x3)
new_pePe(False, x0)
new_sr(x0, x1)
new_ltEs5(False, False)
new_primCompAux0(x0, GT)
new_lt8(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_foldFM_GE30(x0, x1, x2, x3, x4)
new_ltEs6(Just(x0), Just(x1), ty_@0)
new_esEs28(x0, x1, ty_@0)
new_primCompAux0(x0, EQ)
new_esEs12(x0, x1, ty_Double)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs27(x0, x1, ty_Char)
new_lt8(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs13(Char(x0), Char(x1))
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, False, x2, x3)
new_ltEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Just(x0), Just(x1), ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs10(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Zero)
new_sr0(Integer(x0), Integer(x1))
new_lt19(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_ltEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare18(Double(x0, x1), Double(x2, x3))
new_foldFM_GE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_compare10(x0, x1, True, x2, x3)
new_esEs4(Just(x0), Nothing, x1)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_GE5(x0, EmptyFM, x1, x2)
new_esEs28(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Integer)
new_compare11(x0, x1, True)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_esEs18(:(x0, x1), [], x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs12(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_asAs(False, x0)
new_ltEs19(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Bool)
new_ltEs4(GT, GT)
new_ltEs18(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, ty_Float)
new_compare30(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Just(x0), Just(x1), ty_Int)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs10(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_compare32(x0, x1, app(ty_[], x2))
new_compare14(x0, x1, True, x2)
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs4(Nothing, Nothing, x0)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs10(x0, x1, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_lt17(x0, x1)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs27(x0, x1, ty_Bool)
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare16(@0, @0)
new_esEs26(x0, x1, ty_@0)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs11(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_foldFM_GE12(x0, x1, x2, x3, Branch(x4, x5, x6, x7, x8), x9, True, x10, x11)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt20(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare([], [], x0)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs11(x0, x1, x2)
new_esEs28(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_@0)
new_primPlusNat1(Zero, Zero)
new_esEs11(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare32(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_compare26(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_@0)
new_lt15(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs6(Just(x0), Just(x1), ty_Char)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs4(EQ, EQ)
new_ltEs18(x0, x1, ty_Int)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Integer)
new_compare110(x0, x1, False)
new_compare6(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare32(x0, x1, app(ty_Ratio, x2))
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare7(x0, x1, x2)
new_ltEs4(EQ, LT)
new_ltEs19(x0, x1, ty_Double)
new_ltEs4(LT, EQ)
new_esEs21(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs18(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Float)
new_compare5(x0, x1)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_lt7(x0, x1, x2)
new_compare25(x0, x1, True)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs11(x0, x1, ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs6(Just(x0), Nothing, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt8(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare11(x0, x1, False)
new_ltEs18(x0, x1, ty_Ordering)
new_lt8(x0, x1, ty_@0)
new_esEs12(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs6(Nothing, Nothing, x0)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs6(Just(x0), Just(x1), ty_Integer)
new_esEs12(x0, x1, ty_Float)
new_compare32(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_primCompAux0(x0, LT)
new_compare111(x0, x1, False, x2, x3, x4)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpNat2(Succ(x0), x1)
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(LT, LT)
new_esEs10(x0, x1, ty_Double)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_compare17(x0, x1, False, x2, x3)
new_compare31(Char(x0), Char(x1))
new_esEs11(x0, x1, ty_Char)
new_ltEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare([], :(x0, x1), x2)
new_ltEs8(x0, x1)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare9(x0, x1, x2, x3, x4)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_lt8(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs9(@0, @0)
new_esEs10(x0, x1, ty_Char)
new_lt8(x0, x1, ty_Double)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, ty_Integer)
new_esEs18([], :(x0, x1), x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, ty_Float)
new_compare32(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs19(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_ltEs18(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_lt12(x0, x1)
new_foldFM_GE5(x0, Branch(x1, x2, x3, x4, x5), x6, x7)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare19(Integer(x0), Integer(x1))
new_compare32(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs12(x0, x1)
new_lt8(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_primCompAux1(x0, x1, x2, x3)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCmpNat0(Zero, Zero)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare24(x0, x1, True)
new_esEs10(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Int)
new_primCmpNat0(Zero, Succ(x0))
new_compare24(x0, x1, False)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_compare28(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs12(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs11(x0, x1, ty_Double)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Integer)
new_esEs18([], [], x0)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Char)
new_asAs(True, x0)
new_esEs11(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs17(x0, x1)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_ltEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(True, True)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_@0)
new_lt18(x0, x1)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Int)
new_not(True)
new_lt10(x0, x1)
new_lt5(x0, x1, x2)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_not(False)
new_compare110(x0, x1, True)
new_ltEs19(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs12(x0, x1, ty_Int)
new_lt13(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_@0)
new_primCmpNat1(x0, Succ(x1))
new_primEqNat0(Succ(x0), Succ(x1))
new_compare32(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs6(Just(x0), Just(x1), ty_Bool)
new_compare28(x0, x1, False, x2, x3)
new_compare10(x0, x1, False, x2, x3)
new_foldFM_GE12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_primCmpNat1(x0, Zero)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare26(x0, x1, False, x2)
new_lt4(x0, x1)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_lt8(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(x0, x1)
new_lt8(x0, x1, ty_Bool)
new_ltEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs17(True, False)
new_esEs17(False, True)
new_esEs27(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare25(x0, x1, False)
new_ltEs14(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare12(x0, x1, x2, x3)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs28(x0, x1, ty_Char)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_lt20(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_[], x2))
new_pePe(True, x0)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Char)
new_ltEs9(x0, x1)
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Integer)
new_ltEs6(Nothing, Just(x0), x1)

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

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



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

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

new_primEqNat(Succ(vyy300000), Succ(vyy40000)) → new_primEqNat(vyy300000, vyy40000)

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

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



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

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

new_ltEs1(Left(vyy650), Left(vyy660), app(ty_[], ea), dh) → new_ltEs0(vyy650, vyy660, ea)
new_ltEs1(Left(vyy650), Left(vyy660), app(app(ty_@2, ed), ee), dh) → new_ltEs2(vyy650, vyy660, ed, ee)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), bae, app(app(ty_Either, bcc), bcd), bca) → new_lt1(vyy651, vyy661, bcc, bcd)
new_compare0(:(vyy650, vyy651), :(vyy660, vyy661), ca) → new_primCompAux(vyy650, vyy660, new_compare(vyy651, vyy661, ca), ca)
new_ltEs1(Left(vyy650), Left(vyy660), app(app(ty_Either, eb), ec), dh) → new_ltEs1(vyy650, vyy660, eb, ec)
new_ltEs0(:(vyy650, vyy651), :(vyy660, vyy661), ca) → new_primCompAux(vyy650, vyy660, new_compare(vyy651, vyy661, ca), ca)
new_lt3(vyy650, vyy660, bab, bac, bad) → new_compare23(vyy650, vyy660, new_esEs7(vyy650, vyy660, bab, bac, bad), bab, bac, bad)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), gd, app(ty_Maybe, ge)) → new_ltEs(vyy651, vyy661, ge)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), gd, app(app(app(ty_@3, hc), hd), he)) → new_ltEs3(vyy651, vyy661, hc, hd, he)
new_ltEs1(Right(vyy650), Right(vyy660), fa, app(app(ty_@2, fg), fh)) → new_ltEs2(vyy650, vyy660, fg, fh)
new_compare0(:(vyy650, vyy651), :(vyy660, vyy661), ca) → new_compare0(vyy651, vyy661, ca)
new_primCompAux(vyy650, vyy660, vyy128, app(app(ty_@2, cf), cg)) → new_compare3(vyy650, vyy660, cf, cg)
new_ltEs1(Right(vyy650), Right(vyy660), fa, app(app(app(ty_@3, ga), gb), gc)) → new_ltEs3(vyy650, vyy660, ga, gb, gc)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), gd, app(app(ty_Either, gg), gh)) → new_ltEs1(vyy651, vyy661, gg, gh)
new_ltEs(Just(vyy6500), Just(vyy6600), app(ty_[], ba)) → new_ltEs0(vyy6500, vyy6600, ba)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), bae, app(ty_[], bcb), bca) → new_lt0(vyy651, vyy661, bcb)
new_compare2(vyy650, vyy660, de, df) → new_compare21(vyy650, vyy660, new_esEs5(vyy650, vyy660, de, df), de, df)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), app(app(ty_Either, bdd), bde), baf, bca) → new_lt1(vyy650, vyy660, bdd, bde)
new_compare3(vyy650, vyy660, hh, baa) → new_compare22(vyy650, vyy660, new_esEs6(vyy650, vyy660, hh, baa), hh, baa)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), app(ty_[], bdc), baf, bca) → new_lt0(vyy650, vyy660, bdc)
new_ltEs(Just(vyy6500), Just(vyy6600), app(ty_Maybe, h)) → new_ltEs(vyy6500, vyy6600, h)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), bae, baf, app(ty_Maybe, bag)) → new_ltEs(vyy652, vyy662, bag)
new_ltEs(Just(vyy6500), Just(vyy6600), app(app(ty_@2, bd), be)) → new_ltEs2(vyy6500, vyy6600, bd, be)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), app(app(ty_@2, bdf), bdg), baf, bca) → new_lt2(vyy650, vyy660, bdf, bdg)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), app(ty_Maybe, bdb), baf, bca) → new_lt(vyy650, vyy660, bdb)
new_primCompAux(vyy650, vyy660, vyy128, app(ty_[], cc)) → new_compare0(vyy650, vyy660, cc)
new_lt(vyy650, vyy660, dd) → new_compare20(vyy650, vyy660, new_esEs4(vyy650, vyy660, dd), dd)
new_compare21(vyy650, vyy660, False, de, df) → new_ltEs1(vyy650, vyy660, de, df)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), gd, app(ty_[], gf)) → new_ltEs0(vyy651, vyy661, gf)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), app(ty_[], hg), hf) → new_compare0(vyy650, vyy660, hg)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), bae, app(app(ty_@2, bce), bcf), bca) → new_lt2(vyy651, vyy661, bce, bcf)
new_primCompAux(vyy650, vyy660, vyy128, app(app(ty_Either, cd), ce)) → new_compare2(vyy650, vyy660, cd, ce)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), bae, baf, app(app(ty_@2, bbc), bbd)) → new_ltEs2(vyy652, vyy662, bbc, bbd)
new_ltEs1(Left(vyy650), Left(vyy660), app(ty_Maybe, dg), dh) → new_ltEs(vyy650, vyy660, dg)
new_ltEs1(Right(vyy650), Right(vyy660), fa, app(ty_Maybe, fb)) → new_ltEs(vyy650, vyy660, fb)
new_compare20(Just(vyy6500), Just(vyy6600), False, app(app(ty_Either, bb), bc)) → new_ltEs1(vyy6500, vyy6600, bb, bc)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), app(app(app(ty_@3, bab), bac), bad), hf) → new_compare23(vyy650, vyy660, new_esEs7(vyy650, vyy660, bab, bac, bad), bab, bac, bad)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), bae, baf, app(ty_[], bah)) → new_ltEs0(vyy652, vyy662, bah)
new_lt0(vyy650, vyy660, hg) → new_compare0(vyy650, vyy660, hg)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), bae, baf, app(app(app(ty_@3, bbe), bbf), bbg)) → new_ltEs3(vyy652, vyy662, bbe, bbf, bbg)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), gd, app(app(ty_@2, ha), hb)) → new_ltEs2(vyy651, vyy661, ha, hb)
new_ltEs(Just(vyy6500), Just(vyy6600), app(app(ty_Either, bb), bc)) → new_ltEs1(vyy6500, vyy6600, bb, bc)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), bae, app(ty_Maybe, bbh), bca) → new_lt(vyy651, vyy661, bbh)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), app(app(app(ty_@3, bdh), bea), beb), baf, bca) → new_lt3(vyy650, vyy660, bdh, bea, beb)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), app(app(ty_Either, de), df), hf) → new_compare21(vyy650, vyy660, new_esEs5(vyy650, vyy660, de, df), de, df)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), bae, baf, app(app(ty_Either, bba), bbb)) → new_ltEs1(vyy652, vyy662, bba, bbb)
new_primCompAux(vyy650, vyy660, vyy128, app(ty_Maybe, cb)) → new_compare1(vyy650, vyy660, cb)
new_compare20(Just(vyy6500), Just(vyy6600), False, app(app(app(ty_@3, bf), bg), bh)) → new_ltEs3(vyy6500, vyy6600, bf, bg, bh)
new_ltEs1(Right(vyy650), Right(vyy660), fa, app(app(ty_Either, fd), ff)) → new_ltEs1(vyy650, vyy660, fd, ff)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), app(app(ty_@2, hh), baa), hf) → new_compare22(vyy650, vyy660, new_esEs6(vyy650, vyy660, hh, baa), hh, baa)
new_ltEs3(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), bae, app(app(app(ty_@3, bcg), bch), bda), bca) → new_lt3(vyy651, vyy661, bcg, bch, bda)
new_compare1(vyy650, vyy660, dd) → new_compare20(vyy650, vyy660, new_esEs4(vyy650, vyy660, dd), dd)
new_lt1(vyy650, vyy660, de, df) → new_compare21(vyy650, vyy660, new_esEs5(vyy650, vyy660, de, df), de, df)
new_lt2(vyy650, vyy660, hh, baa) → new_compare22(vyy650, vyy660, new_esEs6(vyy650, vyy660, hh, baa), hh, baa)
new_compare22(vyy650, vyy660, False, hh, baa) → new_ltEs2(vyy650, vyy660, hh, baa)
new_compare20(Just(vyy6500), Just(vyy6600), False, app(ty_Maybe, h)) → new_ltEs(vyy6500, vyy6600, h)
new_ltEs0(:(vyy650, vyy651), :(vyy660, vyy661), ca) → new_compare0(vyy651, vyy661, ca)
new_ltEs(Just(vyy6500), Just(vyy6600), app(app(app(ty_@3, bf), bg), bh)) → new_ltEs3(vyy6500, vyy6600, bf, bg, bh)
new_compare4(vyy650, vyy660, bab, bac, bad) → new_compare23(vyy650, vyy660, new_esEs7(vyy650, vyy660, bab, bac, bad), bab, bac, bad)
new_ltEs1(Right(vyy650), Right(vyy660), fa, app(ty_[], fc)) → new_ltEs0(vyy650, vyy660, fc)
new_ltEs1(Left(vyy650), Left(vyy660), app(app(app(ty_@3, ef), eg), eh), dh) → new_ltEs3(vyy650, vyy660, ef, eg, eh)
new_compare20(Just(vyy6500), Just(vyy6600), False, app(ty_[], ba)) → new_ltEs0(vyy6500, vyy6600, ba)
new_primCompAux(vyy650, vyy660, vyy128, app(app(app(ty_@3, da), db), dc)) → new_compare4(vyy650, vyy660, da, db, dc)
new_compare23(vyy650, vyy660, False, bab, bac, bad) → new_ltEs3(vyy650, vyy660, bab, bac, bad)
new_ltEs2(@2(vyy650, vyy651), @2(vyy660, vyy661), app(ty_Maybe, dd), hf) → new_compare20(vyy650, vyy660, new_esEs4(vyy650, vyy660, dd), dd)
new_compare20(Just(vyy6500), Just(vyy6600), False, app(app(ty_@2, bd), be)) → new_ltEs2(vyy6500, vyy6600, bd, be)

The TRS R consists of the following rules:

new_lt14(vyy650, vyy660, de, df) → new_esEs8(new_compare12(vyy650, vyy660, de, df), LT)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, cbb)) → new_esEs4(vyy3000, vyy400, cbb)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, cbg)) → new_esEs20(vyy3000, vyy400, cbg)
new_esEs12(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Int) → new_esEs19(vyy3001, vyy401)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt4(vyy650, vyy660) → new_esEs8(new_compare5(vyy650, vyy660), LT)
new_esEs21(vyy650, vyy660, app(app(ty_@2, hh), baa)) → new_esEs6(vyy650, vyy660, hh, baa)
new_primCmpNat2(Zero, vyy6500) → LT
new_lt19(vyy651, vyy661, app(app(ty_Either, bcc), bcd)) → new_lt14(vyy651, vyy661, bcc, bcd)
new_ltEs4(EQ, GT) → True
new_compare29(vyy650, vyy660, False, bab, bac, bad) → new_compare111(vyy650, vyy660, new_ltEs15(vyy650, vyy660, bab, bac, bad), bab, bac, bad)
new_esEs28(vyy650, vyy660, ty_Char) → new_esEs13(vyy650, vyy660)
new_compare24(vyy650, vyy660, False) → new_compare110(vyy650, vyy660, new_ltEs4(vyy650, vyy660))
new_compare([], :(vyy660, vyy661), ca) → LT
new_compare10(vyy650, vyy660, True, hh, baa) → LT
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_ltEs10(vyy65, vyy66, dbd) → new_not(new_esEs8(new_compare8(vyy65, vyy66, dbd), GT))
new_esEs4(Just(vyy3000), Nothing, cae) → False
new_esEs4(Nothing, Just(vyy400), cae) → False
new_lt7(vyy650, vyy660, hg) → new_esEs8(new_compare(vyy650, vyy660, hg), LT)
new_lt20(vyy650, vyy660, app(app(ty_Either, bdd), bde)) → new_lt14(vyy650, vyy660, bdd, bde)
new_ltEs6(Nothing, Just(vyy6600), dd) → True
new_esEs27(vyy651, vyy661, ty_Bool) → new_esEs17(vyy651, vyy661)
new_lt19(vyy651, vyy661, ty_Int) → new_lt4(vyy651, vyy661)
new_ltEs9(vyy65, vyy66) → new_not(new_esEs8(new_compare13(vyy65, vyy66), GT))
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(vyy650), Right(vyy660), fa, dh) → True
new_compare32(vyy650, vyy660, ty_Bool) → new_compare30(vyy650, vyy660)
new_lt20(vyy650, vyy660, ty_@0) → new_lt18(vyy650, vyy660)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs15(vyy3000, vyy400)
new_compare(:(vyy650, vyy651), [], ca) → GT
new_lt8(vyy650, vyy660, app(app(app(ty_@3, bab), bac), bad)) → new_lt6(vyy650, vyy660, bab, bac, bad)
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs21(vyy650, vyy660, ty_Bool) → new_esEs17(vyy650, vyy660)
new_lt19(vyy651, vyy661, ty_Integer) → new_lt11(vyy651, vyy661)
new_esEs12(vyy3000, vyy400, app(ty_[], cab)) → new_esEs18(vyy3000, vyy400, cab)
new_lt20(vyy650, vyy660, app(ty_Maybe, bdb)) → new_lt13(vyy650, vyy660, bdb)
new_lt8(vyy650, vyy660, ty_Bool) → new_lt10(vyy650, vyy660)
new_lt8(vyy650, vyy660, ty_@0) → new_lt18(vyy650, vyy660)
new_esEs5(Right(vyy3000), Right(vyy400), cde, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_esEs11(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_compare16(@0, @0) → EQ
new_esEs17(True, True) → True
new_lt8(vyy650, vyy660, app(app(ty_@2, hh), baa)) → new_lt16(vyy650, vyy660, hh, baa)
new_lt10(vyy650, vyy660) → new_esEs8(new_compare30(vyy650, vyy660), LT)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Ratio, cdd), ccb) → new_esEs20(vyy3000, vyy400, cdd)
new_esEs21(vyy650, vyy660, app(app(app(ty_@3, bab), bac), bad)) → new_esEs7(vyy650, vyy660, bab, bac, bad)
new_lt20(vyy650, vyy660, ty_Float) → new_lt12(vyy650, vyy660)
new_esEs25(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_esEs12(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs7(Left(vyy650), Left(vyy660), app(app(app(ty_@3, ef), eg), eh), dh) → new_ltEs15(vyy650, vyy660, ef, eg, eh)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs28(vyy650, vyy660, ty_Double) → new_esEs14(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs7(vyy3001, vyy401, bge, bgf, bgg)
new_esEs11(vyy3001, vyy401, app(ty_Ratio, bha)) → new_esEs20(vyy3001, vyy401, bha)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, daf)) → new_esEs4(vyy3000, vyy400, daf)
new_primCmpNat1(vyy6500, Succ(vyy6600)) → new_primCmpNat0(vyy6500, vyy6600)
new_esEs27(vyy651, vyy661, ty_Double) → new_esEs14(vyy651, vyy661)
new_compare30(vyy650, vyy660) → new_compare25(vyy650, vyy660, new_esEs17(vyy650, vyy660))
new_ltEs6(Just(vyy6500), Just(vyy6600), app(ty_Ratio, cfa)) → new_ltEs10(vyy6500, vyy6600, cfa)
new_compare32(vyy650, vyy660, app(app(ty_@2, cf), cg)) → new_compare15(vyy650, vyy660, cf, cg)
new_ltEs6(Just(vyy6500), Just(vyy6600), app(app(ty_@2, bd), be)) → new_ltEs13(vyy6500, vyy6600, bd, be)
new_esEs10(vyy3002, vyy402, app(ty_Ratio, bfg)) → new_esEs20(vyy3002, vyy402, bfg)
new_pePe(False, vyy127) → vyy127
new_lt13(vyy650, vyy660, dd) → new_esEs8(new_compare7(vyy650, vyy660, dd), LT)
new_esEs18([], :(vyy400, vyy401), cfb) → False
new_esEs18(:(vyy3000, vyy3001), [], cfb) → False
new_primCmpNat1(vyy6500, Zero) → GT
new_ltEs7(Right(vyy650), Right(vyy660), fa, app(app(ty_@2, fg), fh)) → new_ltEs13(vyy650, vyy660, fg, fh)
new_lt19(vyy651, vyy661, ty_Ordering) → new_lt9(vyy651, vyy661)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Bool) → new_ltEs5(vyy6500, vyy6600)
new_ltEs19(vyy652, vyy662, app(ty_[], bah)) → new_ltEs11(vyy652, vyy662, bah)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Char, dh) → new_ltEs12(vyy650, vyy660)
new_esEs22(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare26(vyy650, vyy660, False, dd) → new_compare14(vyy650, vyy660, new_ltEs6(vyy650, vyy660, dd), dd)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_@2, cce), ccf), ccb) → new_esEs6(vyy3000, vyy400, cce, ccf)
new_esEs20(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cge) → new_asAs(new_esEs24(vyy3000, vyy400, cge), new_esEs23(vyy3001, vyy401, cge))
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Maybe, ccg), ccb) → new_esEs4(vyy3000, vyy400, ccg)
new_ltEs14(vyy65, vyy66) → new_not(new_esEs8(new_compare18(vyy65, vyy66), GT))
new_esEs10(vyy3002, vyy402, app(app(ty_@2, beh), bfa)) → new_esEs6(vyy3002, vyy402, beh, bfa)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Ordering, ccb) → new_esEs8(vyy3000, vyy400)
new_esEs27(vyy651, vyy661, ty_Int) → new_esEs19(vyy651, vyy661)
new_primCmpNat0(Zero, Succ(vyy66000)) → LT
new_esEs22(vyy3000, vyy400, ty_Float) → new_esEs15(vyy3000, vyy400)
new_esEs27(vyy651, vyy661, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs7(vyy651, vyy661, bcg, bch, bda)
new_esEs21(vyy650, vyy660, ty_Char) → new_esEs13(vyy650, vyy660)
new_esEs25(vyy3001, vyy401, app(app(ty_Either, cgh), cha)) → new_esEs5(vyy3001, vyy401, cgh, cha)
new_esEs10(vyy3002, vyy402, ty_Char) → new_esEs13(vyy3002, vyy402)
new_esEs25(vyy3001, vyy401, app(app(ty_@2, chb), chc)) → new_esEs6(vyy3001, vyy401, chb, chc)
new_esEs8(LT, LT) → True
new_esEs5(Left(vyy3000), Left(vyy400), ty_@0, ccb) → new_esEs9(vyy3000, vyy400)
new_lt5(vyy650, vyy660, cad) → new_esEs8(new_compare8(vyy650, vyy660, cad), LT)
new_ltEs6(Just(vyy6500), Just(vyy6600), app(app(ty_Either, bb), bc)) → new_ltEs7(vyy6500, vyy6600, bb, bc)
new_ltEs8(vyy65, vyy66) → new_not(new_esEs8(new_compare19(vyy65, vyy66), GT))
new_lt19(vyy651, vyy661, app(app(ty_@2, bce), bcf)) → new_lt16(vyy651, vyy661, bce, bcf)
new_esEs25(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs5(Right(vyy3000), Right(vyy400), cde, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs7(Right(vyy650), Right(vyy660), fa, ty_Bool) → new_ltEs5(vyy650, vyy660)
new_esEs28(vyy650, vyy660, ty_Integer) → new_esEs16(vyy650, vyy660)
new_lt11(vyy650, vyy660) → new_esEs8(new_compare19(vyy650, vyy660), LT)
new_ltEs5(True, False) → False
new_pePe(True, vyy127) → True
new_primEqNat0(Zero, Zero) → True
new_esEs5(Right(vyy3000), Right(vyy400), cde, app(app(ty_@2, cdh), cea)) → new_esEs6(vyy3000, vyy400, cdh, cea)
new_ltEs12(vyy65, vyy66) → new_not(new_esEs8(new_compare31(vyy65, vyy66), GT))
new_ltEs7(Right(vyy650), Right(vyy660), fa, ty_@0) → new_ltEs16(vyy650, vyy660)
new_esEs25(vyy3001, vyy401, app(ty_[], chh)) → new_esEs18(vyy3001, vyy401, chh)
new_ltEs7(Right(vyy650), Right(vyy660), fa, ty_Double) → new_ltEs14(vyy650, vyy660)
new_esEs12(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_lt8(vyy650, vyy660, ty_Integer) → new_lt11(vyy650, vyy660)
new_esEs27(vyy651, vyy661, ty_Char) → new_esEs13(vyy651, vyy661)
new_esEs14(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs19(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs5(True, True) → True
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_esEs13(Char(vyy3000), Char(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs13(vyy3000, vyy400)
new_compare(:(vyy650, vyy651), :(vyy660, vyy661), ca) → new_primCompAux1(vyy650, vyy660, new_compare(vyy651, vyy661, ca), ca)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, ty_@0) → new_esEs9(vyy3001, vyy401)
new_ltEs7(Right(vyy650), Right(vyy660), fa, app(app(app(ty_@3, ga), gb), gc)) → new_ltEs15(vyy650, vyy660, ga, gb, gc)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(vyy1030), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1030, vyy40100)))
new_primCmpInt(Pos(Succ(vyy6500)), Pos(vyy660)) → new_primCmpNat1(vyy6500, vyy660)
new_esEs11(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_lt20(vyy650, vyy660, ty_Double) → new_lt17(vyy650, vyy660)
new_esEs5(Right(vyy3000), Right(vyy400), cde, app(ty_[], cef)) → new_esEs18(vyy3000, vyy400, cef)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs22(vyy3000, vyy400, app(ty_[], cgc)) → new_esEs18(vyy3000, vyy400, cgc)
new_ltEs19(vyy652, vyy662, app(app(app(ty_@3, bbe), bbf), bbg)) → new_ltEs15(vyy652, vyy662, bbe, bbf, bbg)
new_compare32(vyy650, vyy660, ty_Integer) → new_compare19(vyy650, vyy660)
new_compare9(vyy650, vyy660, bab, bac, bad) → new_compare29(vyy650, vyy660, new_esEs7(vyy650, vyy660, bab, bac, bad), bab, bac, bad)
new_compare17(vyy650, vyy660, True, de, df) → LT
new_compare29(vyy650, vyy660, True, bab, bac, bad) → EQ
new_lt20(vyy650, vyy660, ty_Ordering) → new_lt9(vyy650, vyy660)
new_compare25(vyy650, vyy660, True) → EQ
new_esEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bec, bed, bee) → new_asAs(new_esEs12(vyy3000, vyy400, bec), new_asAs(new_esEs11(vyy3001, vyy401, bed), new_esEs10(vyy3002, vyy402, bee)))
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Integer, ccb) → new_esEs16(vyy3000, vyy400)
new_ltEs18(vyy651, vyy661, app(ty_Ratio, ceh)) → new_ltEs10(vyy651, vyy661, ceh)
new_ltEs19(vyy652, vyy662, ty_Integer) → new_ltEs8(vyy652, vyy662)
new_ltEs5(False, False) → True
new_ltEs18(vyy651, vyy661, app(app(ty_Either, gg), gh)) → new_ltEs7(vyy651, vyy661, gg, gh)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy10300), Zero) → Succ(vyy10300)
new_esEs10(vyy3002, vyy402, app(ty_[], bff)) → new_esEs18(vyy3002, vyy402, bff)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Bool, dh) → new_ltEs5(vyy650, vyy660)
new_compare28(vyy650, vyy660, False, hh, baa) → new_compare10(vyy650, vyy660, new_ltEs13(vyy650, vyy660, hh, baa), hh, baa)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, dag), dah), dba)) → new_esEs7(vyy3000, vyy400, dag, dah, dba)
new_esEs10(vyy3002, vyy402, ty_@0) → new_esEs9(vyy3002, vyy402)
new_esEs28(vyy650, vyy660, app(ty_Maybe, bdb)) → new_esEs4(vyy650, vyy660, bdb)
new_lt20(vyy650, vyy660, ty_Int) → new_lt4(vyy650, vyy660)
new_compare18(Double(vyy650, vyy651), Double(vyy660, vyy661)) → new_compare5(new_sr(vyy650, vyy660), new_sr(vyy651, vyy661))
new_ltEs19(vyy652, vyy662, ty_Float) → new_ltEs9(vyy652, vyy662)
new_esEs21(vyy650, vyy660, ty_Double) → new_esEs14(vyy650, vyy660)
new_esEs21(vyy650, vyy660, app(ty_[], hg)) → new_esEs18(vyy650, vyy660, hg)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, cch), cda), cdb), ccb) → new_esEs7(vyy3000, vyy400, cch, cda, cdb)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(vyy650), Left(vyy660), fa, dh) → False
new_ltEs19(vyy652, vyy662, ty_Ordering) → new_ltEs4(vyy652, vyy662)
new_esEs27(vyy651, vyy661, app(app(ty_Either, bcc), bcd)) → new_esEs5(vyy651, vyy661, bcc, bcd)
new_primCmpNat2(Succ(vyy6600), vyy6500) → new_primCmpNat0(vyy6600, vyy6500)
new_esEs11(vyy3001, vyy401, ty_Float) → new_esEs15(vyy3001, vyy401)
new_esEs10(vyy3002, vyy402, ty_Float) → new_esEs15(vyy3002, vyy402)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primCompAux0(vyy132, GT) → GT
new_ltEs19(vyy652, vyy662, ty_Char) → new_ltEs12(vyy652, vyy662)
new_lt20(vyy650, vyy660, ty_Integer) → new_lt11(vyy650, vyy660)
new_esEs8(EQ, EQ) → True
new_esEs11(vyy3001, vyy401, ty_Int) → new_esEs19(vyy3001, vyy401)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Double, ccb) → new_esEs14(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_esEs12(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs10(vyy3002, vyy402, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs7(vyy3002, vyy402, bfc, bfd, bfe)
new_ltEs7(Left(vyy650), Left(vyy660), ty_@0, dh) → new_ltEs16(vyy650, vyy660)
new_lt19(vyy651, vyy661, app(app(app(ty_@3, bcg), bch), bda)) → new_lt6(vyy651, vyy661, bcg, bch, bda)
new_compare32(vyy650, vyy660, app(ty_Ratio, dbe)) → new_compare8(vyy650, vyy660, dbe)
new_esEs26(vyy3000, vyy400, app(ty_[], dbb)) → new_esEs18(vyy3000, vyy400, dbb)
new_compare([], [], ca) → EQ
new_ltEs18(vyy651, vyy661, ty_Ordering) → new_ltEs4(vyy651, vyy661)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs4(EQ, LT) → False
new_esEs22(vyy3000, vyy400, app(ty_Ratio, cgd)) → new_esEs20(vyy3000, vyy400, cgd)
new_esEs27(vyy651, vyy661, ty_Float) → new_esEs15(vyy651, vyy661)
new_esEs21(vyy650, vyy660, app(ty_Ratio, cad)) → new_esEs20(vyy650, vyy660, cad)
new_lt8(vyy650, vyy660, ty_Float) → new_lt12(vyy650, vyy660)
new_esEs28(vyy650, vyy660, ty_Int) → new_esEs19(vyy650, vyy660)
new_esEs15(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs19(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt20(vyy650, vyy660, app(app(app(ty_@3, bdh), bea), beb)) → new_lt6(vyy650, vyy660, bdh, bea, beb)
new_primCmpNat0(Succ(vyy65000), Succ(vyy66000)) → new_primCmpNat0(vyy65000, vyy66000)
new_esEs22(vyy3000, vyy400, app(ty_Maybe, cfg)) → new_esEs4(vyy3000, vyy400, cfg)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, app(ty_Maybe, chd)) → new_esEs4(vyy3001, vyy401, chd)
new_ltEs18(vyy651, vyy661, ty_Bool) → new_ltEs5(vyy651, vyy661)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare10(vyy650, vyy660, False, hh, baa) → GT
new_compare27(vyy650, vyy660, True, de, df) → EQ
new_lt8(vyy650, vyy660, ty_Char) → new_lt15(vyy650, vyy660)
new_esEs21(vyy650, vyy660, ty_Int) → new_esEs19(vyy650, vyy660)
new_ltEs18(vyy651, vyy661, app(app(app(ty_@3, hc), hd), he)) → new_ltEs15(vyy651, vyy661, hc, hd, he)
new_compare14(vyy650, vyy660, False, dd) → GT
new_esEs5(Right(vyy3000), Right(vyy400), cde, app(app(ty_Either, cdf), cdg)) → new_esEs5(vyy3000, vyy400, cdf, cdg)
new_ltEs19(vyy652, vyy662, app(ty_Ratio, dbf)) → new_ltEs10(vyy652, vyy662, dbf)
new_primEqNat0(Succ(vyy300000), Succ(vyy40000)) → new_primEqNat0(vyy300000, vyy40000)
new_esEs27(vyy651, vyy661, ty_Ordering) → new_esEs8(vyy651, vyy661)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Integer) → new_ltEs8(vyy6500, vyy6600)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Int) → new_ltEs17(vyy6500, vyy6600)
new_primCompAux1(vyy650, vyy660, vyy128, ca) → new_primCompAux0(vyy128, new_compare32(vyy650, vyy660, ca))
new_ltEs19(vyy652, vyy662, ty_Double) → new_ltEs14(vyy652, vyy662)
new_compare111(vyy650, vyy660, True, bab, bac, bad) → LT
new_esEs9(@0, @0) → True
new_ltEs4(GT, EQ) → False
new_ltEs18(vyy651, vyy661, ty_@0) → new_ltEs16(vyy651, vyy661)
new_esEs11(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_ltEs19(vyy652, vyy662, app(app(ty_Either, bba), bbb)) → new_ltEs7(vyy652, vyy662, bba, bbb)
new_compare8(:%(vyy650, vyy651), :%(vyy660, vyy661), ty_Integer) → new_compare19(new_sr0(vyy650, vyy661), new_sr0(vyy660, vyy651))
new_esEs5(Left(vyy3000), Left(vyy400), ty_Int, ccb) → new_esEs19(vyy3000, vyy400)
new_compare32(vyy650, vyy660, app(app(ty_Either, cd), ce)) → new_compare12(vyy650, vyy660, cd, ce)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Char) → new_ltEs12(vyy6500, vyy6600)
new_ltEs19(vyy652, vyy662, ty_Int) → new_ltEs17(vyy652, vyy662)
new_ltEs7(Left(vyy650), Left(vyy660), app(ty_[], ea), dh) → new_ltEs11(vyy650, vyy660, ea)
new_esEs11(vyy3001, vyy401, app(ty_Maybe, bgd)) → new_esEs4(vyy3001, vyy401, bgd)
new_esEs28(vyy650, vyy660, ty_Ordering) → new_esEs8(vyy650, vyy660)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_lt20(vyy650, vyy660, app(ty_Ratio, dbh)) → new_lt5(vyy650, vyy660, dbh)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_esEs11(vyy3001, vyy401, app(ty_[], bgh)) → new_esEs18(vyy3001, vyy401, bgh)
new_ltEs4(EQ, EQ) → True
new_ltEs19(vyy652, vyy662, app(ty_Maybe, bag)) → new_ltEs6(vyy652, vyy662, bag)
new_esEs12(vyy3000, vyy400, app(app(app(ty_@3, bhg), bhh), caa)) → new_esEs7(vyy3000, vyy400, bhg, bhh, caa)
new_ltEs6(Just(vyy6500), Nothing, dd) → False
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy65000), Zero) → GT
new_ltEs7(Right(vyy650), Right(vyy660), fa, ty_Ordering) → new_ltEs4(vyy650, vyy660)
new_ltEs18(vyy651, vyy661, app(ty_[], gf)) → new_ltEs11(vyy651, vyy661, gf)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy6600))) → LT
new_compare32(vyy650, vyy660, ty_Ordering) → new_compare6(vyy650, vyy660)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, caf), cag)) → new_esEs5(vyy3000, vyy400, caf, cag)
new_esEs21(vyy650, vyy660, ty_Float) → new_esEs15(vyy650, vyy660)
new_ltEs4(GT, LT) → False
new_sr0(Integer(vyy6600), Integer(vyy6510)) → Integer(new_primMulInt(vyy6600, vyy6510))
new_lt8(vyy650, vyy660, app(app(ty_Either, de), df)) → new_lt14(vyy650, vyy660, de, df)
new_primPlusNat1(Succ(vyy10300), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy10300, vyy401000)))
new_esEs12(vyy3000, vyy400, ty_Float) → new_esEs15(vyy3000, vyy400)
new_compare28(vyy650, vyy660, True, hh, baa) → EQ
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_esEs28(vyy650, vyy660, app(app(ty_Either, bdd), bde)) → new_esEs5(vyy650, vyy660, bdd, bde)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, cah), cba)) → new_esEs6(vyy3000, vyy400, cah, cba)
new_ltEs5(False, True) → True
new_compare32(vyy650, vyy660, app(ty_[], cc)) → new_compare(vyy650, vyy660, cc)
new_ltEs6(Just(vyy6500), Just(vyy6600), app(ty_Maybe, h)) → new_ltEs6(vyy6500, vyy6600, h)
new_esEs22(vyy3000, vyy400, app(app(ty_@2, cfe), cff)) → new_esEs6(vyy3000, vyy400, cfe, cff)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Ordering, dh) → new_ltEs4(vyy650, vyy660)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_compare24(vyy650, vyy660, True) → EQ
new_ltEs7(Right(vyy650), Right(vyy660), fa, app(ty_[], fc)) → new_ltEs11(vyy650, vyy660, fc)
new_esEs27(vyy651, vyy661, ty_@0) → new_esEs9(vyy651, vyy661)
new_ltEs7(Right(vyy650), Right(vyy660), fa, ty_Char) → new_ltEs12(vyy650, vyy660)
new_esEs5(Right(vyy3000), Right(vyy400), cde, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Float) → new_esEs15(vyy3001, vyy401)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs15(vyy3000, vyy400)
new_ltEs7(Right(vyy650), Right(vyy660), fa, app(ty_Ratio, cca)) → new_ltEs10(vyy650, vyy660, cca)
new_lt15(vyy650, vyy660) → new_esEs8(new_compare31(vyy650, vyy660), LT)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Float) → new_ltEs9(vyy6500, vyy6600)
new_compare17(vyy650, vyy660, False, de, df) → GT
new_compare26(vyy650, vyy660, True, dd) → EQ
new_primCompAux0(vyy132, LT) → LT
new_esEs23(vyy3001, vyy401, ty_Int) → new_esEs19(vyy3001, vyy401)
new_ltEs19(vyy652, vyy662, app(app(ty_@2, bbc), bbd)) → new_ltEs13(vyy652, vyy662, bbc, bbd)
new_compare32(vyy650, vyy660, ty_Int) → new_compare5(vyy650, vyy660)
new_not(False) → True
new_esEs28(vyy650, vyy660, ty_@0) → new_esEs9(vyy650, vyy660)
new_lt18(vyy650, vyy660) → new_esEs8(new_compare16(vyy650, vyy660), LT)
new_compare32(vyy650, vyy660, app(app(app(ty_@3, da), db), dc)) → new_compare9(vyy650, vyy660, da, db, dc)
new_esEs12(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_ltEs7(Left(vyy650), Left(vyy660), app(ty_Ratio, cbh), dh) → new_ltEs10(vyy650, vyy660, cbh)
new_ltEs7(Left(vyy650), Left(vyy660), app(ty_Maybe, dg), dh) → new_ltEs6(vyy650, vyy660, dg)
new_esEs22(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, ty_@0) → new_esEs9(vyy3001, vyy401)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Float, ccb) → new_esEs15(vyy3000, vyy400)
new_esEs27(vyy651, vyy661, app(ty_[], bcb)) → new_esEs18(vyy651, vyy661, bcb)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, dab), dac)) → new_esEs5(vyy3000, vyy400, dab, dac)
new_esEs22(vyy3000, vyy400, app(app(app(ty_@3, cfh), cga), cgb)) → new_esEs7(vyy3000, vyy400, cfh, cga, cgb)
new_primCmpInt(Pos(Succ(vyy6500)), Neg(vyy660)) → GT
new_esEs21(vyy650, vyy660, ty_Integer) → new_esEs16(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_lt6(vyy650, vyy660, bab, bac, bad) → new_esEs8(new_compare9(vyy650, vyy660, bab, bac, bad), LT)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare27(vyy650, vyy660, False, de, df) → new_compare17(vyy650, vyy660, new_ltEs7(vyy650, vyy660, de, df), de, df)
new_compare19(Integer(vyy650), Integer(vyy660)) → new_primCmpInt(vyy650, vyy660)
new_ltEs18(vyy651, vyy661, ty_Float) → new_ltEs9(vyy651, vyy661)
new_esEs24(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs28(vyy650, vyy660, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs7(vyy650, vyy660, bdh, bea, beb)
new_compare32(vyy650, vyy660, ty_@0) → new_compare16(vyy650, vyy660)
new_esEs5(Left(vyy3000), Right(vyy400), cde, ccb) → False
new_esEs5(Right(vyy3000), Left(vyy400), cde, ccb) → False
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs27(vyy651, vyy661, app(app(ty_@2, bce), bcf)) → new_esEs6(vyy651, vyy661, bce, bcf)
new_compare110(vyy650, vyy660, True) → LT
new_esEs11(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_esEs5(Right(vyy3000), Right(vyy400), cde, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), cde, app(ty_Ratio, ceg)) → new_esEs20(vyy3000, vyy400, ceg)
new_primEqNat0(Zero, Succ(vyy40000)) → False
new_primEqNat0(Succ(vyy300000), Zero) → False
new_ltEs7(Left(vyy650), Left(vyy660), app(app(ty_Either, eb), ec), dh) → new_ltEs7(vyy650, vyy660, eb, ec)
new_compare110(vyy650, vyy660, False) → GT
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Double) → new_ltEs14(vyy6500, vyy6600)
new_esEs22(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, cae) → True
new_lt19(vyy651, vyy661, ty_Double) → new_lt17(vyy651, vyy661)
new_compare111(vyy650, vyy660, False, bab, bac, bad) → GT
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_[], cdc), ccb) → new_esEs18(vyy3000, vyy400, cdc)
new_compare32(vyy650, vyy660, ty_Char) → new_compare31(vyy650, vyy660)
new_esEs12(vyy3000, vyy400, app(app(ty_Either, bhb), bhc)) → new_esEs5(vyy3000, vyy400, bhb, bhc)
new_lt19(vyy651, vyy661, app(ty_Ratio, dbg)) → new_lt5(vyy651, vyy661, dbg)
new_esEs27(vyy651, vyy661, ty_Integer) → new_esEs16(vyy651, vyy661)
new_ltEs7(Right(vyy650), Right(vyy660), fa, ty_Float) → new_ltEs9(vyy650, vyy660)
new_ltEs15(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), bae, baf, bca) → new_pePe(new_lt20(vyy650, vyy660, bae), new_asAs(new_esEs28(vyy650, vyy660, bae), new_pePe(new_lt19(vyy651, vyy661, baf), new_asAs(new_esEs27(vyy651, vyy661, baf), new_ltEs19(vyy652, vyy662, bca)))))
new_esEs27(vyy651, vyy661, app(ty_Maybe, bbh)) → new_esEs4(vyy651, vyy661, bbh)
new_ltEs4(LT, GT) → True
new_compare6(vyy650, vyy660) → new_compare24(vyy650, vyy660, new_esEs8(vyy650, vyy660))
new_esEs27(vyy651, vyy661, app(ty_Ratio, dbg)) → new_esEs20(vyy651, vyy661, dbg)
new_esEs25(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_lt8(vyy650, vyy660, ty_Ordering) → new_lt9(vyy650, vyy660)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy6600))) → GT
new_compare5(vyy65, vyy66) → new_primCmpInt(vyy65, vyy66)
new_esEs12(vyy3000, vyy400, ty_Int) → new_esEs19(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), cde, ty_Double) → new_esEs14(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), cde, app(app(app(ty_@3, cec), ced), cee)) → new_esEs7(vyy3000, vyy400, cec, ced, cee)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Integer, dh) → new_ltEs8(vyy650, vyy660)
new_lt8(vyy650, vyy660, ty_Int) → new_lt4(vyy650, vyy660)
new_esEs28(vyy650, vyy660, app(app(ty_@2, bdf), bdg)) → new_esEs6(vyy650, vyy660, bdf, bdg)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs16(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_compare25(vyy650, vyy660, False) → new_compare11(vyy650, vyy660, new_ltEs5(vyy650, vyy660))
new_esEs12(vyy3000, vyy400, app(ty_Ratio, cac)) → new_esEs20(vyy3000, vyy400, cac)
new_esEs21(vyy650, vyy660, app(ty_Maybe, dd)) → new_esEs4(vyy650, vyy660, dd)
new_ltEs17(vyy65, vyy66) → new_not(new_esEs8(new_compare5(vyy65, vyy66), GT))
new_lt12(vyy650, vyy660) → new_esEs8(new_compare13(vyy650, vyy660), LT)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Char, ccb) → new_esEs13(vyy3000, vyy400)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Float, dh) → new_ltEs9(vyy650, vyy660)
new_esEs19(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_lt8(vyy650, vyy660, app(ty_Ratio, cad)) → new_lt5(vyy650, vyy660, cad)
new_esEs11(vyy3001, vyy401, app(app(ty_@2, bgb), bgc)) → new_esEs6(vyy3001, vyy401, bgb, bgc)
new_esEs28(vyy650, vyy660, app(ty_[], bdc)) → new_esEs18(vyy650, vyy660, bdc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs4(LT, EQ) → True
new_compare32(vyy650, vyy660, ty_Float) → new_compare13(vyy650, vyy660)
new_esEs10(vyy3002, vyy402, app(app(ty_Either, bef), beg)) → new_esEs5(vyy3002, vyy402, bef, beg)
new_ltEs7(Right(vyy650), Right(vyy660), fa, ty_Integer) → new_ltEs8(vyy650, vyy660)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs14(vyy3000, vyy400)
new_ltEs7(Right(vyy650), Right(vyy660), fa, app(app(ty_Either, fd), ff)) → new_ltEs7(vyy650, vyy660, fd, ff)
new_lt19(vyy651, vyy661, ty_@0) → new_lt18(vyy651, vyy661)
new_esEs12(vyy3000, vyy400, app(ty_Maybe, bhf)) → new_esEs4(vyy3000, vyy400, bhf)
new_ltEs16(vyy65, vyy66) → new_not(new_esEs8(new_compare16(vyy65, vyy66), GT))
new_asAs(False, vyy91) → False
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs16(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_lt16(vyy650, vyy660, hh, baa) → new_esEs8(new_compare15(vyy650, vyy660, hh, baa), LT)
new_esEs5(Right(vyy3000), Right(vyy400), cde, ty_Char) → new_esEs13(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy6500)), Neg(vyy660)) → new_primCmpNat2(vyy660, vyy6500)
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_ltEs7(Left(vyy650), Left(vyy660), ty_Double, dh) → new_ltEs14(vyy650, vyy660)
new_lt19(vyy651, vyy661, ty_Float) → new_lt12(vyy651, vyy661)
new_compare32(vyy650, vyy660, ty_Double) → new_compare18(vyy650, vyy660)
new_esEs18([], [], cfb) → True
new_ltEs6(Just(vyy6500), Just(vyy6600), app(app(app(ty_@3, bf), bg), bh)) → new_ltEs15(vyy6500, vyy6600, bf, bg, bh)
new_esEs21(vyy650, vyy660, app(app(ty_Either, de), df)) → new_esEs5(vyy650, vyy660, de, df)
new_esEs21(vyy650, vyy660, ty_Ordering) → new_esEs8(vyy650, vyy660)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], cbf)) → new_esEs18(vyy3000, vyy400, cbf)
new_compare32(vyy650, vyy660, app(ty_Maybe, cb)) → new_compare7(vyy650, vyy660, cb)
new_lt20(vyy650, vyy660, app(app(ty_@2, bdf), bdg)) → new_lt16(vyy650, vyy660, bdf, bdg)
new_esEs5(Right(vyy3000), Right(vyy400), cde, ty_Int) → new_esEs19(vyy3000, vyy400)
new_compare14(vyy650, vyy660, True, dd) → LT
new_ltEs18(vyy651, vyy661, ty_Char) → new_ltEs12(vyy651, vyy661)
new_ltEs11(vyy65, vyy66, ca) → new_not(new_esEs8(new_compare(vyy65, vyy66, ca), GT))
new_primCmpInt(Pos(Zero), Pos(Succ(vyy6600))) → new_primCmpNat2(Zero, vyy6600)
new_ltEs18(vyy651, vyy661, ty_Int) → new_ltEs17(vyy651, vyy661)
new_ltEs18(vyy651, vyy661, app(app(ty_@2, ha), hb)) → new_ltEs13(vyy651, vyy661, ha, hb)
new_lt8(vyy650, vyy660, app(ty_Maybe, dd)) → new_lt13(vyy650, vyy660, dd)
new_esEs18(:(vyy3000, vyy3001), :(vyy400, vyy401), cfb) → new_asAs(new_esEs22(vyy3000, vyy400, cfb), new_esEs18(vyy3001, vyy401, cfb))
new_lt19(vyy651, vyy661, ty_Bool) → new_lt10(vyy651, vyy661)
new_compare7(vyy650, vyy660, dd) → new_compare26(vyy650, vyy660, new_esEs4(vyy650, vyy660, dd), dd)
new_compare31(Char(vyy650), Char(vyy660)) → new_primCmpInt(vyy650, vyy660)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_@0) → new_ltEs16(vyy6500, vyy6600)
new_esEs10(vyy3002, vyy402, ty_Int) → new_esEs19(vyy3002, vyy402)
new_ltEs6(Nothing, Nothing, dd) → True
new_ltEs19(vyy652, vyy662, ty_Bool) → new_ltEs5(vyy652, vyy662)
new_esEs25(vyy3001, vyy401, app(app(app(ty_@3, che), chf), chg)) → new_esEs7(vyy3001, vyy401, che, chf, chg)
new_ltEs7(Left(vyy650), Left(vyy660), app(app(ty_@2, ed), ee), dh) → new_ltEs13(vyy650, vyy660, ed, ee)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Bool, ccb) → new_esEs17(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), cde, app(ty_Maybe, ceb)) → new_esEs4(vyy3000, vyy400, ceb)
new_esEs28(vyy650, vyy660, ty_Bool) → new_esEs17(vyy650, vyy660)
new_esEs28(vyy650, vyy660, app(ty_Ratio, dbh)) → new_esEs20(vyy650, vyy660, dbh)
new_esEs22(vyy3000, vyy400, ty_Int) → new_esEs19(vyy3000, vyy400)
new_ltEs4(LT, LT) → True
new_compare11(vyy650, vyy660, False) → GT
new_esEs22(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs19(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, app(app(ty_Either, bfh), bga)) → new_esEs5(vyy3001, vyy401, bfh, bga)
new_ltEs18(vyy651, vyy661, ty_Double) → new_ltEs14(vyy651, vyy661)
new_esEs21(vyy650, vyy660, ty_@0) → new_esEs9(vyy650, vyy660)
new_esEs10(vyy3002, vyy402, ty_Integer) → new_esEs16(vyy3002, vyy402)
new_compare11(vyy650, vyy660, True) → LT
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs19(vyy3000, vyy400)
new_lt8(vyy650, vyy660, ty_Double) → new_lt17(vyy650, vyy660)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_Either, ccc), ccd), ccb) → new_esEs5(vyy3000, vyy400, ccc, ccd)
new_ltEs18(vyy651, vyy661, app(ty_Maybe, ge)) → new_ltEs6(vyy651, vyy661, ge)
new_lt17(vyy650, vyy660) → new_esEs8(new_compare18(vyy650, vyy660), LT)
new_esEs22(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy6600))) → new_primCmpNat1(vyy6600, Zero)
new_lt9(vyy650, vyy660) → new_esEs8(new_compare6(vyy650, vyy660), LT)
new_esEs10(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_ltEs7(Right(vyy650), Right(vyy660), fa, ty_Int) → new_ltEs17(vyy650, vyy660)
new_esEs5(Right(vyy3000), Right(vyy400), cde, ty_Float) → new_esEs15(vyy3000, vyy400)
new_esEs28(vyy650, vyy660, ty_Float) → new_esEs15(vyy650, vyy660)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare8(:%(vyy650, vyy651), :%(vyy660, vyy661), ty_Int) → new_compare5(new_sr(vyy650, vyy661), new_sr(vyy660, vyy651))
new_compare12(vyy650, vyy660, de, df) → new_compare27(vyy650, vyy660, new_esEs5(vyy650, vyy660, de, df), de, df)
new_asAs(True, vyy91) → vyy91
new_lt19(vyy651, vyy661, app(ty_Maybe, bbh)) → new_lt13(vyy651, vyy661, bbh)
new_esEs22(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_lt20(vyy650, vyy660, app(ty_[], bdc)) → new_lt7(vyy650, vyy660, bdc)
new_esEs24(vyy3000, vyy400, ty_Int) → new_esEs19(vyy3000, vyy400)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Ordering) → new_ltEs4(vyy6500, vyy6600)
new_lt20(vyy650, vyy660, ty_Char) → new_lt15(vyy650, vyy660)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, dad), dae)) → new_esEs6(vyy3000, vyy400, dad, dae)
new_ltEs6(Just(vyy6500), Just(vyy6600), app(ty_[], ba)) → new_ltEs11(vyy6500, vyy6600, ba)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, cbc), cbd), cbe)) → new_esEs7(vyy3000, vyy400, cbc, cbd, cbe)
new_compare15(vyy650, vyy660, hh, baa) → new_compare28(vyy650, vyy660, new_esEs6(vyy650, vyy660, hh, baa), hh, baa)
new_ltEs7(Right(vyy650), Right(vyy660), fa, app(ty_Maybe, fb)) → new_ltEs6(vyy650, vyy660, fb)
new_ltEs4(GT, GT) → True
new_ltEs13(@2(vyy650, vyy651), @2(vyy660, vyy661), gd, hf) → new_pePe(new_lt8(vyy650, vyy660, gd), new_asAs(new_esEs21(vyy650, vyy660, gd), new_ltEs18(vyy651, vyy661, hf)))
new_esEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cgf, cgg) → new_asAs(new_esEs26(vyy3000, vyy400, cgf), new_esEs25(vyy3001, vyy401, cgg))
new_esEs22(vyy3000, vyy400, app(app(ty_Either, cfc), cfd)) → new_esEs5(vyy3000, vyy400, cfc, cfd)
new_compare13(Float(vyy650, vyy651), Float(vyy660, vyy661)) → new_compare5(new_sr(vyy650, vyy660), new_sr(vyy651, vyy661))
new_lt8(vyy650, vyy660, app(ty_[], hg)) → new_lt7(vyy650, vyy660, hg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(vyy132, EQ) → vyy132
new_lt19(vyy651, vyy661, ty_Char) → new_lt15(vyy651, vyy661)
new_ltEs18(vyy651, vyy661, ty_Integer) → new_ltEs8(vyy651, vyy661)
new_ltEs19(vyy652, vyy662, ty_@0) → new_ltEs16(vyy652, vyy662)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Int, dh) → new_ltEs17(vyy650, vyy660)
new_esEs10(vyy3002, vyy402, app(ty_Maybe, bfb)) → new_esEs4(vyy3002, vyy402, bfb)
new_esEs25(vyy3001, vyy401, app(ty_Ratio, daa)) → new_esEs20(vyy3001, vyy401, daa)
new_esEs10(vyy3002, vyy402, ty_Bool) → new_esEs17(vyy3002, vyy402)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_lt20(vyy650, vyy660, ty_Bool) → new_lt10(vyy650, vyy660)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, dbc)) → new_esEs20(vyy3000, vyy400, dbc)
new_esEs12(vyy3000, vyy400, app(app(ty_@2, bhd), bhe)) → new_esEs6(vyy3000, vyy400, bhd, bhe)
new_esEs25(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_primCmpInt(Neg(Succ(vyy6500)), Pos(vyy660)) → LT
new_esEs10(vyy3002, vyy402, ty_Double) → new_esEs14(vyy3002, vyy402)
new_not(True) → False
new_lt19(vyy651, vyy661, app(ty_[], bcb)) → new_lt7(vyy651, vyy661, bcb)

The set Q consists of the following terms:

new_ltEs19(x0, x1, ty_Char)
new_compare10(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_Float)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Ordering)
new_lt7(x0, x1, x2)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_compare17(x0, x1, False, x2, x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare27(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat2(Zero, x0)
new_compare32(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_compare13(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs16(Integer(x0), Integer(x1))
new_esEs28(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Bool)
new_lt8(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Ordering)
new_esEs8(GT, GT)
new_compare32(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_lt8(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Nothing, x1)
new_lt11(x0, x1)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt16(x0, x1, x2, x3)
new_ltEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs8(LT, LT)
new_compare111(x0, x1, True, x2, x3, x4)
new_ltEs18(x0, x1, ty_@0)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt9(x0, x1)
new_esEs17(False, False)
new_pePe(False, x0)
new_sr(x0, x1)
new_ltEs5(False, False)
new_primCompAux0(x0, GT)
new_lt8(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs6(Just(x0), Just(x1), ty_@0)
new_esEs28(x0, x1, ty_@0)
new_primCompAux0(x0, EQ)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs12(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs23(x0, x1, ty_Integer)
new_compare17(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs27(x0, x1, ty_Char)
new_ltEs10(x0, x1, x2)
new_lt8(x0, x1, ty_Int)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13(Char(x0), Char(x1))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1, x2)
new_lt5(x0, x1, x2)
new_esEs27(x0, x1, ty_@0)
new_ltEs6(Just(x0), Just(x1), ty_Float)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1, app(ty_[], x2))
new_primEqNat0(Zero, Zero)
new_sr0(Integer(x0), Integer(x1))
new_esEs26(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare32(x0, x1, app(ty_Maybe, x2))
new_compare18(Double(x0, x1), Double(x2, x3))
new_compare32(x0, x1, app(ty_[], x2))
new_compare14(x0, x1, True, x2)
new_compare10(x0, x1, True, x2, x3)
new_esEs28(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Integer)
new_compare11(x0, x1, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs25(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare([], :(x0, x1), x2)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primMulNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs12(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs18([], [], x0)
new_asAs(False, x0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare7(x0, x1, x2)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs4(GT, GT)
new_ltEs18(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Float)
new_compare30(x0, x1)
new_esEs11(x0, x1, app(ty_[], x2))
new_ltEs6(Just(x0), Just(x1), ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt17(x0, x1)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_ltEs6(Nothing, Just(x0), x1)
new_esEs26(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs4(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_@0)
new_primPlusNat1(Zero, Zero)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Succ(x0), Zero)
new_compare32(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare32(x0, x1, ty_Integer)
new_compare27(x0, x1, True, x2, x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs19(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_lt15(x0, x1)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs6(Just(x0), Just(x1), ty_Char)
new_ltEs4(EQ, EQ)
new_ltEs18(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Integer)
new_compare110(x0, x1, False)
new_compare6(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs18(:(x0, x1), [], x2)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs4(EQ, LT)
new_ltEs19(x0, x1, ty_Double)
new_ltEs4(LT, EQ)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs21(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Float)
new_compare5(x0, x1)
new_compare25(x0, x1, True)
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt8(x0, x1, ty_Integer)
new_compare([], [], x0)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, False)
new_ltEs18(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(x0, x1, False, x2)
new_lt8(x0, x1, ty_@0)
new_esEs12(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare28(x0, x1, False, x2, x3)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Just(x0), Just(x1), ty_Integer)
new_esEs12(x0, x1, ty_Float)
new_compare32(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs19(x0, x1, ty_Ordering)
new_primCompAux0(x0, LT)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_primCompAux1(x0, x1, x2, x3)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_lt14(x0, x1, x2, x3)
new_esEs18([], :(x0, x1), x2)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpNat2(Succ(x0), x1)
new_primPlusNat0(Succ(x0), x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs4(LT, LT)
new_compare26(x0, x1, True, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs10(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(Char(x0), Char(x1))
new_esEs11(x0, x1, ty_Char)
new_compare29(x0, x1, False, x2, x3, x4)
new_compare32(x0, x1, app(ty_Ratio, x2))
new_compare9(x0, x1, x2, x3, x4)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(x0, x1)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_esEs9(@0, @0)
new_esEs10(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt8(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_compare(:(x0, x1), [], x2)
new_ltEs18(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_lt12(x0, x1)
new_compare(:(x0, x1), :(x2, x3), x4)
new_compare15(x0, x1, x2, x3)
new_compare19(Integer(x0), Integer(x1))
new_compare32(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_ltEs12(x0, x1)
new_lt8(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Zero, Zero)
new_compare24(x0, x1, True)
new_esEs10(x0, x1, ty_Bool)
new_lt13(x0, x1, x2)
new_esEs26(x0, x1, ty_Double)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_primCmpNat0(Zero, Succ(x0))
new_compare24(x0, x1, False)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs4(Nothing, Just(x0), x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs25(x0, x1, ty_Bool)
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs12(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs11(x0, x1, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs10(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_Char)
new_asAs(True, x0)
new_esEs11(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Char)
new_esEs12(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs17(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare14(x0, x1, False, x2)
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_ltEs5(True, True)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_lt6(x0, x1, x2, x3, x4)
new_lt19(x0, x1, ty_@0)
new_lt18(x0, x1)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_ltEs6(Just(x0), Nothing, x1)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Int)
new_not(True)
new_lt10(x0, x1)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_lt20(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs22(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_not(False)
new_compare110(x0, x1, True)
new_ltEs19(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs12(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_@0)
new_primCmpNat1(x0, Succ(x1))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare32(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs6(Just(x0), Just(x1), ty_Bool)
new_primCmpNat1(x0, Zero)
new_lt4(x0, x1)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_lt19(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Bool)
new_compare29(x0, x1, True, x2, x3, x4)
new_ltEs16(x0, x1)
new_lt8(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17(True, False)
new_esEs17(False, True)
new_esEs27(x0, x1, ty_Int)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs28(x0, 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_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_compare25(x0, x1, False)
new_ltEs14(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1, x2, x3)
new_esEs28(x0, x1, ty_Char)
new_compare28(x0, x1, True, x2, x3)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Int)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs25(x0, x1, ty_Char)
new_pePe(True, x0)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Char)
new_ltEs9(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, 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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP

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

new_foldFM_GE2(vyy330, vyy331, vyy71, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba) → new_foldFM_GE1(new_keysFM_GE0(vyy330, vyy331, vyy71, h, ba), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, h), h, ba)
new_foldFM_GE(vyy50, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba) → new_foldFM_GE1(vyy50, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h), h, ba)
new_foldFM_GE1(vyy50, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE2(vyy330, vyy331, new_foldFM_GE0(vyy50, vyy40, vyy334, h, ba), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba)
new_foldFM_GE1(vyy50, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE(vyy50, vyy40, vyy334, h, ba)
new_foldFM_GE1(vyy50, vyy40, vyy330, vyy331, vyy332, vyy333, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), False, h, ba) → new_foldFM_GE1(vyy50, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h), h, ba)
new_foldFM_GE1(vyy50, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba) → new_foldFM_GE(vyy50, vyy40, vyy334, h, ba)

The TRS R consists of the following rules:

new_lt14(vyy650, vyy660, ge, gf) → new_esEs8(new_compare12(vyy650, vyy660, ge, gf), LT)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, hd)) → new_esEs4(vyy3000, vyy400, hd)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, baa)) → new_esEs20(vyy3000, vyy400, baa)
new_esEs12(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Int) → new_esEs19(vyy3001, vyy401)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt4(vyy650, vyy660) → new_esEs8(new_compare5(vyy650, vyy660), LT)
new_esEs21(vyy650, vyy660, app(app(ty_@2, bb), bc)) → new_esEs6(vyy650, vyy660, bb, bc)
new_primCmpNat2(Zero, vyy6500) → LT
new_lt19(vyy651, vyy661, app(app(ty_Either, dab), dac)) → new_lt14(vyy651, vyy661, dab, dac)
new_ltEs4(EQ, GT) → True
new_compare29(vyy650, vyy660, False, ga, gb, gc) → new_compare111(vyy650, vyy660, new_ltEs15(vyy650, vyy660, ga, gb, gc), ga, gb, gc)
new_esEs28(vyy650, vyy660, ty_Char) → new_esEs13(vyy650, vyy660)
new_compare24(vyy650, vyy660, False) → new_compare110(vyy650, vyy660, new_ltEs4(vyy650, vyy660))
new_compare([], :(vyy660, vyy661), bff) → LT
new_compare10(vyy650, vyy660, True, bb, bc) → LT
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_ltEs10(vyy65, vyy66, ceg) → new_not(new_esEs8(new_compare8(vyy65, vyy66, ceg), GT))
new_esEs4(Just(vyy3000), Nothing, gg) → False
new_esEs4(Nothing, Just(vyy400), gg) → False
new_lt7(vyy650, vyy660, gd) → new_esEs8(new_compare(vyy650, vyy660, gd), LT)
new_foldFM_GE10(vyy50, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba) → new_foldFM_GE3(vyy330, vyy331, new_foldFM_GE0(vyy50, vyy40, vyy334, h, ba), vyy40, h, ba)
new_lt20(vyy650, vyy660, app(app(ty_Either, dbd), dbe)) → new_lt14(vyy650, vyy660, dbd, dbe)
new_ltEs6(Nothing, Just(vyy6600), fg) → True
new_esEs27(vyy651, vyy661, ty_Bool) → new_esEs17(vyy651, vyy661)
new_lt19(vyy651, vyy661, ty_Int) → new_lt4(vyy651, vyy661)
new_ltEs9(vyy65, vyy66) → new_not(new_esEs8(new_compare13(vyy65, vyy66), GT))
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(vyy650), Right(vyy660), bbe, bab) → True
new_compare32(vyy650, vyy660, ty_Bool) → new_compare30(vyy650, vyy660)
new_lt20(vyy650, vyy660, ty_@0) → new_lt18(vyy650, vyy660)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs15(vyy3000, vyy400)
new_compare(:(vyy650, vyy651), [], bff) → GT
new_lt8(vyy650, vyy660, app(app(app(ty_@3, ga), gb), gc)) → new_lt6(vyy650, vyy660, ga, gb, gc)
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs21(vyy650, vyy660, ty_Bool) → new_esEs17(vyy650, vyy660)
new_lt19(vyy651, vyy661, ty_Integer) → new_lt11(vyy651, vyy661)
new_esEs12(vyy3000, vyy400, app(ty_[], fd)) → new_esEs18(vyy3000, vyy400, fd)
new_lt20(vyy650, vyy660, app(ty_Maybe, dbb)) → new_lt13(vyy650, vyy660, dbb)
new_lt8(vyy650, vyy660, ty_Bool) → new_lt10(vyy650, vyy660)
new_lt8(vyy650, vyy660, ty_@0) → new_lt18(vyy650, vyy660)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_esEs11(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_compare16(@0, @0) → EQ
new_esEs17(True, True) → True
new_lt8(vyy650, vyy660, app(app(ty_@2, bb), bc)) → new_lt16(vyy650, vyy660, bb, bc)
new_lt10(vyy650, vyy660) → new_esEs8(new_compare30(vyy650, vyy660), LT)
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Ratio, beb), bch) → new_esEs20(vyy3000, vyy400, beb)
new_esEs21(vyy650, vyy660, app(app(app(ty_@3, ga), gb), gc)) → new_esEs7(vyy650, vyy660, ga, gb, gc)
new_lt20(vyy650, vyy660, ty_Float) → new_lt12(vyy650, vyy660)
new_esEs25(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_esEs12(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs7(Left(vyy650), Left(vyy660), app(app(app(ty_@3, bbb), bbc), bbd), bab) → new_ltEs15(vyy650, vyy660, bbb, bbc, bbd)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs28(vyy650, vyy660, ty_Double) → new_esEs14(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, app(app(app(ty_@3, dg), dh), ea)) → new_esEs7(vyy3001, vyy401, dg, dh, ea)
new_esEs11(vyy3001, vyy401, app(ty_Ratio, ec)) → new_esEs20(vyy3001, vyy401, ec)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, cea)) → new_esEs4(vyy3000, vyy400, cea)
new_primCmpNat1(vyy6500, Succ(vyy6600)) → new_primCmpNat0(vyy6500, vyy6600)
new_esEs27(vyy651, vyy661, ty_Double) → new_esEs14(vyy651, vyy661)
new_compare30(vyy650, vyy660) → new_compare25(vyy650, vyy660, new_esEs17(vyy650, vyy660))
new_ltEs6(Just(vyy6500), Just(vyy6600), app(ty_Ratio, bhc)) → new_ltEs10(vyy6500, vyy6600, bhc)
new_compare32(vyy650, vyy660, app(app(ty_@2, cfe), cff)) → new_compare15(vyy650, vyy660, cfe, cff)
new_ltEs6(Just(vyy6500), Just(vyy6600), app(app(ty_@2, bhh), caa)) → new_ltEs13(vyy6500, vyy6600, bhh, caa)
new_esEs10(vyy3002, vyy402, app(ty_Ratio, da)) → new_esEs20(vyy3002, vyy402, da)
new_pePe(False, vyy127) → vyy127
new_lt13(vyy650, vyy660, fg) → new_esEs8(new_compare7(vyy650, vyy660, fg), LT)
new_esEs18([], :(vyy400, vyy401), cae) → False
new_esEs18(:(vyy3000, vyy3001), [], cae) → False
new_primCmpNat1(vyy6500, Zero) → GT
new_ltEs7(Right(vyy650), Right(vyy660), bbe, app(app(ty_@2, bcc), bcd)) → new_ltEs13(vyy650, vyy660, bcc, bcd)
new_lt19(vyy651, vyy661, ty_Ordering) → new_lt9(vyy651, vyy661)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Bool) → new_ltEs5(vyy6500, vyy6600)
new_ltEs19(vyy652, vyy662, app(ty_[], cgg)) → new_ltEs11(vyy652, vyy662, cgg)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Char, bab) → new_ltEs12(vyy650, vyy660)
new_esEs22(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare26(vyy650, vyy660, False, fg) → new_compare14(vyy650, vyy660, new_ltEs6(vyy650, vyy660, fg), fg)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_@2, bdc), bdd), bch) → new_esEs6(vyy3000, vyy400, bdc, bdd)
new_esEs20(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cbh) → new_asAs(new_esEs24(vyy3000, vyy400, cbh), new_esEs23(vyy3001, vyy401, cbh))
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_Maybe, bde), bch) → new_esEs4(vyy3000, vyy400, bde)
new_ltEs14(vyy65, vyy66) → new_not(new_esEs8(new_compare18(vyy65, vyy66), GT))
new_esEs10(vyy3002, vyy402, app(app(ty_@2, ca), cb)) → new_esEs6(vyy3002, vyy402, ca, cb)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Ordering, bch) → new_esEs8(vyy3000, vyy400)
new_esEs27(vyy651, vyy661, ty_Int) → new_esEs19(vyy651, vyy661)
new_primCmpNat0(Zero, Succ(vyy66000)) → LT
new_esEs22(vyy3000, vyy400, ty_Float) → new_esEs15(vyy3000, vyy400)
new_esEs27(vyy651, vyy661, app(app(app(ty_@3, daf), dag), dah)) → new_esEs7(vyy651, vyy661, daf, dag, dah)
new_esEs21(vyy650, vyy660, ty_Char) → new_esEs13(vyy650, vyy660)
new_esEs25(vyy3001, vyy401, app(app(ty_Either, ccc), ccd)) → new_esEs5(vyy3001, vyy401, ccc, ccd)
new_esEs10(vyy3002, vyy402, ty_Char) → new_esEs13(vyy3002, vyy402)
new_esEs25(vyy3001, vyy401, app(app(ty_@2, cce), ccf)) → new_esEs6(vyy3001, vyy401, cce, ccf)
new_esEs8(LT, LT) → True
new_esEs5(Left(vyy3000), Left(vyy400), ty_@0, bch) → new_esEs9(vyy3000, vyy400)
new_lt5(vyy650, vyy660, fh) → new_esEs8(new_compare8(vyy650, vyy660, fh), LT)
new_ltEs6(Just(vyy6500), Just(vyy6600), app(app(ty_Either, bhf), bhg)) → new_ltEs7(vyy6500, vyy6600, bhf, bhg)
new_ltEs8(vyy65, vyy66) → new_not(new_esEs8(new_compare19(vyy65, vyy66), GT))
new_lt19(vyy651, vyy661, app(app(ty_@2, dad), dae)) → new_lt16(vyy651, vyy661, dad, dae)
new_esEs25(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Bool) → new_ltEs5(vyy650, vyy660)
new_esEs28(vyy650, vyy660, ty_Integer) → new_esEs16(vyy650, vyy660)
new_lt11(vyy650, vyy660) → new_esEs8(new_compare19(vyy650, vyy660), LT)
new_ltEs5(True, False) → False
new_pePe(True, vyy127) → True
new_primEqNat0(Zero, Zero) → True
new_esEs5(Right(vyy3000), Right(vyy400), bec, app(app(ty_@2, bef), beg)) → new_esEs6(vyy3000, vyy400, bef, beg)
new_ltEs12(vyy65, vyy66) → new_not(new_esEs8(new_compare31(vyy65, vyy66), GT))
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_@0) → new_ltEs16(vyy650, vyy660)
new_esEs25(vyy3001, vyy401, app(ty_[], cdc)) → new_esEs18(vyy3001, vyy401, cdc)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Double) → new_ltEs14(vyy650, vyy660)
new_esEs12(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_lt8(vyy650, vyy660, ty_Integer) → new_lt11(vyy650, vyy660)
new_esEs27(vyy651, vyy661, ty_Char) → new_esEs13(vyy651, vyy661)
new_esEs14(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs19(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_ltEs5(True, True) → True
new_esEs17(False, False) → True
new_esEs17(True, False) → False
new_esEs17(False, True) → False
new_esEs13(Char(vyy3000), Char(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs13(vyy3000, vyy400)
new_compare(:(vyy650, vyy651), :(vyy660, vyy661), bff) → new_primCompAux1(vyy650, vyy660, new_compare(vyy651, vyy661, bff), bff)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, ty_@0) → new_esEs9(vyy3001, vyy401)
new_keysFM_GE0(vyy330, vyy331, vyy68, h, ba) → :(vyy330, vyy68)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, app(app(app(ty_@3, bce), bcf), bcg)) → new_ltEs15(vyy650, vyy660, bce, bcf, bcg)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(vyy1030), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1030, vyy40100)))
new_primCmpInt(Pos(Succ(vyy6500)), Pos(vyy660)) → new_primCmpNat1(vyy6500, vyy660)
new_esEs11(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_lt20(vyy650, vyy660, ty_Double) → new_lt17(vyy650, vyy660)
new_esEs5(Right(vyy3000), Right(vyy400), bec, app(ty_[], bfd)) → new_esEs18(vyy3000, vyy400, bfd)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs22(vyy3000, vyy400, app(ty_[], cbf)) → new_esEs18(vyy3000, vyy400, cbf)
new_ltEs19(vyy652, vyy662, app(app(app(ty_@3, chd), che), chf)) → new_ltEs15(vyy652, vyy662, chd, che, chf)
new_compare32(vyy650, vyy660, ty_Integer) → new_compare19(vyy650, vyy660)
new_compare9(vyy650, vyy660, ga, gb, gc) → new_compare29(vyy650, vyy660, new_esEs7(vyy650, vyy660, ga, gb, gc), ga, gb, gc)
new_compare17(vyy650, vyy660, True, ge, gf) → LT
new_compare29(vyy650, vyy660, True, ga, gb, gc) → EQ
new_lt20(vyy650, vyy660, ty_Ordering) → new_lt9(vyy650, vyy660)
new_compare25(vyy650, vyy660, True) → EQ
new_esEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bd, be, bf) → new_asAs(new_esEs12(vyy3000, vyy400, bd), new_asAs(new_esEs11(vyy3001, vyy401, be), new_esEs10(vyy3002, vyy402, bf)))
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Integer, bch) → new_esEs16(vyy3000, vyy400)
new_ltEs18(vyy651, vyy661, app(ty_Ratio, bga)) → new_ltEs10(vyy651, vyy661, bga)
new_ltEs19(vyy652, vyy662, ty_Integer) → new_ltEs8(vyy652, vyy662)
new_ltEs5(False, False) → True
new_ltEs18(vyy651, vyy661, app(app(ty_Either, bgd), bge)) → new_ltEs7(vyy651, vyy661, bgd, bge)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat1(Succ(vyy10300), Zero) → Succ(vyy10300)
new_esEs10(vyy3002, vyy402, app(ty_[], cg)) → new_esEs18(vyy3002, vyy402, cg)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Bool, bab) → new_ltEs5(vyy650, vyy660)
new_compare28(vyy650, vyy660, False, bb, bc) → new_compare10(vyy650, vyy660, new_ltEs13(vyy650, vyy660, bb, bc), bb, bc)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, ceb), cec), ced)) → new_esEs7(vyy3000, vyy400, ceb, cec, ced)
new_esEs10(vyy3002, vyy402, ty_@0) → new_esEs9(vyy3002, vyy402)
new_esEs28(vyy650, vyy660, app(ty_Maybe, dbb)) → new_esEs4(vyy650, vyy660, dbb)
new_lt20(vyy650, vyy660, ty_Int) → new_lt4(vyy650, vyy660)
new_compare18(Double(vyy650, vyy651), Double(vyy660, vyy661)) → new_compare5(new_sr(vyy650, vyy660), new_sr(vyy651, vyy661))
new_ltEs19(vyy652, vyy662, ty_Float) → new_ltEs9(vyy652, vyy662)
new_esEs21(vyy650, vyy660, ty_Double) → new_esEs14(vyy650, vyy660)
new_esEs21(vyy650, vyy660, app(ty_[], gd)) → new_esEs18(vyy650, vyy660, gd)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bdf), bdg), bdh), bch) → new_esEs7(vyy3000, vyy400, bdf, bdg, bdh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(vyy650), Left(vyy660), bbe, bab) → False
new_ltEs19(vyy652, vyy662, ty_Ordering) → new_ltEs4(vyy652, vyy662)
new_esEs27(vyy651, vyy661, app(app(ty_Either, dab), dac)) → new_esEs5(vyy651, vyy661, dab, dac)
new_primCmpNat2(Succ(vyy6600), vyy6500) → new_primCmpNat0(vyy6600, vyy6500)
new_esEs11(vyy3001, vyy401, ty_Float) → new_esEs15(vyy3001, vyy401)
new_esEs10(vyy3002, vyy402, ty_Float) → new_esEs15(vyy3002, vyy402)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primCompAux0(vyy132, GT) → GT
new_ltEs19(vyy652, vyy662, ty_Char) → new_ltEs12(vyy652, vyy662)
new_lt20(vyy650, vyy660, ty_Integer) → new_lt11(vyy650, vyy660)
new_esEs8(EQ, EQ) → True
new_esEs11(vyy3001, vyy401, ty_Int) → new_esEs19(vyy3001, vyy401)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Double, bch) → new_esEs14(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_esEs12(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs10(vyy3002, vyy402, app(app(app(ty_@3, cd), ce), cf)) → new_esEs7(vyy3002, vyy402, cd, ce, cf)
new_ltEs7(Left(vyy650), Left(vyy660), ty_@0, bab) → new_ltEs16(vyy650, vyy660)
new_lt19(vyy651, vyy661, app(app(app(ty_@3, daf), dag), dah)) → new_lt6(vyy651, vyy661, daf, dag, dah)
new_compare32(vyy650, vyy660, app(ty_Ratio, ceh)) → new_compare8(vyy650, vyy660, ceh)
new_esEs26(vyy3000, vyy400, app(ty_[], cee)) → new_esEs18(vyy3000, vyy400, cee)
new_compare([], [], bff) → EQ
new_ltEs18(vyy651, vyy661, ty_Ordering) → new_ltEs4(vyy651, vyy661)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs4(EQ, LT) → False
new_esEs22(vyy3000, vyy400, app(ty_Ratio, cbg)) → new_esEs20(vyy3000, vyy400, cbg)
new_esEs27(vyy651, vyy661, ty_Float) → new_esEs15(vyy651, vyy661)
new_esEs21(vyy650, vyy660, app(ty_Ratio, fh)) → new_esEs20(vyy650, vyy660, fh)
new_lt8(vyy650, vyy660, ty_Float) → new_lt12(vyy650, vyy660)
new_esEs28(vyy650, vyy660, ty_Int) → new_esEs19(vyy650, vyy660)
new_esEs15(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs19(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt20(vyy650, vyy660, app(app(app(ty_@3, dbh), dca), dcb)) → new_lt6(vyy650, vyy660, dbh, dca, dcb)
new_primCmpNat0(Succ(vyy65000), Succ(vyy66000)) → new_primCmpNat0(vyy65000, vyy66000)
new_esEs22(vyy3000, vyy400, app(ty_Maybe, cbb)) → new_esEs4(vyy3000, vyy400, cbb)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, app(ty_Maybe, ccg)) → new_esEs4(vyy3001, vyy401, ccg)
new_ltEs18(vyy651, vyy661, ty_Bool) → new_ltEs5(vyy651, vyy661)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare10(vyy650, vyy660, False, bb, bc) → GT
new_compare27(vyy650, vyy660, True, ge, gf) → EQ
new_lt8(vyy650, vyy660, ty_Char) → new_lt15(vyy650, vyy660)
new_esEs21(vyy650, vyy660, ty_Int) → new_esEs19(vyy650, vyy660)
new_ltEs18(vyy651, vyy661, app(app(app(ty_@3, bgh), bha), bhb)) → new_ltEs15(vyy651, vyy661, bgh, bha, bhb)
new_compare14(vyy650, vyy660, False, fg) → GT
new_esEs5(Right(vyy3000), Right(vyy400), bec, app(app(ty_Either, bed), bee)) → new_esEs5(vyy3000, vyy400, bed, bee)
new_ltEs19(vyy652, vyy662, app(ty_Ratio, cge)) → new_ltEs10(vyy652, vyy662, cge)
new_primEqNat0(Succ(vyy300000), Succ(vyy40000)) → new_primEqNat0(vyy300000, vyy40000)
new_esEs27(vyy651, vyy661, ty_Ordering) → new_esEs8(vyy651, vyy661)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Integer) → new_ltEs8(vyy6500, vyy6600)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Int) → new_ltEs17(vyy6500, vyy6600)
new_primCompAux1(vyy650, vyy660, vyy128, bff) → new_primCompAux0(vyy128, new_compare32(vyy650, vyy660, bff))
new_foldFM_GE10(vyy50, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba) → new_foldFM_GE20(vyy330, vyy331, new_foldFM_GE0(vyy50, vyy40, vyy334, h, ba), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba)
new_ltEs19(vyy652, vyy662, ty_Double) → new_ltEs14(vyy652, vyy662)
new_esEs9(@0, @0) → True
new_compare111(vyy650, vyy660, True, ga, gb, gc) → LT
new_ltEs4(GT, EQ) → False
new_ltEs18(vyy651, vyy661, ty_@0) → new_ltEs16(vyy651, vyy661)
new_esEs11(vyy3001, vyy401, ty_Bool) → new_esEs17(vyy3001, vyy401)
new_ltEs19(vyy652, vyy662, app(app(ty_Either, cgh), cha)) → new_ltEs7(vyy652, vyy662, cgh, cha)
new_compare8(:%(vyy650, vyy651), :%(vyy660, vyy661), ty_Integer) → new_compare19(new_sr0(vyy650, vyy661), new_sr0(vyy660, vyy651))
new_esEs5(Left(vyy3000), Left(vyy400), ty_Int, bch) → new_esEs19(vyy3000, vyy400)
new_compare32(vyy650, vyy660, app(app(ty_Either, cfc), cfd)) → new_compare12(vyy650, vyy660, cfc, cfd)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Char) → new_ltEs12(vyy6500, vyy6600)
new_ltEs19(vyy652, vyy662, ty_Int) → new_ltEs17(vyy652, vyy662)
new_ltEs7(Left(vyy650), Left(vyy660), app(ty_[], bae), bab) → new_ltEs11(vyy650, vyy660, bae)
new_gtEs(vyy3330, vyy40, h) → new_not(new_esEs8(new_compare26(vyy3330, Just(vyy40), new_esEs4(vyy3330, Just(vyy40), h), h), LT))
new_esEs11(vyy3001, vyy401, app(ty_Maybe, df)) → new_esEs4(vyy3001, vyy401, df)
new_esEs28(vyy650, vyy660, ty_Ordering) → new_esEs8(vyy650, vyy660)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_lt20(vyy650, vyy660, app(ty_Ratio, dba)) → new_lt5(vyy650, vyy660, dba)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_foldFM_GE10(vyy50, vyy40, vyy330, vyy331, vyy332, vyy333, vyy334, False, h, ba) → new_foldFM_GE0(vyy50, vyy40, vyy334, h, ba)
new_esEs11(vyy3001, vyy401, app(ty_[], eb)) → new_esEs18(vyy3001, vyy401, eb)
new_ltEs4(EQ, EQ) → True
new_ltEs19(vyy652, vyy662, app(ty_Maybe, cgf)) → new_ltEs6(vyy652, vyy662, cgf)
new_esEs12(vyy3000, vyy400, app(app(app(ty_@3, fa), fb), fc)) → new_esEs7(vyy3000, vyy400, fa, fb, fc)
new_ltEs6(Just(vyy6500), Nothing, fg) → False
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy65000), Zero) → GT
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Ordering) → new_ltEs4(vyy650, vyy660)
new_ltEs18(vyy651, vyy661, app(ty_[], bgc)) → new_ltEs11(vyy651, vyy661, bgc)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy6600))) → LT
new_compare32(vyy650, vyy660, ty_Ordering) → new_compare6(vyy650, vyy660)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, gh), ha)) → new_esEs5(vyy3000, vyy400, gh, ha)
new_esEs21(vyy650, vyy660, ty_Float) → new_esEs15(vyy650, vyy660)
new_ltEs4(GT, LT) → False
new_sr0(Integer(vyy6600), Integer(vyy6510)) → Integer(new_primMulInt(vyy6600, vyy6510))
new_lt8(vyy650, vyy660, app(app(ty_Either, ge), gf)) → new_lt14(vyy650, vyy660, ge, gf)
new_primPlusNat1(Succ(vyy10300), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy10300, vyy401000)))
new_foldFM_GE0(vyy50, vyy40, EmptyFM, h, ba) → vyy50
new_esEs12(vyy3000, vyy400, ty_Float) → new_esEs15(vyy3000, vyy400)
new_compare28(vyy650, vyy660, True, bb, bc) → EQ
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_esEs28(vyy650, vyy660, app(app(ty_Either, dbd), dbe)) → new_esEs5(vyy650, vyy660, dbd, dbe)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, hb), hc)) → new_esEs6(vyy3000, vyy400, hb, hc)
new_ltEs5(False, True) → True
new_compare32(vyy650, vyy660, app(ty_[], cfb)) → new_compare(vyy650, vyy660, cfb)
new_foldFM_GE20(vyy330, vyy331, vyy71, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba) → new_foldFM_GE10(new_keysFM_GE0(vyy330, vyy331, vyy71, h, ba), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, h), h, ba)
new_ltEs6(Just(vyy6500), Just(vyy6600), app(ty_Maybe, bhd)) → new_ltEs6(vyy6500, vyy6600, bhd)
new_esEs22(vyy3000, vyy400, app(app(ty_@2, cah), cba)) → new_esEs6(vyy3000, vyy400, cah, cba)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Ordering, bab) → new_ltEs4(vyy650, vyy660)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_compare24(vyy650, vyy660, True) → EQ
new_ltEs7(Right(vyy650), Right(vyy660), bbe, app(ty_[], bbh)) → new_ltEs11(vyy650, vyy660, bbh)
new_esEs27(vyy651, vyy661, ty_@0) → new_esEs9(vyy651, vyy661)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Char) → new_ltEs12(vyy650, vyy660)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Float) → new_esEs15(vyy3001, vyy401)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs15(vyy3000, vyy400)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, app(ty_Ratio, bbf)) → new_ltEs10(vyy650, vyy660, bbf)
new_lt15(vyy650, vyy660) → new_esEs8(new_compare31(vyy650, vyy660), LT)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Float) → new_ltEs9(vyy6500, vyy6600)
new_compare17(vyy650, vyy660, False, ge, gf) → GT
new_compare26(vyy650, vyy660, True, fg) → EQ
new_primCompAux0(vyy132, LT) → LT
new_esEs23(vyy3001, vyy401, ty_Int) → new_esEs19(vyy3001, vyy401)
new_ltEs19(vyy652, vyy662, app(app(ty_@2, chb), chc)) → new_ltEs13(vyy652, vyy662, chb, chc)
new_compare32(vyy650, vyy660, ty_Int) → new_compare5(vyy650, vyy660)
new_not(False) → True
new_esEs28(vyy650, vyy660, ty_@0) → new_esEs9(vyy650, vyy660)
new_lt18(vyy650, vyy660) → new_esEs8(new_compare16(vyy650, vyy660), LT)
new_compare32(vyy650, vyy660, app(app(app(ty_@3, cfg), cfh), cga)) → new_compare9(vyy650, vyy660, cfg, cfh, cga)
new_esEs12(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_ltEs7(Left(vyy650), Left(vyy660), app(ty_Ratio, bac), bab) → new_ltEs10(vyy650, vyy660, bac)
new_ltEs7(Left(vyy650), Left(vyy660), app(ty_Maybe, bad), bab) → new_ltEs6(vyy650, vyy660, bad)
new_esEs22(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, ty_@0) → new_esEs9(vyy3001, vyy401)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Float, bch) → new_esEs15(vyy3000, vyy400)
new_esEs27(vyy651, vyy661, app(ty_[], daa)) → new_esEs18(vyy651, vyy661, daa)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, cde), cdf)) → new_esEs5(vyy3000, vyy400, cde, cdf)
new_esEs22(vyy3000, vyy400, app(app(app(ty_@3, cbc), cbd), cbe)) → new_esEs7(vyy3000, vyy400, cbc, cbd, cbe)
new_primCmpInt(Pos(Succ(vyy6500)), Neg(vyy660)) → GT
new_esEs21(vyy650, vyy660, ty_Integer) → new_esEs16(vyy650, vyy660)
new_esEs11(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_lt6(vyy650, vyy660, ga, gb, gc) → new_esEs8(new_compare9(vyy650, vyy660, ga, gb, gc), LT)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare27(vyy650, vyy660, False, ge, gf) → new_compare17(vyy650, vyy660, new_ltEs7(vyy650, vyy660, ge, gf), ge, gf)
new_compare19(Integer(vyy650), Integer(vyy660)) → new_primCmpInt(vyy650, vyy660)
new_ltEs18(vyy651, vyy661, ty_Float) → new_ltEs9(vyy651, vyy661)
new_esEs24(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_esEs28(vyy650, vyy660, app(app(app(ty_@3, dbh), dca), dcb)) → new_esEs7(vyy650, vyy660, dbh, dca, dcb)
new_compare32(vyy650, vyy660, ty_@0) → new_compare16(vyy650, vyy660)
new_esEs5(Left(vyy3000), Right(vyy400), bec, bch) → False
new_esEs5(Right(vyy3000), Left(vyy400), bec, bch) → False
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs27(vyy651, vyy661, app(app(ty_@2, dad), dae)) → new_esEs6(vyy651, vyy661, dad, dae)
new_compare110(vyy650, vyy660, True) → LT
new_esEs11(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), bec, app(ty_Ratio, bfe)) → new_esEs20(vyy3000, vyy400, bfe)
new_primEqNat0(Zero, Succ(vyy40000)) → False
new_primEqNat0(Succ(vyy300000), Zero) → False
new_ltEs7(Left(vyy650), Left(vyy660), app(app(ty_Either, baf), bag), bab) → new_ltEs7(vyy650, vyy660, baf, bag)
new_compare110(vyy650, vyy660, False) → GT
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Double) → new_ltEs14(vyy6500, vyy6600)
new_esEs22(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, gg) → True
new_lt19(vyy651, vyy661, ty_Double) → new_lt17(vyy651, vyy661)
new_compare111(vyy650, vyy660, False, ga, gb, gc) → GT
new_esEs5(Left(vyy3000), Left(vyy400), app(ty_[], bea), bch) → new_esEs18(vyy3000, vyy400, bea)
new_compare32(vyy650, vyy660, ty_Char) → new_compare31(vyy650, vyy660)
new_esEs12(vyy3000, vyy400, app(app(ty_Either, ed), ee)) → new_esEs5(vyy3000, vyy400, ed, ee)
new_lt19(vyy651, vyy661, app(ty_Ratio, chg)) → new_lt5(vyy651, vyy661, chg)
new_esEs27(vyy651, vyy661, ty_Integer) → new_esEs16(vyy651, vyy661)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Float) → new_ltEs9(vyy650, vyy660)
new_ltEs15(@3(vyy650, vyy651, vyy652), @3(vyy660, vyy661, vyy662), cgb, cgc, cgd) → new_pePe(new_lt20(vyy650, vyy660, cgb), new_asAs(new_esEs28(vyy650, vyy660, cgb), new_pePe(new_lt19(vyy651, vyy661, cgc), new_asAs(new_esEs27(vyy651, vyy661, cgc), new_ltEs19(vyy652, vyy662, cgd)))))
new_esEs27(vyy651, vyy661, app(ty_Maybe, chh)) → new_esEs4(vyy651, vyy661, chh)
new_ltEs4(LT, GT) → True
new_compare6(vyy650, vyy660) → new_compare24(vyy650, vyy660, new_esEs8(vyy650, vyy660))
new_esEs27(vyy651, vyy661, app(ty_Ratio, chg)) → new_esEs20(vyy651, vyy661, chg)
new_esEs25(vyy3001, vyy401, ty_Integer) → new_esEs16(vyy3001, vyy401)
new_lt8(vyy650, vyy660, ty_Ordering) → new_lt9(vyy650, vyy660)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy6600))) → GT
new_compare5(vyy65, vyy66) → new_primCmpInt(vyy65, vyy66)
new_esEs12(vyy3000, vyy400, ty_Int) → new_esEs19(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Double) → new_esEs14(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), bec, app(app(app(ty_@3, bfa), bfb), bfc)) → new_esEs7(vyy3000, vyy400, bfa, bfb, bfc)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Integer, bab) → new_ltEs8(vyy650, vyy660)
new_lt8(vyy650, vyy660, ty_Int) → new_lt4(vyy650, vyy660)
new_esEs28(vyy650, vyy660, app(app(ty_@2, dbf), dbg)) → new_esEs6(vyy650, vyy660, dbf, dbg)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_esEs16(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_compare25(vyy650, vyy660, False) → new_compare11(vyy650, vyy660, new_ltEs5(vyy650, vyy660))
new_esEs12(vyy3000, vyy400, app(ty_Ratio, ff)) → new_esEs20(vyy3000, vyy400, ff)
new_esEs21(vyy650, vyy660, app(ty_Maybe, fg)) → new_esEs4(vyy650, vyy660, fg)
new_ltEs17(vyy65, vyy66) → new_not(new_esEs8(new_compare5(vyy65, vyy66), GT))
new_lt12(vyy650, vyy660) → new_esEs8(new_compare13(vyy650, vyy660), LT)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Char, bch) → new_esEs13(vyy3000, vyy400)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Float, bab) → new_ltEs9(vyy650, vyy660)
new_esEs19(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_lt8(vyy650, vyy660, app(ty_Ratio, fh)) → new_lt5(vyy650, vyy660, fh)
new_esEs11(vyy3001, vyy401, app(app(ty_@2, dd), de)) → new_esEs6(vyy3001, vyy401, dd, de)
new_esEs28(vyy650, vyy660, app(ty_[], dbc)) → new_esEs18(vyy650, vyy660, dbc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs4(LT, EQ) → True
new_compare32(vyy650, vyy660, ty_Float) → new_compare13(vyy650, vyy660)
new_esEs10(vyy3002, vyy402, app(app(ty_Either, bg), bh)) → new_esEs5(vyy3002, vyy402, bg, bh)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Integer) → new_ltEs8(vyy650, vyy660)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs14(vyy3000, vyy400)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, app(app(ty_Either, bca), bcb)) → new_ltEs7(vyy650, vyy660, bca, bcb)
new_lt19(vyy651, vyy661, ty_@0) → new_lt18(vyy651, vyy661)
new_esEs12(vyy3000, vyy400, app(ty_Maybe, eh)) → new_esEs4(vyy3000, vyy400, eh)
new_ltEs16(vyy65, vyy66) → new_not(new_esEs8(new_compare16(vyy65, vyy66), GT))
new_asAs(False, vyy91) → False
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs16(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_lt16(vyy650, vyy660, bb, bc) → new_esEs8(new_compare15(vyy650, vyy660, bb, bc), LT)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Char) → new_esEs13(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy6500)), Neg(vyy660)) → new_primCmpNat2(vyy660, vyy6500)
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_ltEs7(Left(vyy650), Left(vyy660), ty_Double, bab) → new_ltEs14(vyy650, vyy660)
new_lt19(vyy651, vyy661, ty_Float) → new_lt12(vyy651, vyy661)
new_compare32(vyy650, vyy660, ty_Double) → new_compare18(vyy650, vyy660)
new_esEs18([], [], cae) → True
new_ltEs6(Just(vyy6500), Just(vyy6600), app(app(app(ty_@3, cab), cac), cad)) → new_ltEs15(vyy6500, vyy6600, cab, cac, cad)
new_esEs21(vyy650, vyy660, app(app(ty_Either, ge), gf)) → new_esEs5(vyy650, vyy660, ge, gf)
new_esEs21(vyy650, vyy660, ty_Ordering) → new_esEs8(vyy650, vyy660)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], hh)) → new_esEs18(vyy3000, vyy400, hh)
new_compare32(vyy650, vyy660, app(ty_Maybe, cfa)) → new_compare7(vyy650, vyy660, cfa)
new_foldFM_GE0(vyy50, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba) → new_foldFM_GE10(vyy50, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h), h, ba)
new_lt20(vyy650, vyy660, app(app(ty_@2, dbf), dbg)) → new_lt16(vyy650, vyy660, dbf, dbg)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Int) → new_esEs19(vyy3000, vyy400)
new_compare14(vyy650, vyy660, True, fg) → LT
new_ltEs18(vyy651, vyy661, ty_Char) → new_ltEs12(vyy651, vyy661)
new_ltEs11(vyy65, vyy66, bff) → new_not(new_esEs8(new_compare(vyy65, vyy66, bff), GT))
new_primCmpInt(Pos(Zero), Pos(Succ(vyy6600))) → new_primCmpNat2(Zero, vyy6600)
new_foldFM_GE3(vyy330, vyy331, vyy70, vyy40, h, ba) → new_keysFM_GE0(vyy330, vyy331, vyy70, h, ba)
new_ltEs18(vyy651, vyy661, ty_Int) → new_ltEs17(vyy651, vyy661)
new_ltEs18(vyy651, vyy661, app(app(ty_@2, bgf), bgg)) → new_ltEs13(vyy651, vyy661, bgf, bgg)
new_lt8(vyy650, vyy660, app(ty_Maybe, fg)) → new_lt13(vyy650, vyy660, fg)
new_esEs18(:(vyy3000, vyy3001), :(vyy400, vyy401), cae) → new_asAs(new_esEs22(vyy3000, vyy400, cae), new_esEs18(vyy3001, vyy401, cae))
new_lt19(vyy651, vyy661, ty_Bool) → new_lt10(vyy651, vyy661)
new_compare7(vyy650, vyy660, fg) → new_compare26(vyy650, vyy660, new_esEs4(vyy650, vyy660, fg), fg)
new_compare31(Char(vyy650), Char(vyy660)) → new_primCmpInt(vyy650, vyy660)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_@0) → new_ltEs16(vyy6500, vyy6600)
new_esEs10(vyy3002, vyy402, ty_Int) → new_esEs19(vyy3002, vyy402)
new_ltEs6(Nothing, Nothing, fg) → True
new_ltEs19(vyy652, vyy662, ty_Bool) → new_ltEs5(vyy652, vyy662)
new_esEs25(vyy3001, vyy401, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs7(vyy3001, vyy401, cch, cda, cdb)
new_ltEs7(Left(vyy650), Left(vyy660), app(app(ty_@2, bah), bba), bab) → new_ltEs13(vyy650, vyy660, bah, bba)
new_esEs5(Left(vyy3000), Left(vyy400), ty_Bool, bch) → new_esEs17(vyy3000, vyy400)
new_esEs5(Right(vyy3000), Right(vyy400), bec, app(ty_Maybe, beh)) → new_esEs4(vyy3000, vyy400, beh)
new_esEs28(vyy650, vyy660, ty_Bool) → new_esEs17(vyy650, vyy660)
new_esEs28(vyy650, vyy660, app(ty_Ratio, dba)) → new_esEs20(vyy650, vyy660, dba)
new_esEs22(vyy3000, vyy400, ty_Int) → new_esEs19(vyy3000, vyy400)
new_ltEs4(LT, LT) → True
new_compare11(vyy650, vyy660, False) → GT
new_esEs22(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs17(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs19(vyy3000, vyy400)
new_esEs11(vyy3001, vyy401, app(app(ty_Either, db), dc)) → new_esEs5(vyy3001, vyy401, db, dc)
new_ltEs18(vyy651, vyy661, ty_Double) → new_ltEs14(vyy651, vyy661)
new_esEs21(vyy650, vyy660, ty_@0) → new_esEs9(vyy650, vyy660)
new_esEs10(vyy3002, vyy402, ty_Integer) → new_esEs16(vyy3002, vyy402)
new_compare11(vyy650, vyy660, True) → LT
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs19(vyy3000, vyy400)
new_lt8(vyy650, vyy660, ty_Double) → new_lt17(vyy650, vyy660)
new_esEs5(Left(vyy3000), Left(vyy400), app(app(ty_Either, bda), bdb), bch) → new_esEs5(vyy3000, vyy400, bda, bdb)
new_ltEs18(vyy651, vyy661, app(ty_Maybe, bgb)) → new_ltEs6(vyy651, vyy661, bgb)
new_lt17(vyy650, vyy660) → new_esEs8(new_compare18(vyy650, vyy660), LT)
new_esEs22(vyy3000, vyy400, ty_Integer) → new_esEs16(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy6600))) → new_primCmpNat1(vyy6600, Zero)
new_lt9(vyy650, vyy660) → new_esEs8(new_compare6(vyy650, vyy660), LT)
new_esEs10(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, ty_Int) → new_ltEs17(vyy650, vyy660)
new_esEs5(Right(vyy3000), Right(vyy400), bec, ty_Float) → new_esEs15(vyy3000, vyy400)
new_esEs28(vyy650, vyy660, ty_Float) → new_esEs15(vyy650, vyy660)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare8(:%(vyy650, vyy651), :%(vyy660, vyy661), ty_Int) → new_compare5(new_sr(vyy650, vyy661), new_sr(vyy660, vyy651))
new_compare12(vyy650, vyy660, ge, gf) → new_compare27(vyy650, vyy660, new_esEs5(vyy650, vyy660, ge, gf), ge, gf)
new_asAs(True, vyy91) → vyy91
new_lt19(vyy651, vyy661, app(ty_Maybe, chh)) → new_lt13(vyy651, vyy661, chh)
new_esEs22(vyy3000, vyy400, ty_@0) → new_esEs9(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_lt20(vyy650, vyy660, app(ty_[], dbc)) → new_lt7(vyy650, vyy660, dbc)
new_esEs24(vyy3000, vyy400, ty_Int) → new_esEs19(vyy3000, vyy400)
new_ltEs6(Just(vyy6500), Just(vyy6600), ty_Ordering) → new_ltEs4(vyy6500, vyy6600)
new_lt20(vyy650, vyy660, ty_Char) → new_lt15(vyy650, vyy660)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, cdg), cdh)) → new_esEs6(vyy3000, vyy400, cdg, cdh)
new_ltEs6(Just(vyy6500), Just(vyy6600), app(ty_[], bhe)) → new_ltEs11(vyy6500, vyy6600, bhe)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, he), hf), hg)) → new_esEs7(vyy3000, vyy400, he, hf, hg)
new_compare15(vyy650, vyy660, bb, bc) → new_compare28(vyy650, vyy660, new_esEs6(vyy650, vyy660, bb, bc), bb, bc)
new_ltEs7(Right(vyy650), Right(vyy660), bbe, app(ty_Maybe, bbg)) → new_ltEs6(vyy650, vyy660, bbg)
new_ltEs4(GT, GT) → True
new_ltEs13(@2(vyy650, vyy651), @2(vyy660, vyy661), bfg, bfh) → new_pePe(new_lt8(vyy650, vyy660, bfg), new_asAs(new_esEs21(vyy650, vyy660, bfg), new_ltEs18(vyy651, vyy661, bfh)))
new_esEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cca, ccb) → new_asAs(new_esEs26(vyy3000, vyy400, cca), new_esEs25(vyy3001, vyy401, ccb))
new_esEs22(vyy3000, vyy400, app(app(ty_Either, caf), cag)) → new_esEs5(vyy3000, vyy400, caf, cag)
new_compare13(Float(vyy650, vyy651), Float(vyy660, vyy661)) → new_compare5(new_sr(vyy650, vyy660), new_sr(vyy651, vyy661))
new_lt8(vyy650, vyy660, app(ty_[], gd)) → new_lt7(vyy650, vyy660, gd)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(vyy132, EQ) → vyy132
new_lt19(vyy651, vyy661, ty_Char) → new_lt15(vyy651, vyy661)
new_ltEs18(vyy651, vyy661, ty_Integer) → new_ltEs8(vyy651, vyy661)
new_ltEs19(vyy652, vyy662, ty_@0) → new_ltEs16(vyy652, vyy662)
new_ltEs7(Left(vyy650), Left(vyy660), ty_Int, bab) → new_ltEs17(vyy650, vyy660)
new_esEs10(vyy3002, vyy402, app(ty_Maybe, cc)) → new_esEs4(vyy3002, vyy402, cc)
new_esEs25(vyy3001, vyy401, app(ty_Ratio, cdd)) → new_esEs20(vyy3001, vyy401, cdd)
new_esEs10(vyy3002, vyy402, ty_Bool) → new_esEs17(vyy3002, vyy402)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_lt20(vyy650, vyy660, ty_Bool) → new_lt10(vyy650, vyy660)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, cef)) → new_esEs20(vyy3000, vyy400, cef)
new_esEs12(vyy3000, vyy400, app(app(ty_@2, ef), eg)) → new_esEs6(vyy3000, vyy400, ef, eg)
new_esEs25(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_primCmpInt(Neg(Succ(vyy6500)), Pos(vyy660)) → LT
new_esEs10(vyy3002, vyy402, ty_Double) → new_esEs14(vyy3002, vyy402)
new_not(True) → False
new_lt19(vyy651, vyy661, app(ty_[], daa)) → new_lt7(vyy651, vyy661, daa)

The set Q consists of the following terms:

new_ltEs19(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Ordering)
new_compare(:(x0, x1), [], x2)
new_esEs10(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Ordering)
new_lt6(x0, x1, x2, x3, x4)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, ty_Integer)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs21(x0, x1, app(ty_[], x2))
new_compare29(x0, x1, True, x2, x3, x4)
new_esEs4(Nothing, Just(x0), x1)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_Ordering)
new_lt14(x0, x1, x2, x3)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqNat0(Zero, Succ(x0))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat2(Zero, x0)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_compare32(x0, x1, ty_@0)
new_compare13(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs16(Integer(x0), Integer(x1))
new_compare17(x0, x1, True, x2, x3)
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_compare14(x0, x1, False, x2)
new_keysFM_GE0(x0, x1, x2, x3, x4)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs21(x0, x1, ty_Bool)
new_lt8(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Ordering)
new_esEs8(GT, GT)
new_compare32(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, ty_Float)
new_foldFM_GE0(x0, x1, EmptyFM, x2, x3)
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Bool)
new_esEs8(LT, LT)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs18(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs17(False, False)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_compare15(x0, x1, x2, x3)
new_pePe(False, x0)
new_sr(x0, x1)
new_ltEs5(False, False)
new_primCompAux0(x0, GT)
new_lt8(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs6(Just(x0), Just(x1), ty_@0)
new_esEs28(x0, x1, ty_@0)
new_primCompAux0(x0, EQ)
new_esEs12(x0, x1, ty_Double)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs27(x0, x1, ty_Char)
new_lt8(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs13(Char(x0), Char(x1))
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, False, x2, x3)
new_ltEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Just(x0), Just(x1), ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs10(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Zero)
new_sr0(Integer(x0), Integer(x1))
new_lt19(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_ltEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare18(Double(x0, x1), Double(x2, x3))
new_compare10(x0, x1, True, x2, x3)
new_esEs4(Just(x0), Nothing, x1)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Integer)
new_compare11(x0, x1, True)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_esEs18(:(x0, x1), [], x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_foldFM_GE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs12(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_asAs(False, x0)
new_ltEs19(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Bool)
new_ltEs4(GT, GT)
new_ltEs18(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, ty_Float)
new_compare30(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Just(x0), Just(x1), ty_Int)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs10(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_compare32(x0, x1, app(ty_[], x2))
new_compare14(x0, x1, True, x2)
new_esEs22(x0, x1, ty_Int)
new_foldFM_GE10(x0, x1, x2, x3, x4, EmptyFM, x5, True, x6, x7)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs4(Nothing, Nothing, x0)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs10(x0, x1, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_lt17(x0, x1)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs27(x0, x1, ty_Bool)
new_compare29(x0, x1, False, x2, x3, x4)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_compare16(@0, @0)
new_esEs26(x0, x1, ty_@0)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs11(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_foldFM_GE3(x0, x1, x2, x3, x4, x5)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt20(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare([], [], x0)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs11(x0, x1, x2)
new_esEs28(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_@0)
new_primPlusNat1(Zero, Zero)
new_esEs11(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare32(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_compare26(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_@0)
new_lt15(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs6(Just(x0), Just(x1), ty_Char)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs4(EQ, EQ)
new_ltEs18(x0, x1, ty_Int)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Integer)
new_compare110(x0, x1, False)
new_compare6(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare32(x0, x1, app(ty_Ratio, x2))
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare7(x0, x1, x2)
new_ltEs4(EQ, LT)
new_ltEs19(x0, x1, ty_Double)
new_ltEs4(LT, EQ)
new_esEs21(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs18(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Float)
new_compare5(x0, x1)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_lt7(x0, x1, x2)
new_compare25(x0, x1, True)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs11(x0, x1, ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs6(Just(x0), Nothing, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt8(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare11(x0, x1, False)
new_ltEs18(x0, x1, ty_Ordering)
new_lt8(x0, x1, ty_@0)
new_esEs12(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs6(Nothing, Nothing, x0)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs6(Just(x0), Just(x1), ty_Integer)
new_esEs12(x0, x1, ty_Float)
new_compare32(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(:%(x0, x1), :%(x2, x3), x4)
new_primCompAux0(x0, LT)
new_compare111(x0, x1, False, x2, x3, x4)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpNat2(Succ(x0), x1)
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(LT, LT)
new_esEs10(x0, x1, ty_Double)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_compare17(x0, x1, False, x2, x3)
new_compare31(Char(x0), Char(x1))
new_esEs11(x0, x1, ty_Char)
new_ltEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare([], :(x0, x1), x2)
new_ltEs8(x0, x1)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare9(x0, x1, x2, x3, x4)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_lt8(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs9(@0, @0)
new_esEs10(x0, x1, ty_Char)
new_lt8(x0, x1, ty_Double)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, ty_Integer)
new_esEs18([], :(x0, x1), x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, ty_Float)
new_compare32(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Double)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs19(x0, x1)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_ltEs18(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_lt12(x0, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare19(Integer(x0), Integer(x1))
new_compare32(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs12(x0, x1)
new_lt8(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_primCompAux1(x0, x1, x2, x3)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCmpNat0(Zero, Zero)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare24(x0, x1, True)
new_esEs10(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Int)
new_primCmpNat0(Zero, Succ(x0))
new_compare24(x0, x1, False)
new_foldFM_GE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_compare28(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs12(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs11(x0, x1, ty_Double)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Integer)
new_esEs18([], [], x0)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Char)
new_asAs(True, x0)
new_esEs11(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs17(x0, x1)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_ltEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(True, True)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_@0)
new_lt18(x0, x1)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Int)
new_not(True)
new_lt10(x0, x1)
new_lt5(x0, x1, x2)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_not(False)
new_compare110(x0, x1, True)
new_ltEs19(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs12(x0, x1, ty_Int)
new_lt13(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_@0)
new_primCmpNat1(x0, Succ(x1))
new_primEqNat0(Succ(x0), Succ(x1))
new_compare32(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs6(Just(x0), Just(x1), ty_Bool)
new_compare28(x0, x1, False, x2, x3)
new_compare10(x0, x1, False, x2, x3)
new_primCmpNat1(x0, Zero)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare26(x0, x1, False, x2)
new_lt4(x0, x1)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_lt8(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(x0, x1)
new_lt8(x0, x1, ty_Bool)
new_ltEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs17(True, False)
new_esEs17(False, True)
new_esEs27(x0, x1, ty_Int)
new_foldFM_GE10(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, True, x11, x12)
new_esEs22(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare25(x0, x1, False)
new_ltEs14(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare12(x0, x1, x2, x3)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs28(x0, x1, ty_Char)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Int)
new_foldFM_GE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_lt20(x0, x1, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_[], x2))
new_pePe(True, x0)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Char)
new_ltEs9(x0, x1)
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Integer)
new_gtEs(x0, x1, x2)
new_ltEs6(Nothing, Just(x0), x1)

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

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



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

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

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

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: