YES 7.0520000000000005 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ LR

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

The following Lambda expression
\keyeltrest→elt : rest

is transformed to
eltsFM_LE0 key elt rest = elt : rest



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

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

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

  eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a]
eltsFM_LE fm fr = foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest = elt : rest

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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



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

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

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

  eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a]
eltsFM_LE fm fr = foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest = elt : rest

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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



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

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

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

  eltsFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_LE fm fr = foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest = elt : rest

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

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

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

  eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a]
eltsFM_LE fm fr = foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest = elt : rest

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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

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

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

is transformed to
compare x y = compare3 x y

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

compare0 x y True = GT

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

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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



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

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

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

  eltsFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_LE fm fr = foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest = elt : rest

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

are unpacked to the following functions on top level
reduce2Reduce0 vyw vyx x y True = x `quot` reduce2D vyw vyx :% (y `quot` reduce2D vyw vyx)

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

reduce2D vyw vyx = gcd vyw vyx

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

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

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

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

  eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a]
eltsFM_LE fm fr = foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest = elt : rest

  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 vw fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

  eltsFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_LE fm fr = foldFM_LE eltsFM_LE0 [] fr fm

  
eltsFM_LE0 key elt rest = elt : rest

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Haskell To QDPs


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

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

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

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

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



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

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

new_primPlusNat(Succ(vyy18700), Succ(vyy401000)) → new_primPlusNat(vyy18700, vyy401000)

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

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



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

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

new_primMulNat(Succ(vyy300000), Succ(vyy40100)) → new_primMulNat(vyy300000, Succ(vyy40100))

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

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



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

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

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

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

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



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

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

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

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

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

new_lt2(:(vyy3000, vyy3001), :(vyy400, vyy401), baf) → new_primCompAux(vyy3000, vyy400, new_compare0(vyy3001, vyy401, baf), baf)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), h, app(ty_[], dc), cf) → new_lt2(vyy3011, vyy411, dc)
new_compare20(vyy300, vyy40, False, bbh, bca, bcb) → new_ltEs(vyy300, vyy40, bbh, bca, bcb)
new_lt0(vyy300, vyy40, bcc) → new_compare21(vyy300, vyy40, new_esEs5(vyy300, vyy40, bcc), bcc)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), h, ba, app(ty_[], bh)) → new_ltEs2(vyy3012, vyy412, bh)
new_compare22(vyy300, vyy40, False, bcd, bce) → new_ltEs3(vyy300, vyy40, bcd, bce)
new_ltEs1(Left(vyy3010), Left(vyy410), app(app(ty_Either, gf), gg), gd) → new_ltEs1(vyy3010, vyy410, gf, gg)
new_primCompAux(vyy3000, vyy400, vyy173, app(app(app(ty_@3, bag), bah), bba)) → new_compare1(vyy3000, vyy400, bag, bah, bba)
new_ltEs1(Left(vyy3010), Left(vyy410), app(ty_Maybe, ge), gd) → new_ltEs0(vyy3010, vyy410, ge)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_@2, ee), ef), ba, cf) → new_lt3(vyy3010, vyy410, ee, ef)
new_primCompAux(vyy3000, vyy400, vyy173, app(app(ty_@2, bbc), bbd)) → new_compare3(vyy3000, vyy400, bbc, bbd)
new_ltEs0(Just(vyy3010), Just(vyy410), app(app(ty_@2, fg), fh)) → new_ltEs3(vyy3010, vyy410, fg, fh)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bcf, app(ty_Maybe, bdb)) → new_ltEs0(vyy951, vyy961, bdb)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bcf, app(ty_[], bde)) → new_ltEs2(vyy951, vyy961, bde)
new_compare21(vyy300, vyy40, False, bcc) → new_ltEs0(vyy300, vyy40, bcc)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bcf, app(app(app(ty_@3, bcg), bch), bda)) → new_ltEs(vyy951, vyy961, bcg, bch, bda)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(app(ty_@3, bdh), bea), beb), bec) → new_lt(vyy950, vyy960, bdh, bea, beb)
new_ltEs1(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, ga), gb), gc), gd) → new_ltEs(vyy3010, vyy410, ga, gb, gc)
new_ltEs1(Left(vyy3010), Left(vyy410), app(ty_[], gh), gd) → new_ltEs2(vyy3010, vyy410, gh)
new_ltEs0(Just(vyy3010), Just(vyy410), app(ty_Maybe, fb)) → new_ltEs0(vyy3010, vyy410, fb)
new_compare3(vyy300, vyy40, bcd, bce) → new_compare22(vyy300, vyy40, new_esEs6(vyy300, vyy40, bcd, bce), bcd, bce)
new_primCompAux(vyy3000, vyy400, vyy173, app(ty_[], bbg)) → new_compare(vyy3000, vyy400, bbg)
new_lt3(vyy300, vyy40, bcd, bce) → new_compare22(vyy300, vyy40, new_esEs6(vyy300, vyy40, bcd, bce), bcd, bce)
new_ltEs2(vyy301, vyy41, bae) → new_compare(vyy301, vyy41, bae)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_Either, bee), bef), bec) → new_lt1(vyy950, vyy960, bee, bef)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), h, ba, app(app(ty_@2, ca), cb)) → new_ltEs3(vyy3012, vyy412, ca, cb)
new_primCompAux(vyy3000, vyy400, vyy173, app(ty_Maybe, bbb)) → new_compare2(vyy3000, vyy400, bbb)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bcf, app(app(ty_@2, bdf), bdg)) → new_ltEs3(vyy951, vyy961, bdf, bdg)
new_ltEs1(Right(vyy3010), Right(vyy410), hc, app(ty_Maybe, hg)) → new_ltEs0(vyy3010, vyy410, hg)
new_compare1(vyy300, vyy40, bbh, bca, bcb) → new_compare20(vyy300, vyy40, new_esEs4(vyy300, vyy40, bbh, bca, bcb), bbh, bca, bcb)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), bcf, app(app(ty_Either, bdc), bdd)) → new_ltEs1(vyy951, vyy961, bdc, bdd)
new_primCompAux(vyy3000, vyy400, vyy173, app(app(ty_Either, bbe), bbf)) → new_compare4(vyy3000, vyy400, bbe, bbf)
new_ltEs1(Right(vyy3010), Right(vyy410), hc, app(app(app(ty_@3, hd), he), hf)) → new_ltEs(vyy3010, vyy410, hd, he, hf)
new_ltEs1(Right(vyy3010), Right(vyy410), hc, app(ty_[], bab)) → new_ltEs2(vyy3010, vyy410, bab)
new_compare23(vyy300, vyy40, False, bfb, bfc) → new_ltEs1(vyy300, vyy40, bfb, bfc)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_Maybe, bed), bec) → new_lt0(vyy950, vyy960, bed)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_Either, eb), ec), ba, cf) → new_lt1(vyy3010, vyy410, eb, ec)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_@2, beh), bfa), bec) → new_lt3(vyy950, vyy960, beh, bfa)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), h, app(ty_Maybe, cg), cf) → new_lt0(vyy3011, vyy411, cg)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, df), dg), dh), ba, cf) → new_lt(vyy3010, vyy410, df, dg, dh)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), h, app(app(app(ty_@3, cc), cd), ce), cf) → new_lt(vyy3011, vyy411, cc, cd, ce)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), h, ba, app(ty_Maybe, be)) → new_ltEs0(vyy3012, vyy412, be)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), h, app(app(ty_@2, dd), de), cf) → new_lt3(vyy3011, vyy411, dd, de)
new_ltEs1(Right(vyy3010), Right(vyy410), hc, app(app(ty_@2, bac), bad)) → new_ltEs3(vyy3010, vyy410, bac, bad)
new_ltEs0(Just(vyy3010), Just(vyy410), app(ty_[], ff)) → new_ltEs2(vyy3010, vyy410, ff)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), baf) → new_compare(vyy3001, vyy401, baf)
new_ltEs0(Just(vyy3010), Just(vyy410), app(app(ty_Either, fc), fd)) → new_ltEs1(vyy3010, vyy410, fc, fd)
new_compare(:(vyy3000, vyy3001), :(vyy400, vyy401), baf) → new_primCompAux(vyy3000, vyy400, new_compare0(vyy3001, vyy401, baf), baf)
new_ltEs1(Right(vyy3010), Right(vyy410), hc, app(app(ty_Either, hh), baa)) → new_ltEs1(vyy3010, vyy410, hh, baa)
new_lt2(:(vyy3000, vyy3001), :(vyy400, vyy401), baf) → new_compare(vyy3001, vyy401, baf)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_Maybe, ea), ba, cf) → new_lt0(vyy3010, vyy410, ea)
new_compare2(vyy300, vyy40, bcc) → new_compare21(vyy300, vyy40, new_esEs5(vyy300, vyy40, bcc), bcc)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), h, ba, app(app(app(ty_@3, bb), bc), bd)) → new_ltEs(vyy3012, vyy412, bb, bc, bd)
new_compare4(vyy300, vyy40, bfb, bfc) → new_compare23(vyy300, vyy40, new_esEs7(vyy300, vyy40, bfb, bfc), bfb, bfc)
new_ltEs0(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, eg), eh), fa)) → new_ltEs(vyy3010, vyy410, eg, eh, fa)
new_lt(vyy300, vyy40, bbh, bca, bcb) → new_compare20(vyy300, vyy40, new_esEs4(vyy300, vyy40, bbh, bca, bcb), bbh, bca, bcb)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), h, ba, app(app(ty_Either, bf), bg)) → new_ltEs1(vyy3012, vyy412, bf, bg)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_[], ed), ba, cf) → new_lt2(vyy3010, vyy410, ed)
new_ltEs1(Left(vyy3010), Left(vyy410), app(app(ty_@2, ha), hb), gd) → new_ltEs3(vyy3010, vyy410, ha, hb)
new_ltEs(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), h, app(app(ty_Either, da), db), cf) → new_lt1(vyy3011, vyy411, da, db)
new_ltEs3(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_[], beg), bec) → new_lt2(vyy950, vyy960, beg)
new_lt1(vyy300, vyy40, bfb, bfc) → new_compare23(vyy300, vyy40, new_esEs7(vyy300, vyy40, bfb, bfc), bfb, bfc)

The TRS R consists of the following rules:

new_ltEs10(Left(vyy3010), Left(vyy410), ty_Ordering, gd) → new_ltEs16(vyy3010, vyy410)
new_esEs23(vyy3000, vyy400, app(app(ty_Either, cef), ceg)) → new_esEs7(vyy3000, vyy400, cef, ceg)
new_ltEs10(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, ga), gb), gc), gd) → new_ltEs7(vyy3010, vyy410, ga, gb, gc)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_Either, bgf), bgg), bfc) → new_esEs7(vyy3000, vyy400, bgf, bgg)
new_primCompAux0(vyy3000, vyy400, vyy173, baf) → new_primCompAux00(vyy173, new_compare33(vyy3000, vyy400, baf))
new_esEs21(vyy3010, vyy410, app(app(ty_@2, ee), ef)) → new_esEs6(vyy3010, vyy410, ee, ef)
new_ltEs19(vyy3012, vyy412, ty_Ordering) → new_ltEs16(vyy3012, vyy412)
new_ltEs16(GT, GT) → True
new_esEs27(vyy3001, vyy401, app(ty_[], chd)) → new_esEs16(vyy3001, vyy401, chd)
new_esEs18(vyy950, vyy960, app(app(ty_@2, beh), bfa)) → new_esEs6(vyy950, vyy960, beh, bfa)
new_ltEs10(Left(vyy3010), Left(vyy410), ty_@0, gd) → new_ltEs9(vyy3010, vyy410)
new_ltEs18(vyy951, vyy961, ty_@0) → new_ltEs9(vyy951, vyy961)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs20(vyy3011, vyy411, ty_@0) → new_esEs8(vyy3011, vyy411)
new_ltEs10(Left(vyy3010), Right(vyy410), hc, gd) → True
new_ltEs18(vyy951, vyy961, app(ty_Maybe, bdb)) → new_ltEs4(vyy951, vyy961, bdb)
new_esEs19(vyy3000, vyy400, app(ty_[], bbg)) → new_esEs16(vyy3000, vyy400, bbg)
new_lt15(vyy950, vyy960, ty_Integer) → new_lt4(vyy950, vyy960)
new_esEs26(vyy3002, vyy402, ty_Float) → new_esEs10(vyy3002, vyy402)
new_compare26(vyy300, vyy40, False, bfb, bfc) → new_compare11(vyy300, vyy40, new_ltEs10(vyy300, vyy40, bfb, bfc), bfb, bfc)
new_esEs19(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_lt15(vyy950, vyy960, app(app(ty_Either, bee), bef)) → new_lt11(vyy950, vyy960, bee, bef)
new_ltEs16(LT, GT) → True
new_lt19(vyy3011, vyy411, app(app(ty_@2, dd), de)) → new_lt10(vyy3011, vyy411, dd, de)
new_ltEs10(Right(vyy3010), Right(vyy410), hc, ty_Float) → new_ltEs11(vyy3010, vyy410)
new_esEs23(vyy3000, vyy400, ty_Bool) → new_esEs14(vyy3000, vyy400)
new_ltEs19(vyy3012, vyy412, ty_Float) → new_ltEs11(vyy3012, vyy412)
new_compare14(vyy300, vyy40, True, bbh, bca, bcb) → LT
new_esEs20(vyy3011, vyy411, ty_Double) → new_esEs12(vyy3011, vyy411)
new_esEs22(vyy3001, vyy401, ty_Ordering) → new_esEs9(vyy3001, vyy401)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Double, bfc) → new_esEs12(vyy3000, vyy400)
new_lt15(vyy950, vyy960, ty_Int) → new_lt7(vyy950, vyy960)
new_compare33(vyy3000, vyy400, app(ty_Maybe, bbb)) → new_compare28(vyy3000, vyy400, bbb)
new_primMulNat0(Zero, Zero) → Zero
new_esEs26(vyy3002, vyy402, app(ty_[], cgb)) → new_esEs16(vyy3002, vyy402, cgb)
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs4(vyy3001, vyy401, cgd, cge, cgf)
new_esEs18(vyy950, vyy960, app(ty_[], beg)) → new_esEs16(vyy950, vyy960, beg)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Integer) → new_ltEs6(vyy3010, vyy410)
new_esEs19(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_lt20(vyy3010, vyy410, ty_Integer) → new_lt4(vyy3010, vyy410)
new_ltEs18(vyy951, vyy961, app(ty_[], bde)) → new_ltEs13(vyy951, vyy961, bde)
new_esEs18(vyy950, vyy960, ty_Double) → new_esEs12(vyy950, vyy960)
new_compare6(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs7(Left(vyy3000), Left(vyy400), ty_Bool, bfc) → new_esEs14(vyy3000, vyy400)
new_compare32(vyy300, vyy40, bbh, bca, bcb) → new_compare24(vyy300, vyy40, new_esEs4(vyy300, vyy40, bbh, bca, bcb), bbh, bca, bcb)
new_ltEs18(vyy951, vyy961, ty_Char) → new_ltEs17(vyy951, vyy961)
new_esEs7(Right(vyy3000), Right(vyy400), bfb, app(ty_Ratio, cac)) → new_esEs17(vyy3000, vyy400, cac)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_lt20(vyy3010, vyy410, app(ty_[], ed)) → new_lt6(vyy3010, vyy410, ed)
new_ltEs10(Right(vyy3010), Right(vyy410), hc, ty_Bool) → new_ltEs12(vyy3010, vyy410)
new_ltEs18(vyy951, vyy961, ty_Integer) → new_ltEs6(vyy951, vyy961)
new_ltEs10(Left(vyy3010), Left(vyy410), ty_Float, gd) → new_ltEs11(vyy3010, vyy410)
new_lt19(vyy3011, vyy411, ty_Bool) → new_lt17(vyy3011, vyy411)
new_ltEs4(Just(vyy3010), Just(vyy410), app(ty_Ratio, bfe)) → new_ltEs8(vyy3010, vyy410, bfe)
new_lt19(vyy3011, vyy411, ty_Ordering) → new_lt8(vyy3011, vyy411)
new_compare0(:(vyy3000, vyy3001), :(vyy400, vyy401), baf) → new_primCompAux0(vyy3000, vyy400, new_compare0(vyy3001, vyy401, baf), baf)
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_Maybe, cbc)) → new_esEs5(vyy3000, vyy400, cbc)
new_compare28(vyy300, vyy40, bcc) → new_compare29(vyy300, vyy40, new_esEs5(vyy300, vyy40, bcc), bcc)
new_esEs15(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_@0) → new_ltEs9(vyy3010, vyy410)
new_esEs26(vyy3002, vyy402, ty_Char) → new_esEs13(vyy3002, vyy402)
new_ltEs10(Right(vyy3010), Right(vyy410), hc, ty_Double) → new_ltEs15(vyy3010, vyy410)
new_ltEs19(vyy3012, vyy412, app(ty_Maybe, be)) → new_ltEs4(vyy3012, vyy412, be)
new_lt5(vyy300, vyy40) → new_esEs9(new_compare6(vyy300, vyy40), LT)
new_ltEs10(Right(vyy3010), Right(vyy410), hc, app(ty_[], bab)) → new_ltEs13(vyy3010, vyy410, bab)
new_esEs20(vyy3011, vyy411, app(app(ty_@2, dd), de)) → new_esEs6(vyy3011, vyy411, dd, de)
new_ltEs10(Left(vyy3010), Left(vyy410), app(ty_Ratio, bff), gd) → new_ltEs8(vyy3010, vyy410, bff)
new_compare15(vyy300, vyy40, False) → GT
new_esEs18(vyy950, vyy960, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs4(vyy950, vyy960, bdh, bea, beb)
new_esEs22(vyy3001, vyy401, app(app(ty_Either, cdd), cde)) → new_esEs7(vyy3001, vyy401, cdd, cde)
new_esEs23(vyy3000, vyy400, ty_@0) → new_esEs8(vyy3000, vyy400)
new_pePe(False, vyy139) → vyy139
new_compare33(vyy3000, vyy400, ty_@0) → new_compare7(vyy3000, vyy400)
new_ltEs18(vyy951, vyy961, app(app(app(ty_@3, bcg), bch), bda)) → new_ltEs7(vyy951, vyy961, bcg, bch, bda)
new_esEs7(Left(vyy3000), Right(vyy400), bfb, bfc) → False
new_esEs7(Right(vyy3000), Left(vyy400), bfb, bfc) → False
new_ltEs12(True, False) → False
new_ltEs7(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), h, ba, cf) → new_pePe(new_lt20(vyy3010, vyy410, h), new_asAs(new_esEs21(vyy3010, vyy410, h), new_pePe(new_lt19(vyy3011, vyy411, ba), new_asAs(new_esEs20(vyy3011, vyy411, ba), new_ltEs19(vyy3012, vyy412, cf)))))
new_esEs27(vyy3001, vyy401, app(app(ty_Either, chb), chc)) → new_esEs7(vyy3001, vyy401, chb, chc)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs9(vyy3001, vyy401)
new_ltEs10(Right(vyy3010), Right(vyy410), hc, app(ty_Ratio, bfg)) → new_ltEs8(vyy3010, vyy410, bfg)
new_esEs26(vyy3002, vyy402, ty_Int) → new_esEs11(vyy3002, vyy402)
new_esEs26(vyy3002, vyy402, app(ty_Ratio, cgc)) → new_esEs17(vyy3002, vyy402, cgc)
new_ltEs4(Nothing, Just(vyy410), bfd) → True
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_ltEs19(vyy3012, vyy412, ty_Integer) → new_ltEs6(vyy3012, vyy412)
new_ltEs16(EQ, GT) → True
new_compare15(vyy300, vyy40, True) → LT
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, chf), chg), chh)) → new_esEs4(vyy3000, vyy400, chf, chg, chh)
new_compare9(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_compare27(vyy300, vyy40, False) → new_compare10(vyy300, vyy40, new_ltEs16(vyy300, vyy40))
new_ltEs10(Left(vyy3010), Left(vyy410), app(app(ty_Either, gf), gg), gd) → new_ltEs10(vyy3010, vyy410, gf, gg)
new_lt7(vyy300, vyy40) → new_esEs9(new_compare9(vyy300, vyy40), LT)
new_compare13(vyy300, vyy40, False, bcd, bce) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_lt20(vyy3010, vyy410, ty_Float) → new_lt5(vyy3010, vyy410)
new_esEs19(vyy3000, vyy400, app(app(ty_Either, bbe), bbf)) → new_esEs7(vyy3000, vyy400, bbe, bbf)
new_ltEs18(vyy951, vyy961, app(app(ty_Either, bdc), bdd)) → new_ltEs10(vyy951, vyy961, bdc, bdd)
new_lt15(vyy950, vyy960, ty_Float) → new_lt5(vyy950, vyy960)
new_esEs20(vyy3011, vyy411, app(ty_Ratio, ccd)) → new_esEs17(vyy3011, vyy411, ccd)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs15(vyy3000, vyy400)
new_compare33(vyy3000, vyy400, ty_Double) → new_compare8(vyy3000, vyy400)
new_lt20(vyy3010, vyy410, app(ty_Maybe, ea)) → new_lt16(vyy3010, vyy410, ea)
new_esEs21(vyy3010, vyy410, ty_@0) → new_esEs8(vyy3010, vyy410)
new_compare24(vyy300, vyy40, False, bbh, bca, bcb) → new_compare14(vyy300, vyy40, new_ltEs7(vyy300, vyy40, bbh, bca, bcb), bbh, bca, bcb)
new_esEs21(vyy3010, vyy410, ty_Bool) → new_esEs14(vyy3010, vyy410)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_esEs21(vyy3010, vyy410, ty_Char) → new_esEs13(vyy3010, vyy410)
new_esEs26(vyy3002, vyy402, ty_Double) → new_esEs12(vyy3002, vyy402)
new_lt15(vyy950, vyy960, app(ty_Ratio, cag)) → new_lt13(vyy950, vyy960, cag)
new_lt20(vyy3010, vyy410, app(app(app(ty_@3, df), dg), dh)) → new_lt14(vyy3010, vyy410, df, dg, dh)
new_esEs7(Right(vyy3000), Right(vyy400), bfb, ty_Bool) → new_esEs14(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs8(vyy3000, vyy400)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Int) → new_ltEs5(vyy3010, vyy410)
new_lt16(vyy300, vyy40, bcc) → new_esEs9(new_compare28(vyy300, vyy40, bcc), LT)
new_ltEs19(vyy3012, vyy412, app(app(ty_Either, bf), bg)) → new_ltEs10(vyy3012, vyy412, bf, bg)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Int, bfc) → new_esEs11(vyy3000, vyy400)
new_compare17(vyy300, vyy40, bfb, bfc) → new_compare26(vyy300, vyy40, new_esEs7(vyy300, vyy40, bfb, bfc), bfb, bfc)
new_ltEs14(@2(vyy950, vyy951), @2(vyy960, vyy961), bcf, bec) → new_pePe(new_lt15(vyy950, vyy960, bcf), new_asAs(new_esEs18(vyy950, vyy960, bcf), new_ltEs18(vyy951, vyy961, bec)))
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_compare0([], [], baf) → EQ
new_pePe(True, vyy139) → True
new_primEqNat0(Zero, Zero) → True
new_esEs20(vyy3011, vyy411, ty_Int) → new_esEs11(vyy3011, vyy411)
new_lt15(vyy950, vyy960, ty_Char) → new_lt18(vyy950, vyy960)
new_ltEs12(False, False) → True
new_ltEs10(Right(vyy3010), Right(vyy410), hc, ty_Ordering) → new_ltEs16(vyy3010, vyy410)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Double) → new_ltEs15(vyy3010, vyy410)
new_ltEs15(vyy301, vyy41) → new_fsEs(new_compare8(vyy301, vyy41))
new_lt20(vyy3010, vyy410, app(app(ty_@2, ee), ef)) → new_lt10(vyy3010, vyy410, ee, ef)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Ordering, bfc) → new_esEs9(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_ltEs16(EQ, LT) → False
new_compare12(vyy300, vyy40, False, bcc) → GT
new_ltEs8(vyy301, vyy41, cae) → new_fsEs(new_compare30(vyy301, vyy41, cae))
new_ltEs18(vyy951, vyy961, ty_Int) → new_ltEs5(vyy951, vyy961)
new_ltEs16(GT, EQ) → False
new_sr(vyy3000, vyy401) → new_primMulInt(vyy3000, vyy401)
new_compare33(vyy3000, vyy400, ty_Int) → new_compare9(vyy3000, vyy400)
new_compare18(vyy300, vyy40, bcd, bce) → new_compare210(vyy300, vyy40, new_esEs6(vyy300, vyy40, bcd, bce), bcd, bce)
new_lt15(vyy950, vyy960, app(app(app(ty_@3, bdh), bea), beb)) → new_lt14(vyy950, vyy960, bdh, bea, beb)
new_esEs7(Right(vyy3000), Right(vyy400), bfb, ty_Double) → new_esEs12(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy1870), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1870, vyy40100)))
new_esEs7(Right(vyy3000), Right(vyy400), bfb, app(app(ty_Either, bhh), caa)) → new_esEs7(vyy3000, vyy400, bhh, caa)
new_lt15(vyy950, vyy960, ty_@0) → new_lt12(vyy950, vyy960)
new_ltEs19(vyy3012, vyy412, ty_Bool) → new_ltEs12(vyy3012, vyy412)
new_esEs26(vyy3002, vyy402, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs4(vyy3002, vyy402, cfb, cfc, cfd)
new_esEs19(vyy3000, vyy400, app(ty_Ratio, ccb)) → new_esEs17(vyy3000, vyy400, ccb)
new_esEs21(vyy3010, vyy410, ty_Ordering) → new_esEs9(vyy3010, vyy410)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs12(vyy3000, vyy400)
new_esEs9(EQ, EQ) → True
new_fsEs(vyy174) → new_not(new_esEs9(vyy174, GT))
new_ltEs10(Left(vyy3010), Left(vyy410), app(ty_Maybe, ge), gd) → new_ltEs4(vyy3010, vyy410, ge)
new_compare24(vyy300, vyy40, True, bbh, bca, bcb) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare25(vyy300, vyy40, True) → EQ
new_compare13(vyy300, vyy40, True, bcd, bce) → LT
new_ltEs16(LT, EQ) → True
new_primPlusNat1(Succ(vyy18700), Zero) → Succ(vyy18700)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_ltEs4(Nothing, Nothing, bfd) → True
new_esEs5(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs11(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(vyy3000), Left(vyy400), ty_Integer, bfc) → new_esEs15(vyy3000, vyy400)
new_ltEs19(vyy3012, vyy412, app(ty_Ratio, ccc)) → new_ltEs8(vyy3012, vyy412, ccc)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_@2, bgd), bge), bfc) → new_esEs6(vyy3000, vyy400, bgd, bge)
new_lt14(vyy300, vyy40, bbh, bca, bcb) → new_esEs9(new_compare32(vyy300, vyy40, bbh, bca, bcb), LT)
new_esEs19(vyy3000, vyy400, ty_Bool) → new_esEs14(vyy3000, vyy400)
new_esEs18(vyy950, vyy960, ty_Float) → new_esEs10(vyy950, vyy960)
new_esEs7(Right(vyy3000), Right(vyy400), bfb, app(ty_Maybe, bhe)) → new_esEs5(vyy3000, vyy400, bhe)
new_ltEs10(Right(vyy3010), Right(vyy410), hc, ty_Char) → new_ltEs17(vyy3010, vyy410)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_compare26(vyy300, vyy40, True, bfb, bfc) → EQ
new_compare33(vyy3000, vyy400, app(ty_Ratio, ccb)) → new_compare30(vyy3000, vyy400, ccb)
new_esEs23(vyy3000, vyy400, app(app(app(ty_@3, cdh), cea), ceb)) → new_esEs4(vyy3000, vyy400, cdh, cea, ceb)
new_lt20(vyy3010, vyy410, ty_Ordering) → new_lt8(vyy3010, vyy410)
new_ltEs19(vyy3012, vyy412, ty_Char) → new_ltEs17(vyy3012, vyy412)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs26(vyy3002, vyy402, app(app(ty_Either, cfh), cga)) → new_esEs7(vyy3002, vyy402, cfh, cga)
new_esEs21(vyy3010, vyy410, app(ty_Ratio, cce)) → new_esEs17(vyy3010, vyy410, cce)
new_ltEs9(vyy301, vyy41) → new_fsEs(new_compare7(vyy301, vyy41))
new_ltEs16(GT, LT) → False
new_esEs21(vyy3010, vyy410, ty_Float) → new_esEs10(vyy3010, vyy410)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_esEs23(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs7(Right(vyy3000), Right(vyy400), bfb, app(app(ty_@2, bhf), bhg)) → new_esEs6(vyy3000, vyy400, bhf, bhg)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, cah), cba), cbb)) → new_esEs4(vyy3000, vyy400, cah, cba, cbb)
new_lt9(vyy300, vyy40) → new_esEs9(new_compare8(vyy300, vyy40), LT)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare33(vyy3000, vyy400, app(ty_[], bbg)) → new_compare0(vyy3000, vyy400, bbg)
new_ltEs19(vyy3012, vyy412, app(app(app(ty_@3, bb), bc), bd)) → new_ltEs7(vyy3012, vyy412, bb, bc, bd)
new_lt8(vyy300, vyy40) → new_esEs9(new_compare16(vyy300, vyy40), LT)
new_ltEs10(Left(vyy3010), Left(vyy410), ty_Bool, gd) → new_ltEs12(vyy3010, vyy410)
new_ltEs10(Right(vyy3010), Right(vyy410), hc, app(app(ty_@2, bac), bad)) → new_ltEs14(vyy3010, vyy410, bac, bad)
new_lt20(vyy3010, vyy410, ty_Int) → new_lt7(vyy3010, vyy410)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs26(vyy3002, vyy402, ty_Integer) → new_esEs15(vyy3002, vyy402)
new_esEs7(Right(vyy3000), Right(vyy400), bfb, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs4(vyy3000, vyy400, bhb, bhc, bhd)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_lt20(vyy3010, vyy410, ty_@0) → new_lt12(vyy3010, vyy410)
new_esEs7(Right(vyy3000), Right(vyy400), bfb, app(ty_[], cab)) → new_esEs16(vyy3000, vyy400, cab)
new_compare7(@0, @0) → EQ
new_esEs16(:(vyy3000, vyy3001), :(vyy400, vyy401), baf) → new_asAs(new_esEs19(vyy3000, vyy400, baf), new_esEs16(vyy3001, vyy401, baf))
new_esEs7(Right(vyy3000), Right(vyy400), bfb, ty_@0) → new_esEs8(vyy3000, vyy400)
new_esEs19(vyy3000, vyy400, app(app(ty_@2, bbc), bbd)) → new_esEs6(vyy3000, vyy400, bbc, bbd)
new_esEs7(Right(vyy3000), Right(vyy400), bfb, ty_Float) → new_esEs10(vyy3000, vyy400)
new_ltEs11(vyy301, vyy41) → new_fsEs(new_compare6(vyy301, vyy41))
new_esEs20(vyy3011, vyy411, ty_Float) → new_esEs10(vyy3011, vyy411)
new_primCompAux00(vyy183, LT) → LT
new_lt13(vyy300, vyy40, cad) → new_esEs9(new_compare30(vyy300, vyy40, cad), LT)
new_ltEs10(Left(vyy3010), Left(vyy410), ty_Double, gd) → new_ltEs15(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs26(vyy3002, vyy402, ty_@0) → new_esEs8(vyy3002, vyy402)
new_compare33(vyy3000, vyy400, ty_Integer) → new_compare5(vyy3000, vyy400)
new_esEs22(vyy3001, vyy401, ty_Bool) → new_esEs14(vyy3001, vyy401)
new_ltEs4(Just(vyy3010), Just(vyy410), app(app(ty_Either, fc), fd)) → new_ltEs10(vyy3010, vyy410, fc, fd)
new_ltEs10(Right(vyy3010), Right(vyy410), hc, app(app(ty_Either, hh), baa)) → new_ltEs10(vyy3010, vyy410, hh, baa)
new_compare30(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare5(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_ltEs13(vyy301, vyy41, bae) → new_fsEs(new_compare0(vyy301, vyy41, bae))
new_lt19(vyy3011, vyy411, ty_Float) → new_lt5(vyy3011, vyy411)
new_esEs10(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs21(vyy3010, vyy410, ty_Int) → new_esEs11(vyy3010, vyy410)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_esEs23(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_lt20(vyy3010, vyy410, ty_Char) → new_lt18(vyy3010, vyy410)
new_ltEs18(vyy951, vyy961, ty_Float) → new_ltEs11(vyy951, vyy961)
new_ltEs4(Just(vyy3010), Just(vyy410), app(app(ty_@2, fg), fh)) → new_ltEs14(vyy3010, vyy410, fg, fh)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_compare25(vyy300, vyy40, False) → new_compare15(vyy300, vyy40, new_ltEs12(vyy300, vyy40))
new_compare19(vyy300, vyy40) → new_compare25(vyy300, vyy40, new_esEs14(vyy300, vyy40))
new_esEs20(vyy3011, vyy411, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(vyy3011, vyy411, cc, cd, ce)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_lt10(vyy300, vyy40, bcd, bce) → new_esEs9(new_compare18(vyy300, vyy40, bcd, bce), LT)
new_compare33(vyy3000, vyy400, app(app(app(ty_@3, bag), bah), bba)) → new_compare32(vyy3000, vyy400, bag, bah, bba)
new_compare11(vyy300, vyy40, True, bfb, bfc) → LT
new_esEs18(vyy950, vyy960, ty_Ordering) → new_esEs9(vyy950, vyy960)
new_esEs18(vyy950, vyy960, app(ty_Ratio, cag)) → new_esEs17(vyy950, vyy960, cag)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_sr0(Integer(vyy30000), Integer(vyy4010)) → Integer(new_primMulInt(vyy30000, vyy4010))
new_compare14(vyy300, vyy40, False, bbh, bca, bcb) → GT
new_ltEs10(Right(vyy3010), Right(vyy410), hc, ty_Integer) → new_ltEs6(vyy3010, vyy410)
new_primPlusNat1(Succ(vyy18700), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy18700, vyy401000)))
new_compare12(vyy300, vyy40, True, bcc) → LT
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Ratio, bha), bfc) → new_esEs17(vyy3000, vyy400, bha)
new_esEs20(vyy3011, vyy411, ty_Char) → new_esEs13(vyy3011, vyy411)
new_ltEs18(vyy951, vyy961, app(app(ty_@2, bdf), bdg)) → new_ltEs14(vyy951, vyy961, bdf, bdg)
new_esEs27(vyy3001, vyy401, app(ty_Maybe, cgg)) → new_esEs5(vyy3001, vyy401, cgg)
new_lt19(vyy3011, vyy411, app(ty_Maybe, cg)) → new_lt16(vyy3011, vyy411, cg)
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs12(vyy3001, vyy401)
new_esEs22(vyy3001, vyy401, app(app(ty_@2, cdb), cdc)) → new_esEs6(vyy3001, vyy401, cdb, cdc)
new_lt19(vyy3011, vyy411, ty_Int) → new_lt7(vyy3011, vyy411)
new_esEs18(vyy950, vyy960, ty_@0) → new_esEs8(vyy950, vyy960)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_esEs21(vyy3010, vyy410, ty_Integer) → new_esEs15(vyy3010, vyy410)
new_lt19(vyy3011, vyy411, ty_Char) → new_lt18(vyy3011, vyy411)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCompAux00(vyy183, EQ) → vyy183
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dad), dae)) → new_esEs7(vyy3000, vyy400, dad, dae)
new_lt4(vyy300, vyy40) → new_esEs9(new_compare5(vyy300, vyy40), LT)
new_esEs22(vyy3001, vyy401, ty_@0) → new_esEs8(vyy3001, vyy401)
new_ltEs16(EQ, EQ) → True
new_ltEs5(vyy301, vyy41) → new_fsEs(new_compare9(vyy301, vyy41))
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bfh), bga), bgb), bfc) → new_esEs4(vyy3000, vyy400, bfh, bga, bgb)
new_ltEs18(vyy951, vyy961, app(ty_Ratio, caf)) → new_ltEs8(vyy951, vyy961, caf)
new_not(False) → True
new_esEs11(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_lt15(vyy950, vyy960, ty_Double) → new_lt9(vyy950, vyy960)
new_lt15(vyy950, vyy960, app(app(ty_@2, beh), bfa)) → new_lt10(vyy950, vyy960, beh, bfa)
new_lt15(vyy950, vyy960, ty_Bool) → new_lt17(vyy950, vyy960)
new_esEs28(vyy3000, vyy400, app(ty_[], daf)) → new_esEs16(vyy3000, vyy400, daf)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_compare210(vyy300, vyy40, True, bcd, bce) → EQ
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs23(vyy3000, vyy400, app(app(ty_@2, ced), cee)) → new_esEs6(vyy3000, vyy400, ced, cee)
new_esEs19(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs9(GT, GT) → True
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs19(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_esEs26(vyy3002, vyy402, ty_Bool) → new_esEs14(vyy3002, vyy402)
new_lt19(vyy3011, vyy411, app(ty_[], dc)) → new_lt6(vyy3011, vyy411, dc)
new_compare0(:(vyy3000, vyy3001), [], baf) → GT
new_esEs8(@0, @0) → True
new_lt19(vyy3011, vyy411, ty_Integer) → new_lt4(vyy3011, vyy411)
new_esEs22(vyy3001, vyy401, app(app(app(ty_@3, ccf), ccg), cch)) → new_esEs4(vyy3001, vyy401, ccf, ccg, cch)
new_lt20(vyy3010, vyy410, ty_Double) → new_lt9(vyy3010, vyy410)
new_ltEs18(vyy951, vyy961, ty_Bool) → new_ltEs12(vyy951, vyy961)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_compare11(vyy300, vyy40, False, bfb, bfc) → GT
new_esEs19(vyy3000, vyy400, app(app(app(ty_@3, bag), bah), bba)) → new_esEs4(vyy3000, vyy400, bag, bah, bba)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs7(Right(vyy3000), Right(vyy400), bfb, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_compare31(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs18(vyy950, vyy960, app(app(ty_Either, bee), bef)) → new_esEs7(vyy950, vyy960, bee, bef)
new_esEs22(vyy3001, vyy401, app(ty_[], cdf)) → new_esEs16(vyy3001, vyy401, cdf)
new_lt19(vyy3011, vyy411, app(app(app(ty_@3, cc), cd), ce)) → new_lt14(vyy3011, vyy411, cc, cd, ce)
new_primMulInt(Pos(vyy30000), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30000, vyy4010))
new_esEs23(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_primMulInt(Neg(vyy30000), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30000, vyy4010))
new_esEs27(vyy3001, vyy401, app(app(ty_@2, cgh), cha)) → new_esEs6(vyy3001, vyy401, cgh, cha)
new_esEs20(vyy3011, vyy411, ty_Integer) → new_esEs15(vyy3011, vyy411)
new_ltEs19(vyy3012, vyy412, ty_Int) → new_ltEs5(vyy3012, vyy412)
new_ltEs17(vyy301, vyy41) → new_fsEs(new_compare31(vyy301, vyy41))
new_esEs17(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cad) → new_asAs(new_esEs25(vyy3000, vyy400, cad), new_esEs24(vyy3001, vyy401, cad))
new_esEs5(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs14(vyy3000, vyy400)
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_[], bgh), bfc) → new_esEs16(vyy3000, vyy400, bgh)
new_ltEs10(Right(vyy3010), Right(vyy410), hc, app(app(app(ty_@3, hd), he), hf)) → new_ltEs7(vyy3010, vyy410, hd, he, hf)
new_esEs18(vyy950, vyy960, ty_Integer) → new_esEs15(vyy950, vyy960)
new_esEs20(vyy3011, vyy411, ty_Bool) → new_esEs14(vyy3011, vyy411)
new_lt19(vyy3011, vyy411, app(app(ty_Either, da), db)) → new_lt11(vyy3011, vyy411, da, db)
new_compare16(vyy300, vyy40) → new_compare27(vyy300, vyy40, new_esEs9(vyy300, vyy40))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt15(vyy950, vyy960, app(ty_Maybe, bed)) → new_lt16(vyy950, vyy960, bed)
new_compare33(vyy3000, vyy400, ty_Char) → new_compare31(vyy3000, vyy400)
new_compare210(vyy300, vyy40, False, bcd, bce) → new_compare13(vyy300, vyy40, new_ltEs14(vyy300, vyy40, bcd, bce), bcd, bce)
new_esEs16([], :(vyy400, vyy401), baf) → False
new_esEs16(:(vyy3000, vyy3001), [], baf) → False
new_esEs19(vyy3000, vyy400, app(ty_Maybe, bbb)) → new_esEs5(vyy3000, vyy400, bbb)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bcd, bce) → new_asAs(new_esEs23(vyy3000, vyy400, bcd), new_esEs22(vyy3001, vyy401, bce))
new_esEs21(vyy3010, vyy410, app(app(ty_Either, eb), ec)) → new_esEs7(vyy3010, vyy410, eb, ec)
new_lt19(vyy3011, vyy411, ty_@0) → new_lt12(vyy3011, vyy411)
new_esEs26(vyy3002, vyy402, app(ty_Maybe, cfe)) → new_esEs5(vyy3002, vyy402, cfe)
new_ltEs4(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, eg), eh), fa)) → new_ltEs7(vyy3010, vyy410, eg, eh, fa)
new_lt20(vyy3010, vyy410, app(app(ty_Either, eb), ec)) → new_lt11(vyy3010, vyy410, eb, ec)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dag)) → new_esEs17(vyy3000, vyy400, dag)
new_esEs23(vyy3000, vyy400, app(ty_Ratio, cfa)) → new_esEs17(vyy3000, vyy400, cfa)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_ltEs4(Just(vyy3010), Just(vyy410), app(ty_[], ff)) → new_ltEs13(vyy3010, vyy410, ff)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Ordering) → new_ltEs16(vyy3010, vyy410)
new_compare5(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, app(app(app(ty_@3, df), dg), dh)) → new_esEs4(vyy3010, vyy410, df, dg, dh)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dab), dac)) → new_esEs6(vyy3000, vyy400, dab, dac)
new_compare33(vyy3000, vyy400, app(app(ty_@2, bbc), bbd)) → new_compare18(vyy3000, vyy400, bbc, bbd)
new_esEs20(vyy3011, vyy411, app(app(ty_Either, da), db)) → new_esEs7(vyy3011, vyy411, da, db)
new_ltEs10(Right(vyy3010), Right(vyy410), hc, app(ty_Maybe, hg)) → new_ltEs4(vyy3010, vyy410, hg)
new_compare33(vyy3000, vyy400, app(app(ty_Either, bbe), bbf)) → new_compare17(vyy3000, vyy400, bbe, bbf)
new_lt19(vyy3011, vyy411, ty_Double) → new_lt9(vyy3011, vyy411)
new_lt19(vyy3011, vyy411, app(ty_Ratio, ccd)) → new_lt13(vyy3011, vyy411, ccd)
new_ltEs6(vyy301, vyy41) → new_fsEs(new_compare5(vyy301, vyy41))
new_ltEs4(Just(vyy3010), Just(vyy410), app(ty_Maybe, fb)) → new_ltEs4(vyy3010, vyy410, fb)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(vyy300, vyy40, True, bcc) → EQ
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_[], cbh)) → new_esEs16(vyy3000, vyy400, cbh)
new_esEs20(vyy3011, vyy411, app(ty_Maybe, cg)) → new_esEs5(vyy3011, vyy411, cg)
new_esEs20(vyy3011, vyy411, app(ty_[], dc)) → new_esEs16(vyy3011, vyy411, dc)
new_asAs(False, vyy172) → False
new_esEs22(vyy3001, vyy401, ty_Double) → new_esEs12(vyy3001, vyy401)
new_lt15(vyy950, vyy960, app(ty_[], beg)) → new_lt6(vyy950, vyy960, beg)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(ty_Either, cbf), cbg)) → new_esEs7(vyy3000, vyy400, cbf, cbg)
new_esEs19(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_ltEs18(vyy951, vyy961, ty_Double) → new_ltEs15(vyy951, vyy961)
new_primMulInt(Pos(vyy30000), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30000, vyy4010))
new_primMulInt(Neg(vyy30000), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30000, vyy4010))
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs7(Left(vyy3000), Left(vyy400), ty_Float, bfc) → new_esEs10(vyy3000, vyy400)
new_esEs7(Right(vyy3000), Right(vyy400), bfb, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_ltEs10(Left(vyy3010), Left(vyy410), ty_Integer, gd) → new_ltEs6(vyy3010, vyy410)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Bool) → new_ltEs12(vyy3010, vyy410)
new_compare33(vyy3000, vyy400, ty_Float) → new_compare6(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs14(vyy3000, vyy400)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(ty_@2, cbd), cbe)) → new_esEs6(vyy3000, vyy400, cbd, cbe)
new_esEs18(vyy950, vyy960, app(ty_Maybe, bed)) → new_esEs5(vyy950, vyy960, bed)
new_ltEs12(True, True) → True
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, app(ty_Maybe, cec)) → new_esEs5(vyy3000, vyy400, cec)
new_ltEs12(False, True) → True
new_esEs5(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs8(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_lt18(vyy300, vyy40) → new_esEs9(new_compare31(vyy300, vyy40), LT)
new_compare30(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare9(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_ltEs10(Left(vyy3010), Left(vyy410), ty_Int, gd) → new_ltEs5(vyy3010, vyy410)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Float) → new_ltEs11(vyy3010, vyy410)
new_compare27(vyy300, vyy40, True) → EQ
new_esEs14(True, True) → True
new_esEs7(Right(vyy3000), Right(vyy400), bfb, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs14(vyy3001, vyy401)
new_esEs20(vyy3011, vyy411, ty_Ordering) → new_esEs9(vyy3011, vyy411)
new_esEs5(Just(vyy3000), Nothing, bcc) → False
new_esEs5(Nothing, Just(vyy400), bcc) → False
new_esEs18(vyy950, vyy960, ty_Int) → new_esEs11(vyy950, vyy960)
new_esEs12(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs7(Right(vyy3000), Right(vyy400), bfb, ty_Int) → new_esEs11(vyy3000, vyy400)
new_ltEs10(Left(vyy3010), Left(vyy410), app(app(ty_@2, ha), hb), gd) → new_ltEs14(vyy3010, vyy410, ha, hb)
new_esEs16([], [], baf) → True
new_ltEs10(Left(vyy3010), Left(vyy410), app(ty_[], gh), gd) → new_ltEs13(vyy3010, vyy410, gh)
new_compare33(vyy3000, vyy400, ty_Ordering) → new_compare16(vyy3000, vyy400)
new_compare8(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs22(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_esEs4(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bbh, bca, bcb) → new_asAs(new_esEs28(vyy3000, vyy400, bbh), new_asAs(new_esEs27(vyy3001, vyy401, bca), new_esEs26(vyy3002, vyy402, bcb)))
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_ltEs10(Right(vyy3010), Left(vyy410), hc, gd) → False
new_compare29(vyy300, vyy40, False, bcc) → new_compare12(vyy300, vyy40, new_ltEs4(vyy300, vyy40, bcc), bcc)
new_esEs5(Nothing, Nothing, bcc) → True
new_esEs28(vyy3000, vyy400, app(ty_Maybe, daa)) → new_esEs5(vyy3000, vyy400, daa)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Char) → new_ltEs17(vyy3010, vyy410)
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Maybe, bgc), bfc) → new_esEs5(vyy3000, vyy400, bgc)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, ty_Double) → new_esEs12(vyy3010, vyy410)
new_esEs13(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_lt15(vyy950, vyy960, ty_Ordering) → new_lt8(vyy950, vyy960)
new_esEs14(False, False) → True
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_Ratio, cca)) → new_esEs17(vyy3000, vyy400, cca)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Char, bfc) → new_esEs13(vyy3000, vyy400)
new_esEs22(vyy3001, vyy401, app(ty_Ratio, cdg)) → new_esEs17(vyy3001, vyy401, cdg)
new_esEs22(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_ltEs19(vyy3012, vyy412, ty_Double) → new_ltEs15(vyy3012, vyy412)
new_esEs23(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_esEs18(vyy950, vyy960, ty_Bool) → new_esEs14(vyy950, vyy960)
new_esEs22(vyy3001, vyy401, app(ty_Maybe, cda)) → new_esEs5(vyy3001, vyy401, cda)
new_esEs19(vyy3000, vyy400, ty_@0) → new_esEs8(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, app(ty_Maybe, ea)) → new_esEs5(vyy3010, vyy410, ea)
new_esEs23(vyy3000, vyy400, app(ty_[], ceh)) → new_esEs16(vyy3000, vyy400, ceh)
new_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_compare0([], :(vyy400, vyy401), baf) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs7(Left(vyy3000), Left(vyy400), ty_@0, bfc) → new_esEs8(vyy3000, vyy400)
new_ltEs18(vyy951, vyy961, ty_Ordering) → new_ltEs16(vyy951, vyy961)
new_esEs26(vyy3002, vyy402, ty_Ordering) → new_esEs9(vyy3002, vyy402)
new_esEs19(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_asAs(True, vyy172) → vyy172
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs18(vyy950, vyy960, ty_Char) → new_esEs13(vyy950, vyy960)
new_ltEs4(Just(vyy3010), Nothing, bfd) → False
new_primMulNat0(Succ(vyy300000), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300000, Succ(vyy40100)), vyy40100)
new_ltEs19(vyy3012, vyy412, ty_@0) → new_ltEs9(vyy3012, vyy412)
new_lt20(vyy3010, vyy410, ty_Bool) → new_lt17(vyy3010, vyy410)
new_ltEs16(LT, LT) → True
new_lt12(vyy300, vyy40) → new_esEs9(new_compare7(vyy300, vyy40), LT)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs8(vyy3001, vyy401)
new_esEs26(vyy3002, vyy402, app(app(ty_@2, cff), cfg)) → new_esEs6(vyy3002, vyy402, cff, cfg)
new_ltEs19(vyy3012, vyy412, app(app(ty_@2, ca), cb)) → new_ltEs14(vyy3012, vyy412, ca, cb)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs13(vyy3000, vyy400)
new_compare10(vyy300, vyy40, True) → LT
new_ltEs10(Left(vyy3010), Left(vyy410), ty_Char, gd) → new_ltEs17(vyy3010, vyy410)
new_ltEs10(Right(vyy3010), Right(vyy410), hc, ty_Int) → new_ltEs5(vyy3010, vyy410)
new_esEs27(vyy3001, vyy401, app(ty_Ratio, che)) → new_esEs17(vyy3001, vyy401, che)
new_compare33(vyy3000, vyy400, ty_Bool) → new_compare19(vyy3000, vyy400)
new_lt20(vyy3010, vyy410, app(ty_Ratio, cce)) → new_lt13(vyy3010, vyy410, cce)
new_compare10(vyy300, vyy40, False) → GT
new_lt11(vyy300, vyy40, bfb, bfc) → new_esEs9(new_compare17(vyy300, vyy40, bfb, bfc), LT)
new_esEs9(LT, LT) → True
new_primCompAux00(vyy183, GT) → GT
new_lt6(vyy300, vyy40, baf) → new_esEs9(new_compare0(vyy300, vyy40, baf), LT)
new_ltEs10(Right(vyy3010), Right(vyy410), hc, ty_@0) → new_ltEs9(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, app(ty_[], ed)) → new_esEs16(vyy3010, vyy410, ed)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs19(vyy3012, vyy412, app(ty_[], bh)) → new_ltEs13(vyy3012, vyy412, bh)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_lt17(vyy300, vyy40) → new_esEs9(new_compare19(vyy300, vyy40), LT)
new_not(True) → False

The set Q consists of the following terms:

new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs19(x0, x1, ty_Float)
new_compare17(x0, x1, x2, x3)
new_esEs5(Nothing, Nothing, x0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare33(x0, x1, ty_Double)
new_compare9(x0, x1)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_compare31(Char(x0), Char(x1))
new_ltEs8(x0, x1, x2)
new_esEs16(:(x0, x1), [], x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt20(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Succ(x0), x1)
new_esEs18(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs20(x0, x1, ty_Float)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, x2)
new_lt14(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_primCompAux00(x0, EQ)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_@0)
new_esEs16([], :(x0, x1), x2)
new_ltEs19(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Integer)
new_lt5(x0, x1)
new_compare29(x0, x1, True, x2)
new_ltEs5(x0, x1)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs15(x0, x1)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs17(x0, x1)
new_esEs8(@0, @0)
new_compare15(x0, x1, True)
new_compare18(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs24(x0, x1, ty_Integer)
new_compare11(x0, x1, False, x2, x3)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs23(x0, x1, ty_Double)
new_compare12(x0, x1, True, x2)
new_lt15(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_lt15(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare14(x0, x1, True, x2, x3, x4)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16([], [], x0)
new_compare15(x0, x1, False)
new_esEs26(x0, x1, ty_Ordering)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_lt19(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_esEs13(Char(x0), Char(x1))
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_asAs(True, x0)
new_esEs14(True, True)
new_compare33(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, ty_Int)
new_lt15(x0, x1, ty_Float)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primEqNat0(Zero, Zero)
new_esEs18(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs25(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Integer)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare33(x0, x1, ty_Char)
new_compare30(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1, ty_Double)
new_primPlusNat1(Zero, Succ(x0))
new_compare6(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Zero)
new_lt7(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs11(x0, x1)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare26(x0, x1, False, x2, x3)
new_lt15(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, LT)
new_lt10(x0, x1, x2, x3)
new_ltEs9(x0, x1)
new_ltEs4(Nothing, Nothing, x0)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt15(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Just(x0), Nothing, x1)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt20(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare33(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_Int)
new_compare32(x0, x1, x2, x3, x4)
new_esEs10(Float(x0, x1), Float(x2, x3))
new_lt19(x0, x1, ty_Ordering)
new_compare16(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_compare0([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs12(False, False)
new_esEs5(Nothing, Just(x0), x1)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_@0)
new_compare33(x0, x1, ty_@0)
new_compare25(x0, x1, False)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs13(x0, x1, x2)
new_primPlusNat1(Zero, Zero)
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare19(x0, x1)
new_ltEs16(EQ, EQ)
new_compare14(x0, x1, False, x2, x3, x4)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_lt15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt4(x0, x1)
new_ltEs16(LT, LT)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, ty_Char)
new_lt18(x0, x1)
new_compare26(x0, x1, True, x2, x3)
new_compare33(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs18(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Char)
new_lt15(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs27(x0, x1, ty_Int)
new_ltEs16(GT, LT)
new_ltEs16(LT, GT)
new_esEs19(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs9(GT, GT)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_compare210(x0, x1, True, x2, x3)
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1, False, x2)
new_lt20(x0, x1, ty_Float)
new_lt17(x0, x1)
new_compare27(x0, x1, False)
new_esEs21(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_@0)
new_lt6(x0, x1, x2)
new_esEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare28(x0, x1, x2)
new_esEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, ty_@0)
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_compare0([], [], x0)
new_lt20(x0, x1, ty_Bool)
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare33(x0, x1, ty_Integer)
new_lt15(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt15(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1, ty_Char)
new_esEs9(EQ, EQ)
new_sr(x0, x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs19(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Ordering)
new_lt15(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Double)
new_esEs14(True, False)
new_esEs14(False, True)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare25(x0, x1, True)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt8(x0, x1)
new_ltEs16(GT, GT)
new_compare7(@0, @0)
new_pePe(True, x0)
new_compare11(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs11(x0, x1)
new_pePe(False, x0)
new_esEs18(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs14(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_@0)
new_compare30(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqNat0(Zero, Succ(x0))
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs12(False, True)
new_ltEs12(True, False)
new_esEs21(x0, x1, ty_Double)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Nothing, Just(x0), x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primCmpNat0(Zero, Zero)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare33(x0, x1, app(app(ty_Either, x2), x3))
new_compare33(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, ty_Bool)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs6(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs27(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, False, x2)
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_@0)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs18(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_compare13(x0, x1, False, x2, x3)
new_compare13(x0, x1, True, x2, x3)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Bool)
new_esEs15(Integer(x0), Integer(x1))
new_not(True)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, GT)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_esEs18(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_compare33(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt11(x0, x1, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_compare33(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(True, True)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare33(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs20(x0, x1, ty_Int)
new_lt19(x0, x1, ty_@0)
new_compare10(x0, x1, True)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_fsEs(x0)
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Ordering)
new_asAs(False, x0)
new_esEs5(Just(x0), Nothing, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_lt19(x0, x1, ty_Char)
new_compare5(Integer(x0), Integer(x1))
new_esEs12(Double(x0, x1), Double(x2, x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_Ordering)
new_compare8(Double(x0, x1), Double(x2, x3))
new_esEs14(False, False)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs27(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare27(x0, x1, True)
new_esEs18(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_@0)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, ty_Float)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Float)
new_esEs9(LT, LT)
new_esEs28(x0, x1, ty_Double)
new_compare210(x0, x1, False, x2, x3)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Float)

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

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

new_foldFM_LE1(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, Branch(vyy6140, vyy6141, vyy6142, vyy6143, vyy6144), True, h, ba, bb) → new_foldFM_LE(vyy84, vyy54, vyy55, vyy613, h, ba, bb)
new_foldFM_LE(vyy84, vyy54, vyy55, Branch(vyy6130, vyy6131, vyy6132, vyy6133, vyy6134), h, ba, bb) → new_foldFM_LE1(vyy84, vyy54, vyy55, vyy6130, vyy6131, vyy6132, vyy6133, vyy6134, new_ltEs14(vyy6130, @2(vyy54, vyy55), ba, bb), h, ba, bb)
new_foldFM_LE1(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, EmptyFM, True, h, ba, bb) → new_foldFM_LE(vyy84, vyy54, vyy55, vyy613, h, ba, bb)
new_foldFM_LE1(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, Branch(vyy6130, vyy6131, vyy6132, vyy6133, vyy6134), vyy614, False, h, ba, bb) → new_foldFM_LE1(vyy84, vyy54, vyy55, vyy6130, vyy6131, vyy6132, vyy6133, vyy6134, new_ltEs14(vyy6130, @2(vyy54, vyy55), ba, bb), h, ba, bb)
new_foldFM_LE1(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, Branch(vyy6140, vyy6141, vyy6142, vyy6143, vyy6144), True, h, ba, bb) → new_foldFM_LE2(vyy610, vyy611, new_foldFM_LE0(vyy84, vyy54, vyy55, vyy613, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb)
new_foldFM_LE2(vyy610, vyy611, vyy105, vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb) → new_foldFM_LE1(new_eltsFM_LE0(vyy610, vyy611, vyy105, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, new_ltEs14(vyy6140, @2(vyy54, vyy55), ba, bb), h, ba, bb)

The TRS R consists of the following rules:

new_ltEs10(Left(vyy3010), Left(vyy410), ty_Ordering, dh) → new_ltEs16(vyy3010, vyy410)
new_esEs23(vyy3000, vyy400, app(app(ty_Either, cfa), cfb)) → new_esEs7(vyy3000, vyy400, cfa, cfb)
new_ltEs10(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, ea), eb), ec), dh) → new_ltEs7(vyy3010, vyy410, ea, eb, ec)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_Either, hf), hg), da) → new_esEs7(vyy3000, vyy400, hf, hg)
new_primCompAux0(vyy3000, vyy400, vyy173, bc) → new_primCompAux00(vyy173, new_compare33(vyy3000, vyy400, bc))
new_esEs21(vyy3010, vyy410, app(app(ty_@2, ccg), cch)) → new_esEs6(vyy3010, vyy410, ccg, cch)
new_ltEs19(vyy3012, vyy412, ty_Ordering) → new_ltEs16(vyy3012, vyy412)
new_ltEs16(GT, GT) → True
new_esEs27(vyy3001, vyy401, app(ty_[], chg)) → new_esEs16(vyy3001, vyy401, chg)
new_esEs18(vyy950, vyy960, app(app(ty_@2, beb), bec)) → new_esEs6(vyy950, vyy960, beb, bec)
new_ltEs10(Left(vyy3010), Left(vyy410), ty_@0, dh) → new_ltEs9(vyy3010, vyy410)
new_ltEs18(vyy951, vyy961, ty_@0) → new_ltEs9(vyy951, vyy961)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs20(vyy3011, vyy411, ty_@0) → new_esEs8(vyy3011, vyy411)
new_ltEs10(Left(vyy3010), Right(vyy410), fc, dh) → True
new_ltEs18(vyy951, vyy961, app(ty_Maybe, bcd)) → new_ltEs4(vyy951, vyy961, bcd)
new_esEs19(vyy3000, vyy400, app(ty_[], bgf)) → new_esEs16(vyy3000, vyy400, bgf)
new_lt15(vyy950, vyy960, ty_Integer) → new_lt4(vyy950, vyy960)
new_esEs26(vyy3002, vyy402, ty_Float) → new_esEs10(vyy3002, vyy402)
new_compare26(vyy300, vyy40, False, cg, da) → new_compare11(vyy300, vyy40, new_ltEs10(vyy300, vyy40, cg, da), cg, da)
new_esEs19(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_lt15(vyy950, vyy960, app(app(ty_Either, bdg), bdh)) → new_lt11(vyy950, vyy960, bdg, bdh)
new_ltEs16(LT, GT) → True
new_lt19(vyy3011, vyy411, app(app(ty_@2, cbe), cbf)) → new_lt10(vyy3011, vyy411, cbe, cbf)
new_ltEs10(Right(vyy3010), Right(vyy410), fc, ty_Float) → new_ltEs11(vyy3010, vyy410)
new_ltEs19(vyy3012, vyy412, ty_Float) → new_ltEs11(vyy3012, vyy412)
new_esEs23(vyy3000, vyy400, ty_Bool) → new_esEs14(vyy3000, vyy400)
new_compare14(vyy300, vyy40, True, de, df, dg) → LT
new_esEs20(vyy3011, vyy411, ty_Double) → new_esEs12(vyy3011, vyy411)
new_esEs22(vyy3001, vyy401, ty_Ordering) → new_esEs9(vyy3001, vyy401)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Double, da) → new_esEs12(vyy3000, vyy400)
new_lt15(vyy950, vyy960, ty_Int) → new_lt7(vyy950, vyy960)
new_compare33(vyy3000, vyy400, app(ty_Maybe, bga)) → new_compare28(vyy3000, vyy400, bga)
new_primMulNat0(Zero, Zero) → Zero
new_esEs26(vyy3002, vyy402, app(ty_[], cge)) → new_esEs16(vyy3002, vyy402, cge)
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs4(vyy3001, vyy401, cgg, cgh, cha)
new_esEs18(vyy950, vyy960, app(ty_[], bea)) → new_esEs16(vyy950, vyy960, bea)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Integer) → new_ltEs6(vyy3010, vyy410)
new_esEs19(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_lt20(vyy3010, vyy410, ty_Integer) → new_lt4(vyy3010, vyy410)
new_ltEs18(vyy951, vyy961, app(ty_[], bcg)) → new_ltEs13(vyy951, vyy961, bcg)
new_esEs18(vyy950, vyy960, ty_Double) → new_esEs12(vyy950, vyy960)
new_compare6(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs7(Left(vyy3000), Left(vyy400), ty_Bool, da) → new_esEs14(vyy3000, vyy400)
new_compare32(vyy300, vyy40, de, df, dg) → new_compare24(vyy300, vyy40, new_esEs4(vyy300, vyy40, de, df, dg), de, df, dg)
new_ltEs18(vyy951, vyy961, ty_Char) → new_ltEs17(vyy951, vyy961)
new_esEs7(Right(vyy3000), Right(vyy400), cg, app(ty_Ratio, bbc)) → new_esEs17(vyy3000, vyy400, bbc)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_lt20(vyy3010, vyy410, app(ty_[], ccf)) → new_lt6(vyy3010, vyy410, ccf)
new_ltEs10(Right(vyy3010), Right(vyy410), fc, ty_Bool) → new_ltEs12(vyy3010, vyy410)
new_ltEs18(vyy951, vyy961, ty_Integer) → new_ltEs6(vyy951, vyy961)
new_ltEs10(Left(vyy3010), Left(vyy410), ty_Float, dh) → new_ltEs11(vyy3010, vyy410)
new_lt19(vyy3011, vyy411, ty_Bool) → new_lt17(vyy3011, vyy411)
new_ltEs4(Just(vyy3010), Just(vyy410), app(ty_Ratio, bh)) → new_ltEs8(vyy3010, vyy410, bh)
new_lt19(vyy3011, vyy411, ty_Ordering) → new_lt8(vyy3011, vyy411)
new_compare0(:(vyy3000, vyy3001), :(vyy400, vyy401), bc) → new_primCompAux0(vyy3000, vyy400, new_compare0(vyy3001, vyy401, bc), bc)
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_Maybe, beg)) → new_esEs5(vyy3000, vyy400, beg)
new_compare28(vyy300, vyy40, db) → new_compare29(vyy300, vyy40, new_esEs5(vyy300, vyy40, db), db)
new_esEs15(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_@0) → new_ltEs9(vyy3010, vyy410)
new_esEs26(vyy3002, vyy402, ty_Char) → new_esEs13(vyy3002, vyy402)
new_ltEs10(Right(vyy3010), Right(vyy410), fc, ty_Double) → new_ltEs15(vyy3010, vyy410)
new_ltEs19(vyy3012, vyy412, app(ty_Maybe, bhg)) → new_ltEs4(vyy3012, vyy412, bhg)
new_lt5(vyy300, vyy40) → new_esEs9(new_compare6(vyy300, vyy40), LT)
new_ltEs10(Right(vyy3010), Right(vyy410), fc, app(ty_[], gd)) → new_ltEs13(vyy3010, vyy410, gd)
new_esEs20(vyy3011, vyy411, app(app(ty_@2, cbe), cbf)) → new_esEs6(vyy3011, vyy411, cbe, cbf)
new_ltEs10(Left(vyy3010), Left(vyy410), app(ty_Ratio, ed), dh) → new_ltEs8(vyy3010, vyy410, ed)
new_compare15(vyy300, vyy40, False) → GT
new_esEs18(vyy950, vyy960, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs4(vyy950, vyy960, bdb, bdc, bdd)
new_foldFM_LE0(vyy84, vyy54, vyy55, Branch(vyy6130, vyy6131, vyy6132, vyy6133, vyy6134), h, ba, bb) → new_foldFM_LE10(vyy84, vyy54, vyy55, vyy6130, vyy6131, vyy6132, vyy6133, vyy6134, new_ltEs14(vyy6130, @2(vyy54, vyy55), ba, bb), h, ba, bb)
new_esEs22(vyy3001, vyy401, app(app(ty_Either, cdg), cdh)) → new_esEs7(vyy3001, vyy401, cdg, cdh)
new_esEs23(vyy3000, vyy400, ty_@0) → new_esEs8(vyy3000, vyy400)
new_pePe(False, vyy139) → vyy139
new_compare33(vyy3000, vyy400, ty_@0) → new_compare7(vyy3000, vyy400)
new_ltEs18(vyy951, vyy961, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs7(vyy951, vyy961, bbh, bca, bcb)
new_esEs7(Left(vyy3000), Right(vyy400), cg, da) → False
new_esEs7(Right(vyy3000), Left(vyy400), cg, da) → False
new_ltEs12(True, False) → False
new_ltEs7(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), bgh, bha, bhb) → new_pePe(new_lt20(vyy3010, vyy410, bgh), new_asAs(new_esEs21(vyy3010, vyy410, bgh), new_pePe(new_lt19(vyy3011, vyy411, bha), new_asAs(new_esEs20(vyy3011, vyy411, bha), new_ltEs19(vyy3012, vyy412, bhb)))))
new_esEs27(vyy3001, vyy401, app(app(ty_Either, che), chf)) → new_esEs7(vyy3001, vyy401, che, chf)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs9(vyy3001, vyy401)
new_ltEs10(Right(vyy3010), Right(vyy410), fc, app(ty_Ratio, fh)) → new_ltEs8(vyy3010, vyy410, fh)
new_esEs26(vyy3002, vyy402, ty_Int) → new_esEs11(vyy3002, vyy402)
new_esEs26(vyy3002, vyy402, app(ty_Ratio, cgf)) → new_esEs17(vyy3002, vyy402, cgf)
new_ltEs4(Nothing, Just(vyy410), bd) → True
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_ltEs19(vyy3012, vyy412, ty_Integer) → new_ltEs6(vyy3012, vyy412)
new_ltEs16(EQ, GT) → True
new_compare15(vyy300, vyy40, True) → LT
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, daa), dab), dac)) → new_esEs4(vyy3000, vyy400, daa, dab, dac)
new_foldFM_LE10(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, Branch(vyy6140, vyy6141, vyy6142, vyy6143, vyy6144), True, h, ba, bb) → new_foldFM_LE20(vyy610, vyy611, new_foldFM_LE0(vyy84, vyy54, vyy55, vyy613, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb)
new_compare9(vyy300, vyy40) → new_primCmpInt(vyy300, vyy40)
new_compare27(vyy300, vyy40, False) → new_compare10(vyy300, vyy40, new_ltEs16(vyy300, vyy40))
new_ltEs10(Left(vyy3010), Left(vyy410), app(app(ty_Either, ef), eg), dh) → new_ltEs10(vyy3010, vyy410, ef, eg)
new_lt7(vyy300, vyy40) → new_esEs9(new_compare9(vyy300, vyy40), LT)
new_compare13(vyy300, vyy40, False, dc, dd) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_lt20(vyy3010, vyy410, ty_Float) → new_lt5(vyy3010, vyy410)
new_esEs19(vyy3000, vyy400, app(app(ty_Either, bgd), bge)) → new_esEs7(vyy3000, vyy400, bgd, bge)
new_ltEs18(vyy951, vyy961, app(app(ty_Either, bce), bcf)) → new_ltEs10(vyy951, vyy961, bce, bcf)
new_lt15(vyy950, vyy960, ty_Float) → new_lt5(vyy950, vyy960)
new_esEs20(vyy3011, vyy411, app(ty_Ratio, cah)) → new_esEs17(vyy3011, vyy411, cah)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs15(vyy3000, vyy400)
new_compare33(vyy3000, vyy400, ty_Double) → new_compare8(vyy3000, vyy400)
new_foldFM_LE10(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, vyy614, False, h, ba, bb) → new_foldFM_LE0(vyy84, vyy54, vyy55, vyy613, h, ba, bb)
new_lt20(vyy3010, vyy410, app(ty_Maybe, ccc)) → new_lt16(vyy3010, vyy410, ccc)
new_esEs21(vyy3010, vyy410, ty_@0) → new_esEs8(vyy3010, vyy410)
new_compare24(vyy300, vyy40, False, de, df, dg) → new_compare14(vyy300, vyy40, new_ltEs7(vyy300, vyy40, de, df, dg), de, df, dg)
new_esEs21(vyy3010, vyy410, ty_Bool) → new_esEs14(vyy3010, vyy410)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_esEs21(vyy3010, vyy410, ty_Char) → new_esEs13(vyy3010, vyy410)
new_esEs26(vyy3002, vyy402, ty_Double) → new_esEs12(vyy3002, vyy402)
new_lt15(vyy950, vyy960, app(ty_Ratio, bde)) → new_lt13(vyy950, vyy960, bde)
new_lt20(vyy3010, vyy410, app(app(app(ty_@3, cbg), cbh), cca)) → new_lt14(vyy3010, vyy410, cbg, cbh, cca)
new_esEs7(Right(vyy3000), Right(vyy400), cg, ty_Bool) → new_esEs14(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs8(vyy3000, vyy400)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Int) → new_ltEs5(vyy3010, vyy410)
new_lt16(vyy300, vyy40, db) → new_esEs9(new_compare28(vyy300, vyy40, db), LT)
new_ltEs19(vyy3012, vyy412, app(app(ty_Either, bhh), caa)) → new_ltEs10(vyy3012, vyy412, bhh, caa)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Int, da) → new_esEs11(vyy3000, vyy400)
new_compare17(vyy300, vyy40, cg, da) → new_compare26(vyy300, vyy40, new_esEs7(vyy300, vyy40, cg, da), cg, da)
new_ltEs14(@2(vyy950, vyy951), @2(vyy960, vyy961), bbf, bbg) → new_pePe(new_lt15(vyy950, vyy960, bbf), new_asAs(new_esEs18(vyy950, vyy960, bbf), new_ltEs18(vyy951, vyy961, bbg)))
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_compare0([], [], bc) → EQ
new_pePe(True, vyy139) → True
new_primEqNat0(Zero, Zero) → True
new_esEs20(vyy3011, vyy411, ty_Int) → new_esEs11(vyy3011, vyy411)
new_lt15(vyy950, vyy960, ty_Char) → new_lt18(vyy950, vyy960)
new_ltEs12(False, False) → True
new_ltEs10(Right(vyy3010), Right(vyy410), fc, ty_Ordering) → new_ltEs16(vyy3010, vyy410)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Double) → new_ltEs15(vyy3010, vyy410)
new_ltEs15(vyy301, vyy41) → new_fsEs(new_compare8(vyy301, vyy41))
new_lt20(vyy3010, vyy410, app(app(ty_@2, ccg), cch)) → new_lt10(vyy3010, vyy410, ccg, cch)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Ordering, da) → new_esEs9(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_ltEs16(EQ, LT) → False
new_compare12(vyy300, vyy40, False, db) → GT
new_ltEs8(vyy301, vyy41, bbe) → new_fsEs(new_compare30(vyy301, vyy41, bbe))
new_ltEs18(vyy951, vyy961, ty_Int) → new_ltEs5(vyy951, vyy961)
new_ltEs16(GT, EQ) → False
new_sr(vyy3000, vyy401) → new_primMulInt(vyy3000, vyy401)
new_compare33(vyy3000, vyy400, ty_Int) → new_compare9(vyy3000, vyy400)
new_compare18(vyy300, vyy40, dc, dd) → new_compare210(vyy300, vyy40, new_esEs6(vyy300, vyy40, dc, dd), dc, dd)
new_lt15(vyy950, vyy960, app(app(app(ty_@3, bdb), bdc), bdd)) → new_lt14(vyy950, vyy960, bdb, bdc, bdd)
new_esEs7(Right(vyy3000), Right(vyy400), cg, ty_Double) → new_esEs12(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy1870), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1870, vyy40100)))
new_esEs7(Right(vyy3000), Right(vyy400), cg, app(app(ty_Either, bah), bba)) → new_esEs7(vyy3000, vyy400, bah, bba)
new_lt15(vyy950, vyy960, ty_@0) → new_lt12(vyy950, vyy960)
new_ltEs19(vyy3012, vyy412, ty_Bool) → new_ltEs12(vyy3012, vyy412)
new_esEs26(vyy3002, vyy402, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs4(vyy3002, vyy402, cfe, cff, cfg)
new_esEs19(vyy3000, vyy400, app(ty_Ratio, bgg)) → new_esEs17(vyy3000, vyy400, bgg)
new_esEs21(vyy3010, vyy410, ty_Ordering) → new_esEs9(vyy3010, vyy410)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs12(vyy3000, vyy400)
new_esEs9(EQ, EQ) → True
new_fsEs(vyy174) → new_not(new_esEs9(vyy174, GT))
new_ltEs10(Left(vyy3010), Left(vyy410), app(ty_Maybe, ee), dh) → new_ltEs4(vyy3010, vyy410, ee)
new_compare24(vyy300, vyy40, True, de, df, dg) → EQ
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare25(vyy300, vyy40, True) → EQ
new_compare13(vyy300, vyy40, True, dc, dd) → LT
new_ltEs16(LT, EQ) → True
new_primPlusNat1(Succ(vyy18700), Zero) → Succ(vyy18700)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_ltEs4(Nothing, Nothing, bd) → True
new_esEs5(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs11(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(vyy3000), Left(vyy400), ty_Integer, da) → new_esEs15(vyy3000, vyy400)
new_ltEs19(vyy3012, vyy412, app(ty_Ratio, bhf)) → new_ltEs8(vyy3012, vyy412, bhf)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_@2, hd), he), da) → new_esEs6(vyy3000, vyy400, hd, he)
new_lt14(vyy300, vyy40, de, df, dg) → new_esEs9(new_compare32(vyy300, vyy40, de, df, dg), LT)
new_esEs19(vyy3000, vyy400, ty_Bool) → new_esEs14(vyy3000, vyy400)
new_esEs18(vyy950, vyy960, ty_Float) → new_esEs10(vyy950, vyy960)
new_esEs7(Right(vyy3000), Right(vyy400), cg, app(ty_Maybe, bae)) → new_esEs5(vyy3000, vyy400, bae)
new_ltEs10(Right(vyy3010), Right(vyy410), fc, ty_Char) → new_ltEs17(vyy3010, vyy410)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_compare26(vyy300, vyy40, True, cg, da) → EQ
new_compare33(vyy3000, vyy400, app(ty_Ratio, bgg)) → new_compare30(vyy3000, vyy400, bgg)
new_lt20(vyy3010, vyy410, ty_Ordering) → new_lt8(vyy3010, vyy410)
new_esEs23(vyy3000, vyy400, app(app(app(ty_@3, cec), ced), cee)) → new_esEs4(vyy3000, vyy400, cec, ced, cee)
new_ltEs19(vyy3012, vyy412, ty_Char) → new_ltEs17(vyy3012, vyy412)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs26(vyy3002, vyy402, app(app(ty_Either, cgc), cgd)) → new_esEs7(vyy3002, vyy402, cgc, cgd)
new_esEs21(vyy3010, vyy410, app(ty_Ratio, ccb)) → new_esEs17(vyy3010, vyy410, ccb)
new_ltEs9(vyy301, vyy41) → new_fsEs(new_compare7(vyy301, vyy41))
new_ltEs16(GT, LT) → False
new_esEs21(vyy3010, vyy410, ty_Float) → new_esEs10(vyy3010, vyy410)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_esEs23(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs7(Right(vyy3000), Right(vyy400), cg, app(app(ty_@2, baf), bag)) → new_esEs6(vyy3000, vyy400, baf, bag)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bed), bee), bef)) → new_esEs4(vyy3000, vyy400, bed, bee, bef)
new_lt9(vyy300, vyy40) → new_esEs9(new_compare8(vyy300, vyy40), LT)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare33(vyy3000, vyy400, app(ty_[], bgf)) → new_compare0(vyy3000, vyy400, bgf)
new_ltEs19(vyy3012, vyy412, app(app(app(ty_@3, bhc), bhd), bhe)) → new_ltEs7(vyy3012, vyy412, bhc, bhd, bhe)
new_lt8(vyy300, vyy40) → new_esEs9(new_compare16(vyy300, vyy40), LT)
new_foldFM_LE20(vyy610, vyy611, vyy105, vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb) → new_foldFM_LE10(new_eltsFM_LE0(vyy610, vyy611, vyy105, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, new_ltEs14(vyy6140, @2(vyy54, vyy55), ba, bb), h, ba, bb)
new_ltEs10(Left(vyy3010), Left(vyy410), ty_Bool, dh) → new_ltEs12(vyy3010, vyy410)
new_ltEs10(Right(vyy3010), Right(vyy410), fc, app(app(ty_@2, ge), gf)) → new_ltEs14(vyy3010, vyy410, ge, gf)
new_lt20(vyy3010, vyy410, ty_Int) → new_lt7(vyy3010, vyy410)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_esEs26(vyy3002, vyy402, ty_Integer) → new_esEs15(vyy3002, vyy402)
new_esEs7(Right(vyy3000), Right(vyy400), cg, app(app(app(ty_@3, bab), bac), bad)) → new_esEs4(vyy3000, vyy400, bab, bac, bad)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_lt20(vyy3010, vyy410, ty_@0) → new_lt12(vyy3010, vyy410)
new_esEs7(Right(vyy3000), Right(vyy400), cg, app(ty_[], bbb)) → new_esEs16(vyy3000, vyy400, bbb)
new_compare7(@0, @0) → EQ
new_esEs16(:(vyy3000, vyy3001), :(vyy400, vyy401), bc) → new_asAs(new_esEs19(vyy3000, vyy400, bc), new_esEs16(vyy3001, vyy401, bc))
new_esEs7(Right(vyy3000), Right(vyy400), cg, ty_@0) → new_esEs8(vyy3000, vyy400)
new_esEs19(vyy3000, vyy400, app(app(ty_@2, bgb), bgc)) → new_esEs6(vyy3000, vyy400, bgb, bgc)
new_esEs7(Right(vyy3000), Right(vyy400), cg, ty_Float) → new_esEs10(vyy3000, vyy400)
new_ltEs11(vyy301, vyy41) → new_fsEs(new_compare6(vyy301, vyy41))
new_esEs20(vyy3011, vyy411, ty_Float) → new_esEs10(vyy3011, vyy411)
new_primCompAux00(vyy183, LT) → LT
new_lt13(vyy300, vyy40, bbd) → new_esEs9(new_compare30(vyy300, vyy40, bbd), LT)
new_ltEs10(Left(vyy3010), Left(vyy410), ty_Double, dh) → new_ltEs15(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs26(vyy3002, vyy402, ty_@0) → new_esEs8(vyy3002, vyy402)
new_compare33(vyy3000, vyy400, ty_Integer) → new_compare5(vyy3000, vyy400)
new_esEs22(vyy3001, vyy401, ty_Bool) → new_esEs14(vyy3001, vyy401)
new_compare30(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Integer) → new_compare5(new_sr0(vyy3000, vyy401), new_sr0(vyy400, vyy3001))
new_ltEs4(Just(vyy3010), Just(vyy410), app(app(ty_Either, cb), cc)) → new_ltEs10(vyy3010, vyy410, cb, cc)
new_ltEs10(Right(vyy3010), Right(vyy410), fc, app(app(ty_Either, gb), gc)) → new_ltEs10(vyy3010, vyy410, gb, gc)
new_ltEs13(vyy301, vyy41, gg) → new_fsEs(new_compare0(vyy301, vyy41, gg))
new_lt19(vyy3011, vyy411, ty_Float) → new_lt5(vyy3011, vyy411)
new_esEs10(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs21(vyy3010, vyy410, ty_Int) → new_esEs11(vyy3010, vyy410)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_esEs23(vyy3000, vyy400, ty_Char) → new_esEs13(vyy3000, vyy400)
new_lt20(vyy3010, vyy410, ty_Char) → new_lt18(vyy3010, vyy410)
new_ltEs18(vyy951, vyy961, ty_Float) → new_ltEs11(vyy951, vyy961)
new_ltEs4(Just(vyy3010), Just(vyy410), app(app(ty_@2, ce), cf)) → new_ltEs14(vyy3010, vyy410, ce, cf)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_compare25(vyy300, vyy40, False) → new_compare15(vyy300, vyy40, new_ltEs12(vyy300, vyy40))
new_compare19(vyy300, vyy40) → new_compare25(vyy300, vyy40, new_esEs14(vyy300, vyy40))
new_esEs20(vyy3011, vyy411, app(app(app(ty_@3, cae), caf), cag)) → new_esEs4(vyy3011, vyy411, cae, caf, cag)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_lt10(vyy300, vyy40, dc, dd) → new_esEs9(new_compare18(vyy300, vyy40, dc, dd), LT)
new_compare33(vyy3000, vyy400, app(app(app(ty_@3, bff), bfg), bfh)) → new_compare32(vyy3000, vyy400, bff, bfg, bfh)
new_compare11(vyy300, vyy40, True, cg, da) → LT
new_esEs18(vyy950, vyy960, ty_Ordering) → new_esEs9(vyy950, vyy960)
new_esEs18(vyy950, vyy960, app(ty_Ratio, bde)) → new_esEs17(vyy950, vyy960, bde)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_sr0(Integer(vyy30000), Integer(vyy4010)) → Integer(new_primMulInt(vyy30000, vyy4010))
new_compare14(vyy300, vyy40, False, de, df, dg) → GT
new_ltEs10(Right(vyy3010), Right(vyy410), fc, ty_Integer) → new_ltEs6(vyy3010, vyy410)
new_primPlusNat1(Succ(vyy18700), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy18700, vyy401000)))
new_compare12(vyy300, vyy40, True, db) → LT
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Ratio, baa), da) → new_esEs17(vyy3000, vyy400, baa)
new_esEs20(vyy3011, vyy411, ty_Char) → new_esEs13(vyy3011, vyy411)
new_ltEs18(vyy951, vyy961, app(app(ty_@2, bch), bda)) → new_ltEs14(vyy951, vyy961, bch, bda)
new_esEs27(vyy3001, vyy401, app(ty_Maybe, chb)) → new_esEs5(vyy3001, vyy401, chb)
new_lt19(vyy3011, vyy411, app(ty_Maybe, cba)) → new_lt16(vyy3011, vyy411, cba)
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs12(vyy3001, vyy401)
new_esEs22(vyy3001, vyy401, app(app(ty_@2, cde), cdf)) → new_esEs6(vyy3001, vyy401, cde, cdf)
new_lt19(vyy3011, vyy411, ty_Int) → new_lt7(vyy3011, vyy411)
new_esEs18(vyy950, vyy960, ty_@0) → new_esEs8(vyy950, vyy960)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_esEs21(vyy3010, vyy410, ty_Integer) → new_esEs15(vyy3010, vyy410)
new_lt19(vyy3011, vyy411, ty_Char) → new_lt18(vyy3011, vyy411)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCompAux00(vyy183, EQ) → vyy183
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dag), dah)) → new_esEs7(vyy3000, vyy400, dag, dah)
new_lt4(vyy300, vyy40) → new_esEs9(new_compare5(vyy300, vyy40), LT)
new_esEs22(vyy3001, vyy401, ty_@0) → new_esEs8(vyy3001, vyy401)
new_ltEs16(EQ, EQ) → True
new_ltEs5(vyy301, vyy41) → new_fsEs(new_compare9(vyy301, vyy41))
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, gh), ha), hb), da) → new_esEs4(vyy3000, vyy400, gh, ha, hb)
new_ltEs18(vyy951, vyy961, app(ty_Ratio, bcc)) → new_ltEs8(vyy951, vyy961, bcc)
new_not(False) → True
new_esEs11(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_lt15(vyy950, vyy960, ty_Double) → new_lt9(vyy950, vyy960)
new_lt15(vyy950, vyy960, app(app(ty_@2, beb), bec)) → new_lt10(vyy950, vyy960, beb, bec)
new_lt15(vyy950, vyy960, ty_Bool) → new_lt17(vyy950, vyy960)
new_esEs28(vyy3000, vyy400, app(ty_[], dba)) → new_esEs16(vyy3000, vyy400, dba)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_compare210(vyy300, vyy40, True, dc, dd) → EQ
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_esEs19(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, app(app(ty_@2, ceg), ceh)) → new_esEs6(vyy3000, vyy400, ceg, ceh)
new_esEs9(GT, GT) → True
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs19(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_esEs26(vyy3002, vyy402, ty_Bool) → new_esEs14(vyy3002, vyy402)
new_lt19(vyy3011, vyy411, app(ty_[], cbd)) → new_lt6(vyy3011, vyy411, cbd)
new_compare0(:(vyy3000, vyy3001), [], bc) → GT
new_esEs8(@0, @0) → True
new_lt19(vyy3011, vyy411, ty_Integer) → new_lt4(vyy3011, vyy411)
new_esEs22(vyy3001, vyy401, app(app(app(ty_@3, cda), cdb), cdc)) → new_esEs4(vyy3001, vyy401, cda, cdb, cdc)
new_lt20(vyy3010, vyy410, ty_Double) → new_lt9(vyy3010, vyy410)
new_ltEs18(vyy951, vyy961, ty_Bool) → new_ltEs12(vyy951, vyy961)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_compare11(vyy300, vyy40, False, cg, da) → GT
new_esEs19(vyy3000, vyy400, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs4(vyy3000, vyy400, bff, bfg, bfh)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs7(Right(vyy3000), Right(vyy400), cg, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_compare31(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_esEs18(vyy950, vyy960, app(app(ty_Either, bdg), bdh)) → new_esEs7(vyy950, vyy960, bdg, bdh)
new_foldFM_LE3(vyy610, vyy611, vyy104, vyy54, vyy55, h, ba, bb) → new_eltsFM_LE0(vyy610, vyy611, vyy104, h, ba, bb)
new_esEs22(vyy3001, vyy401, app(ty_[], cea)) → new_esEs16(vyy3001, vyy401, cea)
new_lt19(vyy3011, vyy411, app(app(app(ty_@3, cae), caf), cag)) → new_lt14(vyy3011, vyy411, cae, caf, cag)
new_primMulInt(Pos(vyy30000), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30000, vyy4010))
new_esEs23(vyy3000, vyy400, ty_Ordering) → new_esEs9(vyy3000, vyy400)
new_primMulInt(Neg(vyy30000), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30000, vyy4010))
new_esEs27(vyy3001, vyy401, app(app(ty_@2, chc), chd)) → new_esEs6(vyy3001, vyy401, chc, chd)
new_esEs20(vyy3011, vyy411, ty_Integer) → new_esEs15(vyy3011, vyy411)
new_ltEs19(vyy3012, vyy412, ty_Int) → new_ltEs5(vyy3012, vyy412)
new_ltEs17(vyy301, vyy41) → new_fsEs(new_compare31(vyy301, vyy41))
new_esEs17(:%(vyy3000, vyy3001), :%(vyy400, vyy401), bbd) → new_asAs(new_esEs25(vyy3000, vyy400, bbd), new_esEs24(vyy3001, vyy401, bbd))
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_esEs5(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs14(vyy3000, vyy400)
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_[], hh), da) → new_esEs16(vyy3000, vyy400, hh)
new_ltEs10(Right(vyy3010), Right(vyy410), fc, app(app(app(ty_@3, fd), ff), fg)) → new_ltEs7(vyy3010, vyy410, fd, ff, fg)
new_esEs18(vyy950, vyy960, ty_Integer) → new_esEs15(vyy950, vyy960)
new_esEs20(vyy3011, vyy411, ty_Bool) → new_esEs14(vyy3011, vyy411)
new_lt19(vyy3011, vyy411, app(app(ty_Either, cbb), cbc)) → new_lt11(vyy3011, vyy411, cbb, cbc)
new_compare16(vyy300, vyy40) → new_compare27(vyy300, vyy40, new_esEs9(vyy300, vyy40))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt15(vyy950, vyy960, app(ty_Maybe, bdf)) → new_lt16(vyy950, vyy960, bdf)
new_compare33(vyy3000, vyy400, ty_Char) → new_compare31(vyy3000, vyy400)
new_compare210(vyy300, vyy40, False, dc, dd) → new_compare13(vyy300, vyy40, new_ltEs14(vyy300, vyy40, dc, dd), dc, dd)
new_esEs16([], :(vyy400, vyy401), bc) → False
new_esEs16(:(vyy3000, vyy3001), [], bc) → False
new_esEs19(vyy3000, vyy400, app(ty_Maybe, bga)) → new_esEs5(vyy3000, vyy400, bga)
new_esEs6(@2(vyy3000, vyy3001), @2(vyy400, vyy401), dc, dd) → new_asAs(new_esEs23(vyy3000, vyy400, dc), new_esEs22(vyy3001, vyy401, dd))
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, app(app(ty_Either, ccd), cce)) → new_esEs7(vyy3010, vyy410, ccd, cce)
new_lt19(vyy3011, vyy411, ty_@0) → new_lt12(vyy3011, vyy411)
new_esEs26(vyy3002, vyy402, app(ty_Maybe, cfh)) → new_esEs5(vyy3002, vyy402, cfh)
new_ltEs4(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, be), bf), bg)) → new_ltEs7(vyy3010, vyy410, be, bf, bg)
new_lt20(vyy3010, vyy410, app(app(ty_Either, ccd), cce)) → new_lt11(vyy3010, vyy410, ccd, cce)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dbb)) → new_esEs17(vyy3000, vyy400, dbb)
new_esEs23(vyy3000, vyy400, app(ty_Ratio, cfd)) → new_esEs17(vyy3000, vyy400, cfd)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_ltEs4(Just(vyy3010), Just(vyy410), app(ty_[], cd)) → new_ltEs13(vyy3010, vyy410, cd)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Ordering) → new_ltEs16(vyy3010, vyy410)
new_compare5(Integer(vyy3000), Integer(vyy400)) → new_primCmpInt(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, app(app(app(ty_@3, cbg), cbh), cca)) → new_esEs4(vyy3010, vyy410, cbg, cbh, cca)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dae), daf)) → new_esEs6(vyy3000, vyy400, dae, daf)
new_compare33(vyy3000, vyy400, app(app(ty_@2, bgb), bgc)) → new_compare18(vyy3000, vyy400, bgb, bgc)
new_esEs20(vyy3011, vyy411, app(app(ty_Either, cbb), cbc)) → new_esEs7(vyy3011, vyy411, cbb, cbc)
new_ltEs10(Right(vyy3010), Right(vyy410), fc, app(ty_Maybe, ga)) → new_ltEs4(vyy3010, vyy410, ga)
new_compare33(vyy3000, vyy400, app(app(ty_Either, bgd), bge)) → new_compare17(vyy3000, vyy400, bgd, bge)
new_lt19(vyy3011, vyy411, ty_Double) → new_lt9(vyy3011, vyy411)
new_lt19(vyy3011, vyy411, app(ty_Ratio, cah)) → new_lt13(vyy3011, vyy411, cah)
new_ltEs6(vyy301, vyy41) → new_fsEs(new_compare5(vyy301, vyy41))
new_eltsFM_LE0(vyy610, vyy611, vyy104, h, ba, bb) → :(vyy611, vyy104)
new_ltEs4(Just(vyy3010), Just(vyy410), app(ty_Maybe, ca)) → new_ltEs4(vyy3010, vyy410, ca)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(vyy300, vyy40, True, db) → EQ
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_[], bfd)) → new_esEs16(vyy3000, vyy400, bfd)
new_esEs20(vyy3011, vyy411, app(ty_Maybe, cba)) → new_esEs5(vyy3011, vyy411, cba)
new_esEs20(vyy3011, vyy411, app(ty_[], cbd)) → new_esEs16(vyy3011, vyy411, cbd)
new_asAs(False, vyy172) → False
new_esEs22(vyy3001, vyy401, ty_Double) → new_esEs12(vyy3001, vyy401)
new_lt15(vyy950, vyy960, app(ty_[], bea)) → new_lt6(vyy950, vyy960, bea)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(ty_Either, bfb), bfc)) → new_esEs7(vyy3000, vyy400, bfb, bfc)
new_esEs19(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_ltEs18(vyy951, vyy961, ty_Double) → new_ltEs15(vyy951, vyy961)
new_primMulInt(Pos(vyy30000), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30000, vyy4010))
new_primMulInt(Neg(vyy30000), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30000, vyy4010))
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs7(Left(vyy3000), Left(vyy400), ty_Float, da) → new_esEs10(vyy3000, vyy400)
new_esEs7(Right(vyy3000), Right(vyy400), cg, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_ltEs10(Left(vyy3010), Left(vyy410), ty_Integer, dh) → new_ltEs6(vyy3010, vyy410)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Bool) → new_ltEs12(vyy3010, vyy410)
new_compare33(vyy3000, vyy400, ty_Float) → new_compare6(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs14(vyy3000, vyy400)
new_esEs5(Just(vyy3000), Just(vyy400), app(app(ty_@2, beh), bfa)) → new_esEs6(vyy3000, vyy400, beh, bfa)
new_esEs18(vyy950, vyy960, app(ty_Maybe, bdf)) → new_esEs5(vyy950, vyy960, bdf)
new_ltEs12(True, True) → True
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, app(ty_Maybe, cef)) → new_esEs5(vyy3000, vyy400, cef)
new_ltEs12(False, True) → True
new_esEs5(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs8(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_lt18(vyy300, vyy40) → new_esEs9(new_compare31(vyy300, vyy40), LT)
new_compare30(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ty_Int) → new_compare9(new_sr(vyy3000, vyy401), new_sr(vyy400, vyy3001))
new_ltEs10(Left(vyy3010), Left(vyy410), ty_Int, dh) → new_ltEs5(vyy3010, vyy410)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Float) → new_ltEs11(vyy3010, vyy410)
new_compare27(vyy300, vyy40, True) → EQ
new_esEs14(True, True) → True
new_esEs7(Right(vyy3000), Right(vyy400), cg, ty_Char) → new_esEs13(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs14(vyy3001, vyy401)
new_esEs20(vyy3011, vyy411, ty_Ordering) → new_esEs9(vyy3011, vyy411)
new_esEs5(Just(vyy3000), Nothing, db) → False
new_esEs5(Nothing, Just(vyy400), db) → False
new_esEs18(vyy950, vyy960, ty_Int) → new_esEs11(vyy950, vyy960)
new_esEs12(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_foldFM_LE10(vyy84, vyy54, vyy55, vyy610, vyy611, vyy612, vyy613, EmptyFM, True, h, ba, bb) → new_foldFM_LE3(vyy610, vyy611, new_foldFM_LE0(vyy84, vyy54, vyy55, vyy613, h, ba, bb), vyy54, vyy55, h, ba, bb)
new_esEs7(Right(vyy3000), Right(vyy400), cg, ty_Int) → new_esEs11(vyy3000, vyy400)
new_ltEs10(Left(vyy3010), Left(vyy410), app(app(ty_@2, fa), fb), dh) → new_ltEs14(vyy3010, vyy410, fa, fb)
new_esEs16([], [], bc) → True
new_ltEs10(Left(vyy3010), Left(vyy410), app(ty_[], eh), dh) → new_ltEs13(vyy3010, vyy410, eh)
new_compare33(vyy3000, vyy400, ty_Ordering) → new_compare16(vyy3000, vyy400)
new_compare8(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare9(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs22(vyy3001, vyy401, ty_Char) → new_esEs13(vyy3001, vyy401)
new_esEs4(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), de, df, dg) → new_asAs(new_esEs28(vyy3000, vyy400, de), new_asAs(new_esEs27(vyy3001, vyy401, df), new_esEs26(vyy3002, vyy402, dg)))
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_ltEs10(Right(vyy3010), Left(vyy410), fc, dh) → False
new_compare29(vyy300, vyy40, False, db) → new_compare12(vyy300, vyy40, new_ltEs4(vyy300, vyy40, db), db)
new_esEs5(Nothing, Nothing, db) → True
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dad)) → new_esEs5(vyy3000, vyy400, dad)
new_ltEs4(Just(vyy3010), Just(vyy410), ty_Char) → new_ltEs17(vyy3010, vyy410)
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Maybe, hc), da) → new_esEs5(vyy3000, vyy400, hc)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, ty_Double) → new_esEs12(vyy3010, vyy410)
new_esEs13(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_lt15(vyy950, vyy960, ty_Ordering) → new_lt8(vyy950, vyy960)
new_esEs14(False, False) → True
new_esEs5(Just(vyy3000), Just(vyy400), app(ty_Ratio, bfe)) → new_esEs17(vyy3000, vyy400, bfe)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Char, da) → new_esEs13(vyy3000, vyy400)
new_esEs22(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_ltEs19(vyy3012, vyy412, ty_Double) → new_ltEs15(vyy3012, vyy412)
new_esEs22(vyy3001, vyy401, app(ty_Ratio, ceb)) → new_esEs17(vyy3001, vyy401, ceb)
new_esEs23(vyy3000, vyy400, ty_Double) → new_esEs12(vyy3000, vyy400)
new_esEs18(vyy950, vyy960, ty_Bool) → new_esEs14(vyy950, vyy960)
new_esEs22(vyy3001, vyy401, app(ty_Maybe, cdd)) → new_esEs5(vyy3001, vyy401, cdd)
new_esEs19(vyy3000, vyy400, ty_@0) → new_esEs8(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, app(ty_Maybe, ccc)) → new_esEs5(vyy3010, vyy410, ccc)
new_esEs23(vyy3000, vyy400, app(ty_[], cfc)) → new_esEs16(vyy3000, vyy400, cfc)
new_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_compare0([], :(vyy400, vyy401), bc) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs7(Left(vyy3000), Left(vyy400), ty_@0, da) → new_esEs8(vyy3000, vyy400)
new_ltEs18(vyy951, vyy961, ty_Ordering) → new_ltEs16(vyy951, vyy961)
new_esEs26(vyy3002, vyy402, ty_Ordering) → new_esEs9(vyy3002, vyy402)
new_esEs19(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_asAs(True, vyy172) → vyy172
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs18(vyy950, vyy960, ty_Char) → new_esEs13(vyy950, vyy960)
new_ltEs4(Just(vyy3010), Nothing, bd) → False
new_primMulNat0(Succ(vyy300000), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300000, Succ(vyy40100)), vyy40100)
new_ltEs19(vyy3012, vyy412, ty_@0) → new_ltEs9(vyy3012, vyy412)
new_lt20(vyy3010, vyy410, ty_Bool) → new_lt17(vyy3010, vyy410)
new_ltEs16(LT, LT) → True
new_lt12(vyy300, vyy40) → new_esEs9(new_compare7(vyy300, vyy40), LT)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs8(vyy3001, vyy401)
new_esEs26(vyy3002, vyy402, app(app(ty_@2, cga), cgb)) → new_esEs6(vyy3002, vyy402, cga, cgb)
new_ltEs19(vyy3012, vyy412, app(app(ty_@2, cac), cad)) → new_ltEs14(vyy3012, vyy412, cac, cad)
new_esEs5(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs13(vyy3000, vyy400)
new_compare10(vyy300, vyy40, True) → LT
new_ltEs10(Left(vyy3010), Left(vyy410), ty_Char, dh) → new_ltEs17(vyy3010, vyy410)
new_ltEs10(Right(vyy3010), Right(vyy410), fc, ty_Int) → new_ltEs5(vyy3010, vyy410)
new_esEs27(vyy3001, vyy401, app(ty_Ratio, chh)) → new_esEs17(vyy3001, vyy401, chh)
new_compare33(vyy3000, vyy400, ty_Bool) → new_compare19(vyy3000, vyy400)
new_lt20(vyy3010, vyy410, app(ty_Ratio, ccb)) → new_lt13(vyy3010, vyy410, ccb)
new_compare10(vyy300, vyy40, False) → GT
new_lt11(vyy300, vyy40, cg, da) → new_esEs9(new_compare17(vyy300, vyy40, cg, da), LT)
new_esEs9(LT, LT) → True
new_primCompAux00(vyy183, GT) → GT
new_lt6(vyy300, vyy40, bc) → new_esEs9(new_compare0(vyy300, vyy40, bc), LT)
new_ltEs10(Right(vyy3010), Right(vyy410), fc, ty_@0) → new_ltEs9(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, app(ty_[], ccf)) → new_esEs16(vyy3010, vyy410, ccf)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs19(vyy3012, vyy412, app(ty_[], cab)) → new_ltEs13(vyy3012, vyy412, cab)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_lt17(vyy300, vyy40) → new_esEs9(new_compare19(vyy300, vyy40), LT)
new_foldFM_LE0(vyy84, vyy54, vyy55, EmptyFM, h, ba, bb) → vyy84
new_not(True) → False

The set Q consists of the following terms:

new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs19(x0, x1, ty_Float)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Ordering)
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare33(x0, x1, ty_Double)
new_compare9(x0, x1)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_compare31(Char(x0), Char(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt15(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_lt20(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Integer)
new_primPlusNat0(Succ(x0), x1)
new_lt15(x0, x1, app(ty_[], x2))
new_ltEs14(@2(x0, x1), @2(x2, x3), x4, x5)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, EmptyFM, True, x7, x8, x9)
new_esEs18(x0, x1, ty_Float)
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs28(x0, x1, ty_Int)
new_compare0([], [], x0)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs27(x0, x1, ty_Float)
new_lt14(x0, x1, x2, x3, x4)
new_esEs26(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_primCompAux00(x0, EQ)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_foldFM_LE3(x0, x1, x2, x3, x4, x5, x6, x7)
new_esEs21(x0, x1, ty_@0)
new_compare0([], :(x0, x1), x2)
new_ltEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_Float)
new_foldFM_LE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs27(x0, x1, ty_Integer)
new_lt5(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs5(x0, x1)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs15(x0, x1)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs17(x0, x1)
new_esEs8(@0, @0)
new_compare15(x0, x1, True)
new_ltEs19(x0, x1, ty_Int)
new_compare33(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_foldFM_LE0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10)
new_esEs23(x0, x1, ty_Double)
new_lt15(x0, x1, ty_Ordering)
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_@0)
new_lt15(x0, x1, ty_Int)
new_compare15(x0, x1, False)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_ltEs4(Nothing, Nothing, x0)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs4(Nothing, Just(x0), x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs13(Char(x0), Char(x1))
new_primEqNat0(Succ(x0), Succ(x1))
new_primCompAux0(x0, x1, x2, x3)
new_asAs(True, x0)
new_compare14(x0, x1, True, x2, x3, x4)
new_esEs14(True, True)
new_esEs20(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs23(x0, x1, ty_Int)
new_lt15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt15(x0, x1, ty_Float)
new_lt6(x0, x1, x2)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_primEqNat0(Zero, Zero)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs25(x0, x1, ty_Int)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare14(x0, x1, False, x2, x3, x4)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Integer)
new_ltEs4(Just(x0), Nothing, x1)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primPlusNat1(Succ(x0), Zero)
new_compare33(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare30(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1, ty_Double)
new_primPlusNat1(Zero, Succ(x0))
new_compare6(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Zero)
new_lt7(x0, x1)
new_esEs11(x0, x1)
new_ltEs19(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare26(x0, x1, False, x2, x3)
new_compare13(x0, x1, False, x2, x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1, ty_@0)
new_compare26(x0, x1, True, x2, x3)
new_compare210(x0, x1, False, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Integer)
new_primCompAux00(x0, LT)
new_ltEs9(x0, x1)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, ty_Bool)
new_compare11(x0, x1, False, x2, x3)
new_lt12(x0, x1)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare29(x0, x1, True, x2)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt19(x0, x1, ty_Integer)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare33(x0, x1, ty_Int)
new_esEs16([], [], x0)
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_esEs18(x0, x1, ty_Int)
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs19(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Ordering)
new_compare16(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs12(False, False)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_compare17(x0, x1, x2, x3)
new_compare11(x0, x1, True, x2, x3)
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_ltEs18(x0, x1, ty_@0)
new_compare33(x0, x1, ty_@0)
new_compare25(x0, x1, False)
new_lt16(x0, x1, x2)
new_esEs21(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_compare33(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare210(x0, x1, True, x2, x3)
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_primPlusNat1(Zero, Zero)
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_compare19(x0, x1)
new_ltEs16(EQ, EQ)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_lt9(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs16(LT, LT)
new_lt15(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Char)
new_lt18(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs22(x0, x1, ty_Char)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt15(x0, x1, ty_Integer)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs22(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_ltEs16(GT, LT)
new_ltEs16(LT, GT)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_compare0(:(x0, x1), [], x2)
new_esEs20(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Double)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs18(x0, x1, ty_Double)
new_compare29(x0, x1, False, x2)
new_esEs9(GT, GT)
new_esEs18(x0, x1, app(ty_[], x2))
new_lt10(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Float)
new_lt17(x0, x1)
new_compare27(x0, x1, False)
new_esEs21(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare33(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare24(x0, x1, True, x2, x3, x4)
new_compare33(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_lt20(x0, x1, ty_Bool)
new_compare33(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt15(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs9(EQ, EQ)
new_sr(x0, x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs19(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Ordering)
new_lt15(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, ty_Double)
new_esEs14(False, True)
new_esEs14(True, False)
new_compare25(x0, x1, True)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt8(x0, x1)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs16(GT, GT)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_compare7(@0, @0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs11(x0, x1)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(False, x0)
new_compare24(x0, x1, False, x2, x3, x4)
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs18(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_@0)
new_compare30(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare18(x0, x1, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Succ(x0))
new_compare28(x0, x1, x2)
new_compare10(x0, x1, False)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs5(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs12(False, True)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs12(True, False)
new_esEs21(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat0(Zero, x0)
new_compare32(x0, x1, x2, x3, x4)
new_eltsFM_LE0(x0, x1, x2, x3, x4, x5)
new_esEs28(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs16(:(x0, x1), [], x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_compare33(x0, x1, ty_Bool)
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs6(x0, x1)
new_compare13(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs27(x0, x1, ty_Double)
new_esEs5(Just(x0), Nothing, x1)
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_@0)
new_esEs16([], :(x0, x1), x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Bool)
new_esEs15(Integer(x0), Integer(x1))
new_not(True)
new_compare33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, GT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs13(x0, x1, x2)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_esEs18(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_foldFM_LE0(x0, x1, x2, EmptyFM, x3, x4, x5)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_lt13(x0, x1, x2)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Bool)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, x7, False, x8, x9, x10)
new_esEs5(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Ordering)
new_compare33(x0, x1, ty_Ordering)
new_ltEs12(True, True)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), True, x12, x13, x14)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, ty_Char)
new_lt15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs20(x0, x1, ty_Char)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs20(x0, x1, ty_Int)
new_lt19(x0, x1, ty_@0)
new_compare10(x0, x1, True)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_fsEs(x0)
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Ordering)
new_asAs(False, x0)
new_lt19(x0, x1, ty_Char)
new_compare5(Integer(x0), Integer(x1))
new_esEs12(Double(x0, x1), Double(x2, x3))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_primEqNat0(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_Ordering)
new_compare8(Double(x0, x1), Double(x2, x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs14(False, False)
new_lt15(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(ty_[], x2))
new_compare12(x0, x1, False, x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare27(x0, x1, True)
new_esEs18(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_@0)
new_compare33(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Float)
new_esEs9(LT, LT)
new_esEs28(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Int)
new_ltEs8(x0, x1, x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Float)

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: