YES 8.041 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ LR

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

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

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

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

  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 c => (c  ->  b  ->  a  ->  a)  ->  a  ->  c  ->  FiniteMap c b  ->  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


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→(key,elt) : rest

is transformed to
fmToList_LE0 key elt rest = (key,elt) : rest



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

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

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

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

  fmToList_LE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_LE fm fr = foldFM_LE fmToList_LE0 [] fr fm

  
fmToList_LE0 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 a => (a  ->  c  ->  b  ->  b)  ->  b  ->  a  ->  FiniteMap a c  ->  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


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

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



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

mainModule FiniteMap
  ((fmToList_LE :: (Ord c, Ord b) => FiniteMap (b,c) a  ->  (b,c)  ->  [((b,c),a)]) :: (Ord c, Ord b) => FiniteMap (b,c) a  ->  (b,c)  ->  [((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 b a) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

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

  fmToList_LE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_LE fm fr = foldFM_LE fmToList_LE0 [] fr fm

  
fmToList_LE0 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  ->  b  ->  a  ->  a)  ->  a  ->  c  ->  FiniteMap c b  ->  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


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

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

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

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



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

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

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

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

  fmToList_LE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_LE fm fr = foldFM_LE fmToList_LE0 [] fr fm

  
fmToList_LE0 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 a => (a  ->  c  ->  b  ->  b)  ->  b  ->  a  ->  FiniteMap a c  ->  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


Replaced joker patterns by fresh variables and removed binding patterns.

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

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

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

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

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

  fmToList_LE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_LE fm fr = foldFM_LE fmToList_LE0 [] fr fm

  
fmToList_LE0 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 c => (c  ->  b  ->  a  ->  a)  ->  a  ->  c  ->  FiniteMap c b  ->  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 b a  ->  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

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

compare0 x y True = GT

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

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
  ((fmToList_LE :: (Ord b, Ord c) => FiniteMap (b,c) a  ->  (b,c)  ->  [((b,c),a)]) :: (Ord c, Ord b) => FiniteMap (b,c) a  ->  (b,c)  ->  [((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 b a) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

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

  fmToList_LE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_LE fm fr = foldFM_LE fmToList_LE0 [] fr fm

  
fmToList_LE0 key elt rest = (key,elt) : rest

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

  foldFM_LE :: Ord c => (c  ->  a  ->  b  ->  b)  ->  b  ->  c  ->  FiniteMap c a  ->  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 a b  ->  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
reduce2Reduce1 vyw vyx x y True = error []
reduce2Reduce1 vyw vyx x y False = reduce2Reduce0 vyw vyx x y otherwise

reduce2D vyw vyx = gcd vyw vyx

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

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

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

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

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

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



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

mainModule FiniteMap
  ((fmToList_LE :: (Ord c, Ord a) => FiniteMap (a,c) b  ->  (a,c)  ->  [((a,c),b)]) :: (Ord c, Ord a) => FiniteMap (a,c) b  ->  (a,c)  ->  [((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 b a) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

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

  fmToList_LE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_LE fm fr = foldFM_LE fmToList_LE0 [] fr fm

  
fmToList_LE0 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 b => (b  ->  a  ->  c  ->  c)  ->  c  ->  b  ->  FiniteMap b a  ->  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 = 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
  (fmToList_LE :: (Ord a, Ord b) => FiniteMap (a,b) c  ->  (a,b)  ->  [((a,b),c)])

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

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

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

  fmToList_LE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_LE fm fr = foldFM_LE fmToList_LE0 [] fr fm

  
fmToList_LE0 key elt rest = (key,elt) : rest

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

  foldFM_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 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_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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primPlusNat(Succ(vyy17400), Succ(vyy401000)) → new_primPlusNat(vyy17400, 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(vyy300100), Succ(vyy40100)) → new_primMulNat(vyy300100, Succ(vyy40100))

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

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



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

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP

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

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

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
                                    ↳ DependencyGraphProof
                                  ↳ QDP

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

new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(ty_Maybe, bfa)) → new_compare32(vyy3000, vyy400, bfa)
new_ltEs1(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bae) → new_ltEs2(vyy3010, vyy410, bbc)
new_lt(vyy300, vyy40, h, ba) → new_compare2(vyy300, vyy40, new_esEs4(vyy300, vyy40, h, ba), h, ba)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_[], fd), ed, ee) → new_lt3(vyy3010, vyy410, fd)
new_primCompAux0(vyy164, vyy165, EQ, app(app(app(ty_@3, bfe), bff), bfg)) → new_compare4(vyy164, vyy165, bfe, bff, bfg)
new_compare2(vyy300, vyy40, False, h, ba) → new_ltEs(vyy300, vyy40, h, ba)
new_ltEs1(Left(vyy3010), Left(vyy410), app(app(ty_Either, bba), bbb), bae) → new_ltEs1(vyy3010, vyy410, bba, bbb)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs0(vyy3010, vyy410, bbh, bca, bcb)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(ty_Maybe, bce)) → new_ltEs2(vyy3010, vyy410, bce)
new_compare1(vyy3000, vyy400, beb, bec) → new_compare3(vyy3000, vyy400, beb, bec)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, ef), eg), eh), ed, ee) → new_lt0(vyy3010, vyy410, ef, eg, eh)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(ty_Maybe, de)) → new_ltEs2(vyy951, vyy961, de)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_Maybe, cb), bd) → new_lt2(vyy950, vyy960, cb)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(app(ty_@2, gh), ha)) → new_ltEs(vyy3012, vyy412, gh, ha)
new_ltEs2(Just(vyy3010), Just(vyy410), app(ty_[], bdg)) → new_ltEs3(vyy3010, vyy410, bdg)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(app(ty_@3, bef), beg), beh)) → new_compare30(vyy3000, vyy400, bef, beg, beh)
new_ltEs1(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, baf), bag), bah), bae) → new_ltEs0(vyy3010, vyy410, baf, bag, bah)
new_ltEs1(Left(vyy3010), Left(vyy410), app(app(ty_@2, bac), bad), bae) → new_ltEs(vyy3010, vyy410, bac, bad)
new_compare(:(vyy3010, vyy3011), :(vyy410, vyy411), bdh) → new_primCompAux(vyy3010, vyy410, vyy3011, vyy411, bdh)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_Maybe, fc), ed, ee) → new_lt2(vyy3010, vyy410, fc)
new_compare31(vyy300, vyy40, baa, bab) → new_compare21(vyy300, vyy40, new_esEs6(vyy300, vyy40, baa, bab), baa, bab)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(ty_[], hh)) → new_ltEs3(vyy3012, vyy412, hh)
new_ltEs3(:(vyy3010, vyy3011), :(vyy410, vyy411), bdh) → new_primCompAux(vyy3010, vyy410, vyy3011, vyy411, bdh)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_[], bfb)) → new_compare(vyy3000, vyy400, bfb)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, bea) → new_primCompAux0(vyy3001, vyy401, new_compare0(vyy3000, vyy400, bea), app(ty_[], bea))
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_@2, beb), bec)) → new_compare3(vyy3000, vyy400, beb, bec)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_Either, fa), fb), ed, ee) → new_lt1(vyy3010, vyy410, fa, fb)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(ty_@2, beb), bec)) → new_compare3(vyy3000, vyy400, beb, bec)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(ty_[], df)) → new_ltEs3(vyy951, vyy961, df)
new_primCompAux0(vyy164, vyy165, EQ, app(ty_Maybe, bgb)) → new_compare6(vyy164, vyy165, bgb)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_@2, bb), bc), bd) → new_lt(vyy950, vyy960, bb, bc)
new_ltEs2(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bda), bdb), bdc)) → new_ltEs0(vyy3010, vyy410, bda, bdb, bdc)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(app(ty_@2, bbf), bbg)) → new_ltEs(vyy3010, vyy410, bbf, bbg)
new_compare4(vyy3000, vyy400, bef, beg, beh) → new_compare30(vyy3000, vyy400, bef, beg, beh)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(app(ty_@3, be), bf), bg), bd) → new_lt0(vyy950, vyy960, be, bf, bg)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_Either, bed), bee)) → new_compare31(vyy3000, vyy400, bed, bee)
new_primCompAux0(vyy164, vyy165, EQ, app(app(ty_@2, bfc), bfd)) → new_compare1(vyy164, vyy165, bfc, bfd)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(app(app(ty_@3, ga), gb), gc), ee) → new_lt0(vyy3011, vyy411, ga, gb, gc)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(ty_[], bcf)) → new_ltEs3(vyy3010, vyy410, bcf)
new_compare5(vyy3000, vyy400, bed, bee) → new_compare31(vyy3000, vyy400, bed, bee)
new_compare30(vyy300, vyy40, dg, dh, ea) → new_compare20(vyy300, vyy40, new_esEs5(vyy300, vyy40, dg, dh, ea), dg, dh, ea)
new_compare21(vyy300, vyy40, False, baa, bab) → new_ltEs1(vyy300, vyy40, baa, bab)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(app(ty_@3, bef), beg), beh)) → new_compare30(vyy3000, vyy400, bef, beg, beh)
new_lt0(vyy300, vyy40, dg, dh, ea) → new_compare20(vyy300, vyy40, new_esEs5(vyy300, vyy40, dg, dh, ea), dg, dh, ea)
new_compare3(vyy300, vyy40, h, ba) → new_compare2(vyy300, vyy40, new_esEs4(vyy300, vyy40, h, ba), h, ba)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_Either, bh), ca), bd) → new_lt1(vyy950, vyy960, bh, ca)
new_ltEs2(Just(vyy3010), Just(vyy410), app(app(ty_Either, bdd), bde)) → new_ltEs1(vyy3010, vyy410, bdd, bde)
new_lt1(vyy300, vyy40, baa, bab) → new_compare21(vyy300, vyy40, new_esEs6(vyy300, vyy40, baa, bab), baa, bab)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(ty_[], bfb)) → new_compare(vyy3000, vyy400, bfb)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(app(ty_Either, gd), ge), ee) → new_lt1(vyy3011, vyy411, gd, ge)
new_primCompAux0(vyy164, vyy165, EQ, app(ty_[], bgc)) → new_compare(vyy164, vyy165, bgc)
new_lt2(vyy300, vyy40, bgd) → new_compare22(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgd), bgd)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs0(vyy3012, vyy412, hb, hc, hd)
new_compare22(vyy300, vyy40, False, bgd) → new_ltEs2(vyy300, vyy40, bgd)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(app(ty_@2, fg), fh), ee) → new_lt(vyy3011, vyy411, fg, fh)
new_ltEs2(Just(vyy3010), Just(vyy410), app(app(ty_@2, bcg), bch)) → new_ltEs(vyy3010, vyy410, bcg, bch)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(ty_Maybe, hg)) → new_ltEs2(vyy3012, vyy412, hg)
new_primCompAux0(vyy164, vyy165, EQ, app(app(ty_Either, bfh), bga)) → new_compare5(vyy164, vyy165, bfh, bga)
new_ltEs2(Just(vyy3010), Just(vyy410), app(ty_Maybe, bdf)) → new_ltEs2(vyy3010, vyy410, bdf)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(app(ty_Either, he), hf)) → new_ltEs1(vyy3012, vyy412, he, hf)
new_ltEs1(Left(vyy3010), Left(vyy410), app(ty_[], bbd), bae) → new_ltEs3(vyy3010, vyy410, bbd)
new_compare6(vyy3000, vyy400, bfa) → new_compare32(vyy3000, vyy400, bfa)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(app(ty_@2, ce), cf)) → new_ltEs(vyy951, vyy961, ce, cf)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_[], cc), bd) → new_lt3(vyy950, vyy960, cc)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(app(ty_Either, bcc), bcd)) → new_ltEs1(vyy3010, vyy410, bcc, bcd)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(ty_Either, bed), bee)) → new_compare31(vyy3000, vyy400, bed, bee)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(ty_[], gg), ee) → new_lt3(vyy3011, vyy411, gg)
new_compare32(vyy300, vyy40, bgd) → new_compare22(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgd), bgd)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(ty_Maybe, gf), ee) → new_lt2(vyy3011, vyy411, gf)
new_compare20(vyy300, vyy40, False, dg, dh, ea) → new_ltEs0(vyy300, vyy40, dg, dh, ea)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(app(ty_Either, dc), dd)) → new_ltEs1(vyy951, vyy961, dc, dd)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_Maybe, bfa)) → new_compare32(vyy3000, vyy400, bfa)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(app(app(ty_@3, cg), da), db)) → new_ltEs0(vyy951, vyy961, cg, da, db)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), bea) → new_primCompAux0(vyy3001, vyy401, new_compare0(vyy3000, vyy400, bea), app(ty_[], bea))
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_@2, eb), ec), ed, ee) → new_lt(vyy3010, vyy410, eb, ec)

The TRS R consists of the following rules:

new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, ccc)) → new_esEs7(vyy3000, vyy400, ccc)
new_esEs20(vyy3011, vyy411, app(ty_Maybe, gf)) → new_esEs7(vyy3011, vyy411, gf)
new_compare0(vyy3000, vyy400, ty_Integer) → new_compare25(vyy3000, vyy400)
new_ltEs16(vyy301, vyy41, bdh) → new_not(new_esEs15(new_compare26(vyy301, vyy41, bdh), GT))
new_ltEs18(vyy3012, vyy412, ty_Float) → new_ltEs8(vyy3012, vyy412)
new_esEs25(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), dg, dh, ea) → new_asAs(new_esEs26(vyy3000, vyy400, dg), new_asAs(new_esEs25(vyy3001, vyy401, dh), new_esEs24(vyy3002, vyy402, ea)))
new_compare10(vyy300, vyy40, True, dg, dh, ea) → LT
new_esEs16(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs10(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs24(vyy3002, vyy402, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs5(vyy3002, vyy402, cgg, cgh, cha)
new_esEs20(vyy3011, vyy411, ty_Double) → new_esEs19(vyy3011, vyy411)
new_esEs13(True, False) → False
new_esEs13(False, True) → False
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs18(:(vyy3000, vyy3001), :(vyy400, vyy401), bea) → new_asAs(new_esEs28(vyy3000, vyy400, bea), new_esEs18(vyy3001, vyy401, bea))
new_compare15(vyy3000, vyy400, beb, bec) → new_compare38(vyy3000, vyy400, beb, bec)
new_ltEs18(vyy3012, vyy412, ty_Integer) → new_ltEs14(vyy3012, vyy412)
new_primCompAux00(vyy164, vyy165, EQ, app(ty_[], bgc)) → new_compare26(vyy164, vyy165, bgc)
new_esEs17(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_primCompAux00(vyy164, vyy165, EQ, ty_Float) → new_compare16(vyy164, vyy165)
new_lt20(vyy950, vyy960, ty_Int) → new_lt10(vyy950, vyy960)
new_esEs24(vyy3002, vyy402, ty_Char) → new_esEs17(vyy3002, vyy402)
new_compare110(vyy300, vyy40, True, baa, bab) → LT
new_compare23(vyy300, vyy40, False, dg, dh, ea) → new_compare10(vyy300, vyy40, new_ltEs4(vyy300, vyy40, dg, dh, ea), dg, dh, ea)
new_lt20(vyy950, vyy960, ty_Float) → new_lt14(vyy950, vyy960)
new_esEs15(EQ, EQ) → True
new_esEs27(vyy950, vyy960, app(ty_Maybe, cb)) → new_esEs7(vyy950, vyy960, cb)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Char) → new_esEs17(vyy3000, vyy400)
new_lt19([], :(vyy400, vyy401), bea) → new_esEs15(LT, LT)
new_ltEs19(vyy951, vyy961, ty_Double) → new_ltEs11(vyy951, vyy961)
new_esEs25(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs19(vyy3000, vyy400)
new_ltEs6(True, False) → False
new_ltEs12(Nothing, Nothing, cfd) → True
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, cbe), cbf)) → new_esEs6(vyy3000, vyy400, cbe, cbf)
new_primMulNat0(Zero, Zero) → Zero
new_lt13(vyy3011, vyy411, ty_@0) → new_lt7(vyy3011, vyy411)
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_Ratio, ccf), bae) → new_ltEs9(vyy3010, vyy410, ccf)
new_lt20(vyy950, vyy960, ty_@0) → new_lt7(vyy950, vyy960)
new_ltEs18(vyy3012, vyy412, ty_Bool) → new_ltEs6(vyy3012, vyy412)
new_esEs25(vyy3001, vyy401, app(app(ty_Either, chf), chg)) → new_esEs6(vyy3001, vyy401, chf, chg)
new_esEs25(vyy3001, vyy401, app(app(ty_@2, chd), che)) → new_esEs4(vyy3001, vyy401, chd, che)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, bab) → new_esEs19(vyy3000, vyy400)
new_ltEs19(vyy951, vyy961, ty_Integer) → new_ltEs14(vyy951, vyy961)
new_lt13(vyy3011, vyy411, app(ty_Maybe, gf)) → new_lt17(vyy3011, vyy411, gf)
new_lt20(vyy950, vyy960, app(app(ty_@2, bb), bc)) → new_lt8(vyy950, vyy960, bb, bc)
new_lt12(vyy3010, vyy410, ty_Char) → new_lt4(vyy3010, vyy410)
new_primCompAux00(vyy164, vyy165, EQ, ty_Bool) → new_compare13(vyy164, vyy165)
new_esEs27(vyy950, vyy960, ty_Integer) → new_esEs12(vyy950, vyy960)
new_esEs24(vyy3002, vyy402, ty_Bool) → new_esEs13(vyy3002, vyy402)
new_esEs20(vyy3011, vyy411, app(ty_Ratio, cfh)) → new_esEs14(vyy3011, vyy411, cfh)
new_compare24(vyy3000, vyy400, bed, bee) → new_compare37(vyy3000, vyy400, bed, bee)
new_ltEs18(vyy3012, vyy412, app(ty_Ratio, cga)) → new_ltEs9(vyy3012, vyy412, cga)
new_ltEs18(vyy3012, vyy412, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs4(vyy3012, vyy412, hb, hc, hd)
new_ltEs13(LT, EQ) → True
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Integer) → new_ltEs14(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Right(vyy410), bbe, bae) → True
new_ltEs12(Just(vyy3010), Just(vyy410), ty_@0) → new_ltEs17(vyy3010, vyy410)
new_esEs9(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Bool) → new_compare13(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, app(ty_Ratio, cfg)) → new_esEs14(vyy3010, vyy410, cfg)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, cbc), cbd)) → new_esEs4(vyy3000, vyy400, cbc, cbd)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(app(ty_Either, bcc), bcd)) → new_ltEs5(vyy3010, vyy410, bcc, bcd)
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, app(app(ty_Either, fa), fb)) → new_esEs6(vyy3010, vyy410, fa, fb)
new_esEs12(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs8(vyy3001, vyy401, app(app(ty_Either, bgg), bgh)) → new_esEs6(vyy3001, vyy401, bgg, bgh)
new_lt19(:(vyy3000, vyy3001), [], bea) → new_esEs15(GT, LT)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, cbg)) → new_esEs14(vyy3000, vyy400, cbg)
new_primCompAux00(vyy164, vyy165, EQ, app(app(app(ty_@3, bfe), bff), bfg)) → new_compare18(vyy164, vyy165, bfe, bff, bfg)
new_esEs9(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_ltEs19(vyy951, vyy961, app(ty_Maybe, de)) → new_ltEs12(vyy951, vyy961, de)
new_esEs8(vyy3001, vyy401, app(app(ty_@2, bge), bgf)) → new_esEs4(vyy3001, vyy401, bge, bgf)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, bef), beg), beh)) → new_esEs5(vyy3000, vyy400, bef, beg, beh)
new_esEs25(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, bab) → new_esEs12(vyy3000, vyy400)
new_compare26([], [], bdh) → EQ
new_ltEs5(Right(vyy3010), Left(vyy410), bbe, bae) → False
new_lt8(vyy300, vyy40, h, ba) → new_esEs15(new_compare38(vyy300, vyy40, h, ba), LT)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Char) → new_ltEs10(vyy3010, vyy410)
new_lt20(vyy950, vyy960, ty_Char) → new_lt4(vyy950, vyy960)
new_esEs8(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_esEs9(vyy3000, vyy400, app(ty_[], cah)) → new_esEs18(vyy3000, vyy400, cah)
new_compare0(vyy3000, vyy400, app(ty_Maybe, bfa)) → new_compare12(vyy3000, vyy400, bfa)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs10(vyy3000, vyy400)
new_primCompAux00(vyy164, vyy165, EQ, ty_@0) → new_compare14(vyy164, vyy165)
new_pePe(False, vyy133) → vyy133
new_esEs24(vyy3002, vyy402, app(ty_Ratio, cgf)) → new_esEs14(vyy3002, vyy402, cgf)
new_primCompAux00(vyy164, vyy165, EQ, app(app(ty_Either, bfh), bga)) → new_compare24(vyy164, vyy165, bfh, bga)
new_primCompAux00(vyy164, vyy165, EQ, app(app(ty_@2, bfc), bfd)) → new_compare15(vyy164, vyy165, bfc, bfd)
new_esEs18(:(vyy3000, vyy3001), [], bea) → False
new_esEs18([], :(vyy400, vyy401), bea) → False
new_esEs14(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cce) → new_asAs(new_esEs23(vyy3000, vyy400, cce), new_esEs22(vyy3001, vyy401, cce))
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, cch), cda), bab) → new_esEs4(vyy3000, vyy400, cch, cda)
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(ty_Ratio, cef)) → new_esEs14(vyy3000, vyy400, cef)
new_esEs8(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_esEs27(vyy950, vyy960, ty_Ordering) → new_esEs15(vyy950, vyy960)
new_esEs24(vyy3002, vyy402, app(ty_Maybe, chb)) → new_esEs7(vyy3002, vyy402, chb)
new_esEs24(vyy3002, vyy402, ty_@0) → new_esEs11(vyy3002, vyy402)
new_compare14(@0, @0) → EQ
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_lt14(vyy300, vyy40) → new_esEs15(new_primCmpFloat(vyy300, vyy40), LT)
new_compare23(vyy300, vyy40, True, dg, dh, ea) → EQ
new_compare9(vyy301, vyy41) → new_primCmpInt(vyy301, vyy41)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Integer) → new_ltEs14(vyy3010, vyy410)
new_ltEs13(EQ, GT) → True
new_esEs15(LT, EQ) → False
new_esEs15(EQ, LT) → False
new_esEs20(vyy3011, vyy411, app(ty_[], gg)) → new_esEs18(vyy3011, vyy411, gg)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_@0) → new_esEs11(vyy3000, vyy400)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_compare0(vyy3000, vyy400, app(app(ty_@2, beb), bec)) → new_compare15(vyy3000, vyy400, beb, bec)
new_compare27(vyy300, vyy40, False, baa, bab) → new_compare110(vyy300, vyy40, new_ltEs5(vyy300, vyy40, baa, bab), baa, bab)
new_esEs21(vyy3010, vyy410, ty_Double) → new_esEs19(vyy3010, vyy410)
new_esEs15(EQ, GT) → False
new_esEs15(GT, EQ) → False
new_ltEs19(vyy951, vyy961, ty_Bool) → new_ltEs6(vyy951, vyy961)
new_esEs6(Left(vyy3000), Right(vyy400), baa, bab) → False
new_esEs6(Right(vyy3000), Left(vyy400), baa, bab) → False
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_Ratio, cfe)) → new_ltEs9(vyy3010, vyy410, cfe)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_lt5(vyy300, vyy40) → new_esEs15(new_compare35(vyy300, vyy40), LT)
new_lt20(vyy950, vyy960, app(ty_Ratio, dca)) → new_lt9(vyy950, vyy960, dca)
new_compare213(vyy300, vyy40, False) → new_compare113(vyy300, vyy40, new_ltEs13(vyy300, vyy40))
new_compare29(vyy3000, vyy400, vyy3001, vyy401) → new_primCmpInt(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt4(vyy300, vyy40) → new_esEs15(new_primCmpChar(vyy300, vyy40), LT)
new_esEs20(vyy3011, vyy411, ty_@0) → new_esEs11(vyy3011, vyy411)
new_esEs9(vyy3000, vyy400, app(ty_Ratio, cac)) → new_esEs14(vyy3000, vyy400, cac)
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_[], bbd), bae) → new_ltEs16(vyy3010, vyy410, bbd)
new_compare0(vyy3000, vyy400, ty_Int) → new_compare9(vyy3000, vyy400)
new_ltEs19(vyy951, vyy961, app(app(app(ty_@3, cg), da), db)) → new_ltEs4(vyy951, vyy961, cg, da, db)
new_primCompAux00(vyy164, vyy165, EQ, ty_Char) → new_compare8(vyy164, vyy165)
new_pePe(True, vyy133) → True
new_primEqNat0(Zero, Zero) → True
new_esEs8(vyy3001, vyy401, app(ty_Maybe, bhe)) → new_esEs7(vyy3001, vyy401, bhe)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_ltEs7(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, bd) → new_pePe(new_lt20(vyy950, vyy960, cd), new_asAs(new_esEs27(vyy950, vyy960, cd), new_ltEs19(vyy951, vyy961, bd)))
new_compare11(vyy300, vyy40, True, bgd) → LT
new_esEs25(vyy3001, vyy401, app(ty_[], dae)) → new_esEs18(vyy3001, vyy401, dae)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat1(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_compare111(vyy300, vyy40, False, h, ba) → GT
new_esEs24(vyy3002, vyy402, app(ty_[], chc)) → new_esEs18(vyy3002, vyy402, chc)
new_esEs20(vyy3011, vyy411, ty_Bool) → new_esEs13(vyy3011, vyy411)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Int, bae) → new_ltEs15(vyy3010, vyy410)
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(app(ty_Either, ced), cee)) → new_esEs6(vyy3000, vyy400, ced, cee)
new_ltEs19(vyy951, vyy961, ty_Float) → new_ltEs8(vyy951, vyy961)
new_compare0(vyy3000, vyy400, ty_Ordering) → new_compare7(vyy3000, vyy400)
new_lt12(vyy3010, vyy410, ty_Ordering) → new_lt18(vyy3010, vyy410)
new_compare110(vyy300, vyy40, False, baa, bab) → GT
new_compare35(vyy300, vyy40) → new_compare211(vyy300, vyy40, new_esEs13(vyy300, vyy40))
new_ltEs18(vyy3012, vyy412, ty_Char) → new_ltEs10(vyy3012, vyy412)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_compare0(vyy3000, vyy400, ty_Float) → new_compare16(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(app(ty_Either, bed), bee)) → new_esEs6(vyy3000, vyy400, bed, bee)
new_ltEs10(vyy301, vyy41) → new_not(new_esEs15(new_compare8(vyy301, vyy41), GT))
new_ltEs4(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, ee) → new_pePe(new_lt12(vyy3010, vyy410, ff), new_asAs(new_esEs21(vyy3010, vyy410, ff), new_pePe(new_lt13(vyy3011, vyy411, ed), new_asAs(new_esEs20(vyy3011, vyy411, ed), new_ltEs18(vyy3012, vyy412, ee)))))
new_ltEs19(vyy951, vyy961, ty_Char) → new_ltEs10(vyy951, vyy961)
new_compare0(vyy3000, vyy400, ty_@0) → new_compare14(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Bool) → new_ltEs6(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(app(ty_Either, he), hf)) → new_ltEs5(vyy3012, vyy412, he, hf)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Bool) → new_ltEs6(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs19(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs10(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs27(vyy950, vyy960, ty_Bool) → new_esEs13(vyy950, vyy960)
new_compare10(vyy300, vyy40, False, dg, dh, ea) → GT
new_compare0(vyy3000, vyy400, app(ty_[], bfb)) → new_compare26(vyy3000, vyy400, bfb)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Integer, bae) → new_ltEs14(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, app(ty_Maybe, fc)) → new_lt17(vyy3010, vyy410, fc)
new_compare26([], :(vyy410, vyy411), bdh) → LT
new_ltEs19(vyy951, vyy961, app(ty_Ratio, dcb)) → new_ltEs9(vyy951, vyy961, dcb)
new_ltEs13(LT, GT) → True
new_compare26(:(vyy3010, vyy3011), [], bdh) → GT
new_esEs21(vyy3010, vyy410, app(ty_[], fd)) → new_esEs18(vyy3010, vyy410, fd)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Double) → new_ltEs11(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_@0) → new_ltEs17(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Char) → new_ltEs10(vyy3010, vyy410)
new_compare7(vyy3000, vyy400) → new_compare33(vyy3000, vyy400)
new_ltEs11(vyy301, vyy41) → new_not(new_esEs15(new_compare19(vyy301, vyy41), GT))
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_lt20(vyy950, vyy960, ty_Integer) → new_lt11(vyy950, vyy960)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, cdd), bab) → new_esEs14(vyy3000, vyy400, cdd)
new_lt13(vyy3011, vyy411, ty_Double) → new_lt15(vyy3011, vyy411)
new_esEs21(vyy3010, vyy410, ty_Ordering) → new_esEs15(vyy3010, vyy410)
new_primPlusNat1(Zero, vyy40100) → Succ(vyy40100)
new_esEs4(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, ba) → new_asAs(new_esEs9(vyy3000, vyy400, h), new_esEs8(vyy3001, vyy401, ba))
new_ltEs9(vyy301, vyy41, cff) → new_not(new_esEs15(new_compare17(vyy301, vyy41, cff), GT))
new_esEs26(vyy3000, vyy400, app(ty_[], dbg)) → new_esEs18(vyy3000, vyy400, dbg)
new_compare0(vyy3000, vyy400, ty_Char) → new_compare8(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_lt20(vyy950, vyy960, app(app(app(ty_@3, be), bf), bg)) → new_lt6(vyy950, vyy960, be, bf, bg)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bae) → new_ltEs12(vyy3010, vyy410, bbc)
new_lt13(vyy3011, vyy411, ty_Float) → new_lt14(vyy3011, vyy411)
new_compare11(vyy300, vyy40, False, bgd) → GT
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Float) → new_ltEs8(vyy3010, vyy410)
new_compare112(vyy300, vyy40, True) → LT
new_ltEs13(GT, LT) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_lt12(vyy3010, vyy410, ty_Double) → new_lt15(vyy3010, vyy410)
new_compare27(vyy300, vyy40, True, baa, bab) → EQ
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(ty_Either, bba), bbb), bae) → new_ltEs5(vyy3010, vyy410, bba, bbb)
new_ltEs13(EQ, EQ) → True
new_ltEs18(vyy3012, vyy412, ty_Ordering) → new_ltEs13(vyy3012, vyy412)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, cde), cdf), cdg), bab) → new_esEs5(vyy3000, vyy400, cde, cdf, cdg)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs20(vyy3011, vyy411, ty_Int) → new_esEs10(vyy3011, vyy411)
new_lt7(@0, @0) → new_esEs15(EQ, LT)
new_ltEs6(False, True) → True
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Int) → new_compare9(new_sr(vyy3010, vyy411), new_sr(vyy410, vyy3011))
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(app(ty_@2, bbf), bbg)) → new_ltEs7(vyy3010, vyy410, bbf, bbg)
new_ltEs15(vyy301, vyy41) → new_not(new_esEs15(new_compare9(vyy301, vyy41), GT))
new_ltEs6(True, True) → True
new_lt9(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cce) → new_esEs15(new_compare28(vyy3000, vyy401, vyy400, vyy3001, cce), LT)
new_lt13(vyy3011, vyy411, app(ty_[], gg)) → new_lt19(vyy3011, vyy411, gg)
new_esEs20(vyy3011, vyy411, ty_Ordering) → new_esEs15(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, app(app(ty_Either, gd), ge)) → new_lt16(vyy3011, vyy411, gd, ge)
new_esEs9(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Ordering, bae) → new_ltEs13(vyy3010, vyy410)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, bab) → new_esEs16(vyy3000, vyy400)
new_primCompAux00(vyy164, vyy165, EQ, ty_Integer) → new_compare25(vyy164, vyy165)
new_esEs9(vyy3000, vyy400, app(app(ty_Either, caa), cab)) → new_esEs6(vyy3000, vyy400, caa, cab)
new_compare212(vyy300, vyy40, True, bgd) → EQ
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs26(vyy3000, vyy400, app(app(ty_@2, daf), dag)) → new_esEs4(vyy3000, vyy400, daf, dag)
new_esEs27(vyy950, vyy960, app(app(app(ty_@3, be), bf), bg)) → new_esEs5(vyy950, vyy960, be, bf, bg)
new_esEs9(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_ltEs18(vyy3012, vyy412, ty_Double) → new_ltEs11(vyy3012, vyy412)
new_esEs7(Nothing, Nothing, bgd) → True
new_ltEs17(vyy301, vyy41) → new_not(new_esEs15(new_compare14(vyy301, vyy41), GT))
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_compare18(vyy3000, vyy400, bef, beg, beh) → new_compare36(vyy3000, vyy400, bef, beg, beh)
new_primPlusNat0(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat0(Succ(vyy17400), Zero) → Succ(vyy17400)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(ty_Maybe, cfb)) → new_esEs7(vyy3000, vyy400, cfb)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_lt20(vyy950, vyy960, ty_Bool) → new_lt5(vyy950, vyy960)
new_esEs8(vyy3001, vyy401, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs5(vyy3001, vyy401, bhb, bhc, bhd)
new_compare210(vyy300, vyy40, False, h, ba) → new_compare111(vyy300, vyy40, new_ltEs7(vyy300, vyy40, h, ba), h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs4(vyy3010, vyy410, bbh, bca, bcb)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Char, bae) → new_ltEs10(vyy3010, vyy410)
new_esEs8(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, app(ty_[], bhf)) → new_esEs18(vyy3001, vyy401, bhf)
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, bab) → new_esEs17(vyy3000, vyy400)
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_lt6(vyy300, vyy40, dg, dh, ea) → new_esEs15(new_compare36(vyy300, vyy40, dg, dh, ea), LT)
new_esEs25(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_lt20(vyy950, vyy960, app(ty_[], cc)) → new_lt19(vyy950, vyy960, cc)
new_esEs24(vyy3002, vyy402, app(app(ty_@2, cgb), cgc)) → new_esEs4(vyy3002, vyy402, cgb, cgc)
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_Maybe, bdf)) → new_ltEs12(vyy3010, vyy410, bdf)
new_esEs7(Just(vyy3000), Nothing, bgd) → False
new_esEs7(Nothing, Just(vyy400), bgd) → False
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Int) → new_ltEs15(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, app(ty_Ratio, cfg)) → new_lt9(vyy3010, vyy410, cfg)
new_compare37(vyy300, vyy40, baa, bab) → new_compare27(vyy300, vyy40, new_esEs6(vyy300, vyy40, baa, bab), baa, bab)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bda), bdb), bdc)) → new_ltEs4(vyy3010, vyy410, bda, bdb, bdc)
new_lt12(vyy3010, vyy410, ty_Float) → new_lt14(vyy3010, vyy410)
new_esEs8(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_ltEs13(GT, EQ) → False
new_ltEs13(EQ, LT) → False
new_lt12(vyy3010, vyy410, ty_Bool) → new_lt5(vyy3010, vyy410)
new_ltEs8(vyy301, vyy41) → new_not(new_esEs15(new_compare16(vyy301, vyy41), GT))
new_compare16(vyy301, vyy41) → new_primCmpFloat(vyy301, vyy41)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dbh)) → new_esEs14(vyy3000, vyy400, dbh)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_lt12(vyy3010, vyy410, ty_Integer) → new_lt11(vyy3010, vyy410)
new_compare113(vyy300, vyy40, True) → LT
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_not(False) → True
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, cdb), cdc), bab) → new_esEs6(vyy3000, vyy400, cdb, cdc)
new_compare210(vyy300, vyy40, True, h, ba) → EQ
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_esEs9(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(ty_@2, bcg), bch)) → new_ltEs7(vyy3010, vyy410, bcg, bch)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, dbb)) → new_esEs14(vyy3000, vyy400, dbb)
new_lt15(vyy300, vyy40) → new_esEs15(new_primCmpDouble(vyy300, vyy40), LT)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_@0, bae) → new_ltEs17(vyy3010, vyy410)
new_compare28(vyy3000, vyy401, vyy400, vyy3001, ty_Int) → new_compare29(vyy3000, vyy401, vyy400, vyy3001)
new_esEs24(vyy3002, vyy402, app(app(ty_Either, cgd), cge)) → new_esEs6(vyy3002, vyy402, cgd, cge)
new_compare113(vyy300, vyy40, False) → GT
new_ltEs18(vyy3012, vyy412, ty_@0) → new_ltEs17(vyy3012, vyy412)
new_lt13(vyy3011, vyy411, ty_Char) → new_lt4(vyy3011, vyy411)
new_compare0(vyy3000, vyy400, app(app(ty_Either, bed), bee)) → new_compare24(vyy3000, vyy400, bed, bee)
new_compare0(vyy3000, vyy400, app(app(app(ty_@3, bef), beg), beh)) → new_compare18(vyy3000, vyy400, bef, beg, beh)
new_lt20(vyy950, vyy960, app(app(ty_Either, bh), ca)) → new_lt16(vyy950, vyy960, bh, ca)
new_esEs24(vyy3002, vyy402, ty_Integer) → new_esEs12(vyy3002, vyy402)
new_lt20(vyy950, vyy960, app(ty_Maybe, cb)) → new_lt17(vyy950, vyy960, cb)
new_lt20(vyy950, vyy960, ty_Ordering) → new_lt18(vyy950, vyy960)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, bab) → new_esEs13(vyy3000, vyy400)
new_esEs27(vyy950, vyy960, app(app(ty_Either, bh), ca)) → new_esEs6(vyy950, vyy960, bh, ca)
new_esEs27(vyy950, vyy960, app(ty_[], cc)) → new_esEs18(vyy950, vyy960, cc)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Ordering) → new_ltEs13(vyy3010, vyy410)
new_lt13(vyy3011, vyy411, ty_Ordering) → new_lt18(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, app(ty_Ratio, cfh)) → new_lt9(vyy3011, vyy411, cfh)
new_lt12(vyy3010, vyy410, app(ty_[], fd)) → new_lt19(vyy3010, vyy410, fd)
new_esEs20(vyy3011, vyy411, app(app(app(ty_@3, ga), gb), gc)) → new_esEs5(vyy3011, vyy411, ga, gb, gc)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs28(vyy3000, vyy400, app(ty_Maybe, bfa)) → new_esEs7(vyy3000, vyy400, bfa)
new_esEs21(vyy3010, vyy410, app(app(app(ty_@3, ef), eg), eh)) → new_esEs5(vyy3010, vyy410, ef, eg, eh)
new_esEs21(vyy3010, vyy410, app(ty_Maybe, fc)) → new_esEs7(vyy3010, vyy410, fc)
new_ltEs19(vyy951, vyy961, app(ty_[], df)) → new_ltEs16(vyy951, vyy961, df)
new_primCompAux00(vyy164, vyy165, EQ, ty_Double) → new_compare19(vyy164, vyy165)
new_lt20(vyy950, vyy960, ty_Double) → new_lt15(vyy950, vyy960)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs21(vyy3010, vyy410, app(app(ty_@2, eb), ec)) → new_esEs4(vyy3010, vyy410, eb, ec)
new_ltEs14(vyy301, vyy41) → new_not(new_esEs15(new_compare25(vyy301, vyy41), GT))
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_lt19(:(vyy3000, vyy3001), :(vyy400, vyy401), bea) → new_esEs15(new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, bea), LT)
new_esEs27(vyy950, vyy960, ty_Char) → new_esEs17(vyy950, vyy960)
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_compare34(vyy300, vyy40, bgd) → new_compare212(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgd), bgd)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Double) → new_esEs19(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs19(vyy951, vyy961, app(app(ty_Either, dc), dd)) → new_ltEs5(vyy951, vyy961, dc, dd)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_esEs27(vyy950, vyy960, ty_@0) → new_esEs11(vyy950, vyy960)
new_primCompAux00(vyy164, vyy165, EQ, ty_Ordering) → new_compare7(vyy164, vyy165)
new_esEs9(vyy3000, vyy400, app(app(app(ty_@3, cad), cae), caf)) → new_esEs5(vyy3000, vyy400, cad, cae, caf)
new_esEs15(LT, GT) → False
new_esEs15(GT, LT) → False
new_esEs8(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_compare211(vyy300, vyy40, False) → new_compare112(vyy300, vyy40, new_ltEs6(vyy300, vyy40))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare12(vyy3000, vyy400, bfa) → new_compare34(vyy3000, vyy400, bfa)
new_lt12(vyy3010, vyy410, app(app(ty_Either, fa), fb)) → new_lt16(vyy3010, vyy410, fa, fb)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(ty_[], bcf)) → new_ltEs16(vyy3010, vyy410, bcf)
new_esEs15(LT, LT) → True
new_esEs11(@0, @0) → True
new_esEs25(vyy3001, vyy401, ty_@0) → new_esEs11(vyy3001, vyy401)
new_esEs20(vyy3011, vyy411, app(app(ty_Either, gd), ge)) → new_esEs6(vyy3011, vyy411, gd, ge)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Double) → new_ltEs11(vyy3010, vyy410)
new_esEs9(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy951, vyy961, ty_@0) → new_ltEs17(vyy951, vyy961)
new_primPlusNat1(Succ(vyy1740), vyy40100) → Succ(Succ(new_primPlusNat0(vyy1740, vyy40100)))
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], cea), bab) → new_esEs18(vyy3000, vyy400, cea)
new_esEs24(vyy3002, vyy402, ty_Double) → new_esEs19(vyy3002, vyy402)
new_compare0(vyy3000, vyy400, app(ty_Ratio, dbh)) → new_compare17(vyy3000, vyy400, dbh)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, bab) → new_esEs15(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, ty_Char) → new_esEs17(vyy3010, vyy410)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, cdh), bab) → new_esEs7(vyy3000, vyy400, cdh)
new_esEs25(vyy3001, vyy401, app(ty_Ratio, chh)) → new_esEs14(vyy3001, vyy401, chh)
new_compare33(vyy300, vyy40) → new_compare213(vyy300, vyy40, new_esEs15(vyy300, vyy40))
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(app(ty_@2, ceb), cec)) → new_esEs4(vyy3000, vyy400, ceb, cec)
new_lt13(vyy3011, vyy411, ty_Bool) → new_lt5(vyy3011, vyy411)
new_esEs8(vyy3001, vyy401, ty_Ordering) → new_esEs15(vyy3001, vyy401)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(ty_Either, bdd), bde)) → new_ltEs5(vyy3010, vyy410, bdd, bde)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Float) → new_ltEs8(vyy3010, vyy410)
new_esEs25(vyy3001, vyy401, app(ty_Maybe, dad)) → new_esEs7(vyy3001, vyy401, dad)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs5(vyy3000, vyy400, cbh, cca, ccb)
new_primCmpFloat(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_esEs9(vyy3000, vyy400, app(app(ty_@2, bhg), bhh)) → new_esEs4(vyy3000, vyy400, bhg, bhh)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Float, bae) → new_ltEs8(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, app(ty_[], bfb)) → new_esEs18(vyy3000, vyy400, bfb)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(vyy950, vyy960, app(ty_Ratio, dca)) → new_esEs14(vyy950, vyy960, dca)
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs11(vyy3000, vyy400)
new_compare8(vyy301, vyy41) → new_primCmpChar(vyy301, vyy41)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(ty_Ratio, ccg)) → new_ltEs9(vyy3010, vyy410, ccg)
new_esEs24(vyy3002, vyy402, ty_Int) → new_esEs10(vyy3002, vyy402)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], ccd)) → new_esEs18(vyy3000, vyy400, ccd)
new_ltEs13(GT, GT) → True
new_lt13(vyy3011, vyy411, ty_Int) → new_lt10(vyy3011, vyy411)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, beb), bec)) → new_esEs4(vyy3000, vyy400, beb, bec)
new_asAs(False, vyy159) → False
new_ltEs19(vyy951, vyy961, app(app(ty_@2, ce), cf)) → new_ltEs7(vyy951, vyy961, ce, cf)
new_lt17(vyy300, vyy40, bgd) → new_esEs15(new_compare34(vyy300, vyy40, bgd), LT)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, bab) → new_esEs11(vyy3000, vyy400)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_lt18(vyy300, vyy40) → new_esEs15(new_compare33(vyy300, vyy40), LT)
new_compare0(vyy3000, vyy400, ty_Double) → new_compare19(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs18([], [], bea) → True
new_esEs21(vyy3010, vyy410, ty_Bool) → new_esEs13(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(app(ty_@2, gh), ha)) → new_ltEs7(vyy3012, vyy412, gh, ha)
new_primCompAux00(vyy164, vyy165, EQ, app(ty_Ratio, cbb)) → new_compare17(vyy164, vyy165, cbb)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, dbf)) → new_esEs7(vyy3000, vyy400, dbf)
new_esEs20(vyy3011, vyy411, ty_Float) → new_esEs16(vyy3011, vyy411)
new_esEs24(vyy3002, vyy402, ty_Ordering) → new_esEs15(vyy3002, vyy402)
new_ltEs18(vyy3012, vyy412, app(ty_Maybe, hg)) → new_ltEs12(vyy3012, vyy412, hg)
new_compare38(vyy300, vyy40, h, ba) → new_compare210(vyy300, vyy40, new_esEs4(vyy300, vyy40, h, ba), h, ba)
new_esEs13(False, False) → True
new_primCompAux00(vyy164, vyy165, LT, cba) → LT
new_primCompAux00(vyy164, vyy165, GT, cba) → GT
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Int) → new_esEs10(vyy3000, vyy400)
new_ltEs12(Nothing, Just(vyy410), cfd) → True
new_esEs20(vyy3011, vyy411, app(app(ty_@2, fg), fh)) → new_esEs4(vyy3011, vyy411, fg, fh)
new_esEs20(vyy3011, vyy411, ty_Integer) → new_esEs12(vyy3011, vyy411)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Ordering) → new_ltEs13(vyy3010, vyy410)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs27(vyy950, vyy960, app(app(ty_@2, bb), bc)) → new_esEs4(vyy950, vyy960, bb, bc)
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Integer) → new_compare25(new_sr0(vyy3010, vyy411), new_sr0(vyy410, vyy3011))
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_[], bdg)) → new_ltEs16(vyy3010, vyy410, bdg)
new_lt12(vyy3010, vyy410, app(app(app(ty_@3, ef), eg), eh)) → new_lt6(vyy3010, vyy410, ef, eg, eh)
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(ty_@2, bac), bad), bae) → new_ltEs7(vyy3010, vyy410, bac, bad)
new_esEs8(vyy3001, vyy401, app(ty_Ratio, bha)) → new_esEs14(vyy3001, vyy401, bha)
new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, bea) → new_primCompAux00(vyy3001, vyy401, new_compare0(vyy3000, vyy400, bea), app(ty_[], bea))
new_compare28(Integer(vyy30000), Integer(vyy4010), vyy400, vyy3001, ty_Integer) → new_compare25(Integer(new_primMulInt(vyy30000, vyy4010)), new_sr0(vyy400, vyy3001))
new_ltEs19(vyy951, vyy961, ty_Int) → new_ltEs15(vyy951, vyy961)
new_lt16(vyy300, vyy40, baa, bab) → new_esEs15(new_compare37(vyy300, vyy40, baa, bab), LT)
new_lt12(vyy3010, vyy410, app(app(ty_@2, eb), ec)) → new_lt8(vyy3010, vyy410, eb, ec)
new_primCompAux00(vyy164, vyy165, EQ, app(ty_Maybe, bgb)) → new_compare12(vyy164, vyy165, bgb)
new_esEs9(vyy3000, vyy400, app(ty_Maybe, cag)) → new_esEs7(vyy3000, vyy400, cag)
new_lt19([], [], bea) → new_esEs15(EQ, LT)
new_esEs25(vyy3001, vyy401, app(app(app(ty_@3, daa), dab), dac)) → new_esEs5(vyy3001, vyy401, daa, dab, dac)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_compare112(vyy300, vyy40, False) → GT
new_primCmpDouble(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_lt13(vyy3011, vyy411, ty_Integer) → new_lt11(vyy3011, vyy411)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_compare36(vyy300, vyy40, dg, dh, ea) → new_compare23(vyy300, vyy40, new_esEs5(vyy300, vyy40, dg, dh, ea), dg, dh, ea)
new_compare19(vyy301, vyy41) → new_primCmpDouble(vyy301, vyy41)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_ltEs13(LT, LT) → True
new_compare213(vyy300, vyy40, True) → EQ
new_esEs25(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(ty_[], cfc)) → new_esEs18(vyy3000, vyy400, cfc)
new_esEs20(vyy3011, vyy411, ty_Char) → new_esEs17(vyy3011, vyy411)
new_lt11(Integer(vyy3000), Integer(vyy400)) → new_esEs15(new_primCmpInt(vyy3000, vyy400), LT)
new_compare212(vyy300, vyy40, False, bgd) → new_compare11(vyy300, vyy40, new_ltEs12(vyy300, vyy40, bgd), bgd)
new_primPlusNat0(Succ(vyy17400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat0(vyy17400, vyy401000)))
new_esEs26(vyy3000, vyy400, app(app(ty_Either, dah), dba)) → new_esEs6(vyy3000, vyy400, dah, dba)
new_esEs21(vyy3010, vyy410, ty_@0) → new_esEs11(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(ty_[], hh)) → new_ltEs16(vyy3012, vyy412, hh)
new_compare111(vyy300, vyy40, True, h, ba) → LT
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(ty_Maybe, bce)) → new_ltEs12(vyy3010, vyy410, bce)
new_compare26(:(vyy3010, vyy3011), :(vyy410, vyy411), bdh) → new_primCompAux1(vyy3010, vyy410, vyy3011, vyy411, bdh)
new_lt12(vyy3010, vyy410, ty_@0) → new_lt7(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Int) → new_ltEs15(vyy3010, vyy410)
new_esEs24(vyy3002, vyy402, ty_Float) → new_esEs16(vyy3002, vyy402)
new_asAs(True, vyy159) → vyy159
new_primCmpChar(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_compare25(Integer(vyy3010), Integer(vyy410)) → new_primCmpInt(vyy3010, vyy410)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs5(vyy3000, vyy400, dbc, dbd, dbe)
new_esEs27(vyy950, vyy960, ty_Float) → new_esEs16(vyy950, vyy960)
new_esEs9(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs13(True, True) → True
new_lt13(vyy3011, vyy411, app(app(app(ty_@3, ga), gb), gc)) → new_lt6(vyy3011, vyy411, ga, gb, gc)
new_esEs8(vyy3001, vyy401, ty_@0) → new_esEs11(vyy3001, vyy401)
new_esEs27(vyy950, vyy960, ty_Int) → new_esEs10(vyy950, vyy960)
new_ltEs12(Just(vyy3010), Nothing, cfd) → False
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, ty_Int) → new_esEs10(vyy3010, vyy410)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Float) → new_esEs16(vyy3000, vyy400)
new_compare211(vyy300, vyy40, True) → EQ
new_lt13(vyy3011, vyy411, app(app(ty_@2, fg), fh)) → new_lt8(vyy3011, vyy411, fg, fh)
new_ltEs6(False, False) → True
new_esEs21(vyy3010, vyy410, ty_Integer) → new_esEs12(vyy3010, vyy410)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs15(GT, GT) → True
new_lt12(vyy3010, vyy410, ty_Int) → new_lt10(vyy3010, vyy410)
new_esEs8(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs10(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Bool, bae) → new_ltEs6(vyy3010, vyy410)
new_esEs25(vyy3001, vyy401, ty_Ordering) → new_esEs15(vyy3001, vyy401)
new_esEs21(vyy3010, vyy410, ty_Float) → new_esEs16(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, baf), bag), bah), bae) → new_ltEs4(vyy3010, vyy410, baf, bag, bah)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs5(vyy3000, vyy400, ceg, ceh, cfa)
new_primCompAux00(vyy164, vyy165, EQ, ty_Int) → new_compare9(vyy164, vyy165)
new_lt10(vyy300, vyy40) → new_esEs15(new_primCmpInt(vyy300, vyy40), LT)
new_ltEs18(vyy3012, vyy412, ty_Int) → new_ltEs15(vyy3012, vyy412)
new_compare13(vyy3000, vyy400) → new_compare35(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Double, bae) → new_ltEs11(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, bab) → new_esEs10(vyy3000, vyy400)
new_not(True) → False
new_ltEs19(vyy951, vyy961, ty_Ordering) → new_ltEs13(vyy951, vyy961)
new_esEs27(vyy950, vyy960, ty_Double) → new_esEs19(vyy950, vyy960)

The set Q consists of the following terms:

new_ltEs18(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_lt14(x0, x1)
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_compare213(x0, x1, False)
new_esEs9(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, x2, x3, ty_Int)
new_esEs25(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(x0, x1, ty_Char)
new_lt11(Integer(x0), Integer(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare110(x0, x1, False, x2, x3)
new_esEs7(Just(x0), Nothing, x1)
new_compare36(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, ty_@0)
new_primCompAux00(x0, x1, LT, x2)
new_lt19(:(x0, x1), :(x2, x3), x4)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_ltEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, ty_Float)
new_compare211(x0, x1, False)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Right(x0), Right(x1), x2, ty_Double)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_esEs28(x0, x1, ty_Int)
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_compare37(x0, x1, x2, x3)
new_compare7(x0, x1)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare0(x0, x1, ty_Char)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_primCompAux00(x0, x1, EQ, ty_@0)
new_esEs11(@0, @0)
new_lt5(x0, x1)
new_esEs8(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_compare26([], :(x0, x1), x2)
new_compare113(x0, x1, True)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_@0)
new_ltEs17(x0, x1)
new_compare26([], [], x0)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare26(:(x0, x1), :(x2, x3), x4)
new_esEs17(Char(x0), Char(x1))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare111(x0, x1, False, x2, x3)
new_lt12(x0, x1, app(ty_[], x2))
new_ltEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs16(x0, x1, x2)
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_primCompAux00(x0, x1, EQ, ty_Int)
new_ltEs6(True, True)
new_sr(x0, x1)
new_ltEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_ltEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_esEs7(Nothing, Nothing, x0)
new_ltEs5(Left(x0), Left(x1), ty_@0, x2)
new_lt12(x0, x1, ty_Char)
new_compare210(x0, x1, True, x2, x3)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Int)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare26(:(x0, x1), [], x2)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare212(x0, x1, True, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare11(x0, x1, True, x2)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare112(x0, x1, True)
new_primEqNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs18([], [], x0)
new_esEs23(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, x1, EQ, ty_Float)
new_ltEs13(EQ, EQ)
new_lt13(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, False, x2)
new_esEs13(False, False)
new_primMulNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt13(x0, x1, ty_Int)
new_primPlusNat0(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_@0)
new_ltEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_compare8(x0, x1)
new_compare23(x0, x1, False, x2, x3, x4)
new_primPlusNat1(Zero, x0)
new_esEs27(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare12(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, ty_Integer)
new_compare0(x0, x1, ty_@0)
new_primCompAux1(x0, x1, x2, x3, x4)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Bool)
new_ltEs13(LT, EQ)
new_ltEs13(EQ, LT)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare25(Integer(x0), Integer(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs18(x0, x1, ty_Integer)
new_esEs9(x0, x1, ty_Int)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare113(x0, x1, False)
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_ltEs14(x0, x1)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt13(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs8(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_@0)
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt13(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs9(x0, x1, ty_@0)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3, x4)
new_esEs26(x0, x1, ty_@0)
new_compare0(x0, x1, ty_Ordering)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_compare213(x0, x1, True)
new_ltEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs9(x0, x1, ty_Char)
new_compare0(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Integer)
new_primCmpChar(Char(x0), Char(x1))
new_lt19([], :(x0, x1), x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt19([], [], x0)
new_compare9(x0, x1)
new_ltEs19(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1, x2)
new_esEs25(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_lt12(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat0(Zero, Zero)
new_compare27(x0, x1, False, x2, x3)
new_lt12(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs5(Left(x0), Right(x1), x2, x3)
new_ltEs5(Right(x0), Left(x1), x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, ty_Double)
new_lt12(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_ltEs19(x0, x1, ty_Bool)
new_lt18(x0, x1)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs15(LT, LT)
new_esEs22(x0, x1, ty_Integer)
new_ltEs6(True, False)
new_ltEs6(False, True)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs10(x0, x1)
new_esEs18([], :(x0, x1), x2)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs15(EQ, GT)
new_esEs15(GT, EQ)
new_ltEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Double)
new_ltEs13(EQ, GT)
new_ltEs13(GT, EQ)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare19(x0, x1)
new_esEs21(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare212(x0, x1, False, x2)
new_compare10(x0, x1, True, x2, x3, x4)
new_lt20(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs12(Nothing, Just(x0), x1)
new_esEs22(x0, x1, ty_Int)
new_lt15(x0, x1)
new_ltEs13(LT, GT)
new_ltEs13(GT, LT)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs6(False, False)
new_ltEs19(x0, x1, ty_Double)
new_lt6(x0, x1, x2, x3, x4)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_compare10(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare14(@0, @0)
new_lt20(x0, x1, ty_Int)
new_lt10(x0, x1)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, ty_Integer)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_ltEs12(Nothing, Nothing, x0)
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_compare35(x0, x1)
new_pePe(False, x0)
new_primCompAux00(x0, x1, GT, x2)
new_compare0(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_@0)
new_esEs10(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, x2, x3)
new_primEqNat0(Zero, Succ(x0))
new_ltEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, ty_Float)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Float)
new_lt7(@0, @0)
new_lt20(x0, x1, ty_Double)
new_compare0(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), x1)
new_compare33(x0, x1)
new_primCmpNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs8(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(LT, LT)
new_esEs8(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_compare0(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs15(GT, GT)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_esEs9(x0, x1, ty_Double)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs15(GT, LT)
new_esEs15(LT, GT)
new_ltEs8(x0, x1)
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(GT, GT)
new_esEs13(False, True)
new_esEs13(True, False)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Double)
new_ltEs5(Right(x0), Right(x1), x2, ty_Bool)
new_compare27(x0, x1, True, x2, x3)
new_ltEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(x0, x1, ty_Integer)
new_compare18(x0, x1, x2, x3, x4)
new_primPlusNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_esEs25(x0, x1, ty_Double)
new_compare16(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_esEs16(Float(x0, x1), Float(x2, x3))
new_esEs13(True, True)
new_compare112(x0, x1, False)
new_esEs15(EQ, EQ)
new_compare38(x0, x1, x2, x3)
new_compare210(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_pePe(True, x0)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs18(:(x0, x1), [], x2)
new_compare111(x0, x1, True, x2, x3)
new_compare211(x0, x1, True)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs28(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare0(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt17(x0, x1, x2)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_lt9(:%(x0, x1), :%(x2, x3), x4)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt8(x0, x1, x2, x3)
new_asAs(False, x0)
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs12(Integer(x0), Integer(x1))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Nothing, x1)
new_asAs(True, x0)
new_compare28(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_lt13(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs15(LT, EQ)
new_esEs15(EQ, LT)
new_compare0(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs9(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Char)
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs5(Right(x0), Right(x1), x2, ty_Float)
new_compare15(x0, x1, x2, x3)
new_lt16(x0, x1, x2, x3)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_lt19(:(x0, x1), [], x2)
new_lt12(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(ty_[], x2))
new_esEs7(Nothing, Just(x0), x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Float)
new_ltEs5(Left(x0), Left(x1), ty_Char, x2)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Double)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Double)
new_compare34(x0, x1, x2)
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Float)
new_lt13(x0, x1, ty_@0)
new_compare13(x0, x1)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 8 less nodes.

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

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

new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(ty_Maybe, bfa)) → new_compare32(vyy3000, vyy400, bfa)
new_ltEs1(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bae) → new_ltEs2(vyy3010, vyy410, bbc)
new_lt(vyy300, vyy40, h, ba) → new_compare2(vyy300, vyy40, new_esEs4(vyy300, vyy40, h, ba), h, ba)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_[], fd), ed, ee) → new_lt3(vyy3010, vyy410, fd)
new_compare2(vyy300, vyy40, False, h, ba) → new_ltEs(vyy300, vyy40, h, ba)
new_ltEs1(Left(vyy3010), Left(vyy410), app(app(ty_Either, bba), bbb), bae) → new_ltEs1(vyy3010, vyy410, bba, bbb)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs0(vyy3010, vyy410, bbh, bca, bcb)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(ty_Maybe, bce)) → new_ltEs2(vyy3010, vyy410, bce)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, ef), eg), eh), ed, ee) → new_lt0(vyy3010, vyy410, ef, eg, eh)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(ty_Maybe, de)) → new_ltEs2(vyy951, vyy961, de)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_Maybe, cb), bd) → new_lt2(vyy950, vyy960, cb)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(app(ty_@2, gh), ha)) → new_ltEs(vyy3012, vyy412, gh, ha)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(app(ty_@3, bef), beg), beh)) → new_compare30(vyy3000, vyy400, bef, beg, beh)
new_ltEs2(Just(vyy3010), Just(vyy410), app(ty_[], bdg)) → new_ltEs3(vyy3010, vyy410, bdg)
new_ltEs1(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, baf), bag), bah), bae) → new_ltEs0(vyy3010, vyy410, baf, bag, bah)
new_ltEs1(Left(vyy3010), Left(vyy410), app(app(ty_@2, bac), bad), bae) → new_ltEs(vyy3010, vyy410, bac, bad)
new_compare(:(vyy3010, vyy3011), :(vyy410, vyy411), bdh) → new_primCompAux(vyy3010, vyy410, vyy3011, vyy411, bdh)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_Maybe, fc), ed, ee) → new_lt2(vyy3010, vyy410, fc)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(ty_[], hh)) → new_ltEs3(vyy3012, vyy412, hh)
new_compare31(vyy300, vyy40, baa, bab) → new_compare21(vyy300, vyy40, new_esEs6(vyy300, vyy40, baa, bab), baa, bab)
new_ltEs3(:(vyy3010, vyy3011), :(vyy410, vyy411), bdh) → new_primCompAux(vyy3010, vyy410, vyy3011, vyy411, bdh)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_[], bfb)) → new_compare(vyy3000, vyy400, bfb)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, bea) → new_primCompAux0(vyy3001, vyy401, new_compare0(vyy3000, vyy400, bea), app(ty_[], bea))
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_Either, fa), fb), ed, ee) → new_lt1(vyy3010, vyy410, fa, fb)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_@2, beb), bec)) → new_compare3(vyy3000, vyy400, beb, bec)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(ty_[], df)) → new_ltEs3(vyy951, vyy961, df)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(ty_@2, beb), bec)) → new_compare3(vyy3000, vyy400, beb, bec)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_@2, bb), bc), bd) → new_lt(vyy950, vyy960, bb, bc)
new_ltEs2(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bda), bdb), bdc)) → new_ltEs0(vyy3010, vyy410, bda, bdb, bdc)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(app(ty_@2, bbf), bbg)) → new_ltEs(vyy3010, vyy410, bbf, bbg)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(app(ty_@3, be), bf), bg), bd) → new_lt0(vyy950, vyy960, be, bf, bg)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_Either, bed), bee)) → new_compare31(vyy3000, vyy400, bed, bee)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(ty_[], bcf)) → new_ltEs3(vyy3010, vyy410, bcf)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(app(app(ty_@3, ga), gb), gc), ee) → new_lt0(vyy3011, vyy411, ga, gb, gc)
new_compare30(vyy300, vyy40, dg, dh, ea) → new_compare20(vyy300, vyy40, new_esEs5(vyy300, vyy40, dg, dh, ea), dg, dh, ea)
new_compare21(vyy300, vyy40, False, baa, bab) → new_ltEs1(vyy300, vyy40, baa, bab)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(app(ty_@3, bef), beg), beh)) → new_compare30(vyy3000, vyy400, bef, beg, beh)
new_lt0(vyy300, vyy40, dg, dh, ea) → new_compare20(vyy300, vyy40, new_esEs5(vyy300, vyy40, dg, dh, ea), dg, dh, ea)
new_compare3(vyy300, vyy40, h, ba) → new_compare2(vyy300, vyy40, new_esEs4(vyy300, vyy40, h, ba), h, ba)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_Either, bh), ca), bd) → new_lt1(vyy950, vyy960, bh, ca)
new_ltEs2(Just(vyy3010), Just(vyy410), app(app(ty_Either, bdd), bde)) → new_ltEs1(vyy3010, vyy410, bdd, bde)
new_lt1(vyy300, vyy40, baa, bab) → new_compare21(vyy300, vyy40, new_esEs6(vyy300, vyy40, baa, bab), baa, bab)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(ty_[], bfb)) → new_compare(vyy3000, vyy400, bfb)
new_lt2(vyy300, vyy40, bgd) → new_compare22(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgd), bgd)
new_primCompAux0(vyy164, vyy165, EQ, app(ty_[], bgc)) → new_compare(vyy164, vyy165, bgc)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(app(ty_Either, gd), ge), ee) → new_lt1(vyy3011, vyy411, gd, ge)
new_compare22(vyy300, vyy40, False, bgd) → new_ltEs2(vyy300, vyy40, bgd)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs0(vyy3012, vyy412, hb, hc, hd)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(app(ty_@2, fg), fh), ee) → new_lt(vyy3011, vyy411, fg, fh)
new_ltEs2(Just(vyy3010), Just(vyy410), app(app(ty_@2, bcg), bch)) → new_ltEs(vyy3010, vyy410, bcg, bch)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(ty_Maybe, hg)) → new_ltEs2(vyy3012, vyy412, hg)
new_ltEs2(Just(vyy3010), Just(vyy410), app(ty_Maybe, bdf)) → new_ltEs2(vyy3010, vyy410, bdf)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(app(ty_Either, he), hf)) → new_ltEs1(vyy3012, vyy412, he, hf)
new_ltEs1(Left(vyy3010), Left(vyy410), app(ty_[], bbd), bae) → new_ltEs3(vyy3010, vyy410, bbd)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(app(ty_@2, ce), cf)) → new_ltEs(vyy951, vyy961, ce, cf)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_[], cc), bd) → new_lt3(vyy950, vyy960, cc)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(app(ty_Either, bcc), bcd)) → new_ltEs1(vyy3010, vyy410, bcc, bcd)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(ty_Either, bed), bee)) → new_compare31(vyy3000, vyy400, bed, bee)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(ty_[], gg), ee) → new_lt3(vyy3011, vyy411, gg)
new_compare32(vyy300, vyy40, bgd) → new_compare22(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgd), bgd)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(ty_Maybe, gf), ee) → new_lt2(vyy3011, vyy411, gf)
new_compare20(vyy300, vyy40, False, dg, dh, ea) → new_ltEs0(vyy300, vyy40, dg, dh, ea)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(app(ty_Either, dc), dd)) → new_ltEs1(vyy951, vyy961, dc, dd)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_Maybe, bfa)) → new_compare32(vyy3000, vyy400, bfa)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(app(app(ty_@3, cg), da), db)) → new_ltEs0(vyy951, vyy961, cg, da, db)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), bea) → new_primCompAux0(vyy3001, vyy401, new_compare0(vyy3000, vyy400, bea), app(ty_[], bea))
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_@2, eb), ec), ed, ee) → new_lt(vyy3010, vyy410, eb, ec)

The TRS R consists of the following rules:

new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, ccc)) → new_esEs7(vyy3000, vyy400, ccc)
new_esEs20(vyy3011, vyy411, app(ty_Maybe, gf)) → new_esEs7(vyy3011, vyy411, gf)
new_compare0(vyy3000, vyy400, ty_Integer) → new_compare25(vyy3000, vyy400)
new_ltEs16(vyy301, vyy41, bdh) → new_not(new_esEs15(new_compare26(vyy301, vyy41, bdh), GT))
new_ltEs18(vyy3012, vyy412, ty_Float) → new_ltEs8(vyy3012, vyy412)
new_esEs25(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), dg, dh, ea) → new_asAs(new_esEs26(vyy3000, vyy400, dg), new_asAs(new_esEs25(vyy3001, vyy401, dh), new_esEs24(vyy3002, vyy402, ea)))
new_compare10(vyy300, vyy40, True, dg, dh, ea) → LT
new_esEs16(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs10(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs24(vyy3002, vyy402, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs5(vyy3002, vyy402, cgg, cgh, cha)
new_esEs20(vyy3011, vyy411, ty_Double) → new_esEs19(vyy3011, vyy411)
new_esEs13(True, False) → False
new_esEs13(False, True) → False
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs18(:(vyy3000, vyy3001), :(vyy400, vyy401), bea) → new_asAs(new_esEs28(vyy3000, vyy400, bea), new_esEs18(vyy3001, vyy401, bea))
new_compare15(vyy3000, vyy400, beb, bec) → new_compare38(vyy3000, vyy400, beb, bec)
new_ltEs18(vyy3012, vyy412, ty_Integer) → new_ltEs14(vyy3012, vyy412)
new_primCompAux00(vyy164, vyy165, EQ, app(ty_[], bgc)) → new_compare26(vyy164, vyy165, bgc)
new_esEs17(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_primCompAux00(vyy164, vyy165, EQ, ty_Float) → new_compare16(vyy164, vyy165)
new_lt20(vyy950, vyy960, ty_Int) → new_lt10(vyy950, vyy960)
new_esEs24(vyy3002, vyy402, ty_Char) → new_esEs17(vyy3002, vyy402)
new_compare110(vyy300, vyy40, True, baa, bab) → LT
new_compare23(vyy300, vyy40, False, dg, dh, ea) → new_compare10(vyy300, vyy40, new_ltEs4(vyy300, vyy40, dg, dh, ea), dg, dh, ea)
new_lt20(vyy950, vyy960, ty_Float) → new_lt14(vyy950, vyy960)
new_esEs15(EQ, EQ) → True
new_esEs27(vyy950, vyy960, app(ty_Maybe, cb)) → new_esEs7(vyy950, vyy960, cb)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Char) → new_esEs17(vyy3000, vyy400)
new_lt19([], :(vyy400, vyy401), bea) → new_esEs15(LT, LT)
new_ltEs19(vyy951, vyy961, ty_Double) → new_ltEs11(vyy951, vyy961)
new_esEs25(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs19(vyy3000, vyy400)
new_ltEs6(True, False) → False
new_ltEs12(Nothing, Nothing, cfd) → True
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, cbe), cbf)) → new_esEs6(vyy3000, vyy400, cbe, cbf)
new_primMulNat0(Zero, Zero) → Zero
new_lt13(vyy3011, vyy411, ty_@0) → new_lt7(vyy3011, vyy411)
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_Ratio, ccf), bae) → new_ltEs9(vyy3010, vyy410, ccf)
new_lt20(vyy950, vyy960, ty_@0) → new_lt7(vyy950, vyy960)
new_ltEs18(vyy3012, vyy412, ty_Bool) → new_ltEs6(vyy3012, vyy412)
new_esEs25(vyy3001, vyy401, app(app(ty_Either, chf), chg)) → new_esEs6(vyy3001, vyy401, chf, chg)
new_esEs25(vyy3001, vyy401, app(app(ty_@2, chd), che)) → new_esEs4(vyy3001, vyy401, chd, che)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, bab) → new_esEs19(vyy3000, vyy400)
new_ltEs19(vyy951, vyy961, ty_Integer) → new_ltEs14(vyy951, vyy961)
new_lt13(vyy3011, vyy411, app(ty_Maybe, gf)) → new_lt17(vyy3011, vyy411, gf)
new_lt20(vyy950, vyy960, app(app(ty_@2, bb), bc)) → new_lt8(vyy950, vyy960, bb, bc)
new_lt12(vyy3010, vyy410, ty_Char) → new_lt4(vyy3010, vyy410)
new_primCompAux00(vyy164, vyy165, EQ, ty_Bool) → new_compare13(vyy164, vyy165)
new_esEs27(vyy950, vyy960, ty_Integer) → new_esEs12(vyy950, vyy960)
new_esEs24(vyy3002, vyy402, ty_Bool) → new_esEs13(vyy3002, vyy402)
new_esEs20(vyy3011, vyy411, app(ty_Ratio, cfh)) → new_esEs14(vyy3011, vyy411, cfh)
new_compare24(vyy3000, vyy400, bed, bee) → new_compare37(vyy3000, vyy400, bed, bee)
new_ltEs18(vyy3012, vyy412, app(ty_Ratio, cga)) → new_ltEs9(vyy3012, vyy412, cga)
new_ltEs18(vyy3012, vyy412, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs4(vyy3012, vyy412, hb, hc, hd)
new_ltEs13(LT, EQ) → True
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Integer) → new_ltEs14(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Right(vyy410), bbe, bae) → True
new_ltEs12(Just(vyy3010), Just(vyy410), ty_@0) → new_ltEs17(vyy3010, vyy410)
new_esEs9(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Bool) → new_compare13(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, app(ty_Ratio, cfg)) → new_esEs14(vyy3010, vyy410, cfg)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, cbc), cbd)) → new_esEs4(vyy3000, vyy400, cbc, cbd)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(app(ty_Either, bcc), bcd)) → new_ltEs5(vyy3010, vyy410, bcc, bcd)
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, app(app(ty_Either, fa), fb)) → new_esEs6(vyy3010, vyy410, fa, fb)
new_esEs12(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs8(vyy3001, vyy401, app(app(ty_Either, bgg), bgh)) → new_esEs6(vyy3001, vyy401, bgg, bgh)
new_lt19(:(vyy3000, vyy3001), [], bea) → new_esEs15(GT, LT)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, cbg)) → new_esEs14(vyy3000, vyy400, cbg)
new_primCompAux00(vyy164, vyy165, EQ, app(app(app(ty_@3, bfe), bff), bfg)) → new_compare18(vyy164, vyy165, bfe, bff, bfg)
new_esEs9(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_ltEs19(vyy951, vyy961, app(ty_Maybe, de)) → new_ltEs12(vyy951, vyy961, de)
new_esEs8(vyy3001, vyy401, app(app(ty_@2, bge), bgf)) → new_esEs4(vyy3001, vyy401, bge, bgf)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, bef), beg), beh)) → new_esEs5(vyy3000, vyy400, bef, beg, beh)
new_esEs25(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, bab) → new_esEs12(vyy3000, vyy400)
new_compare26([], [], bdh) → EQ
new_ltEs5(Right(vyy3010), Left(vyy410), bbe, bae) → False
new_lt8(vyy300, vyy40, h, ba) → new_esEs15(new_compare38(vyy300, vyy40, h, ba), LT)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Char) → new_ltEs10(vyy3010, vyy410)
new_lt20(vyy950, vyy960, ty_Char) → new_lt4(vyy950, vyy960)
new_esEs8(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_esEs9(vyy3000, vyy400, app(ty_[], cah)) → new_esEs18(vyy3000, vyy400, cah)
new_compare0(vyy3000, vyy400, app(ty_Maybe, bfa)) → new_compare12(vyy3000, vyy400, bfa)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs10(vyy3000, vyy400)
new_primCompAux00(vyy164, vyy165, EQ, ty_@0) → new_compare14(vyy164, vyy165)
new_pePe(False, vyy133) → vyy133
new_esEs24(vyy3002, vyy402, app(ty_Ratio, cgf)) → new_esEs14(vyy3002, vyy402, cgf)
new_primCompAux00(vyy164, vyy165, EQ, app(app(ty_Either, bfh), bga)) → new_compare24(vyy164, vyy165, bfh, bga)
new_primCompAux00(vyy164, vyy165, EQ, app(app(ty_@2, bfc), bfd)) → new_compare15(vyy164, vyy165, bfc, bfd)
new_esEs18(:(vyy3000, vyy3001), [], bea) → False
new_esEs18([], :(vyy400, vyy401), bea) → False
new_esEs14(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cce) → new_asAs(new_esEs23(vyy3000, vyy400, cce), new_esEs22(vyy3001, vyy401, cce))
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, cch), cda), bab) → new_esEs4(vyy3000, vyy400, cch, cda)
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(ty_Ratio, cef)) → new_esEs14(vyy3000, vyy400, cef)
new_esEs8(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_esEs27(vyy950, vyy960, ty_Ordering) → new_esEs15(vyy950, vyy960)
new_esEs24(vyy3002, vyy402, app(ty_Maybe, chb)) → new_esEs7(vyy3002, vyy402, chb)
new_esEs24(vyy3002, vyy402, ty_@0) → new_esEs11(vyy3002, vyy402)
new_compare14(@0, @0) → EQ
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_lt14(vyy300, vyy40) → new_esEs15(new_primCmpFloat(vyy300, vyy40), LT)
new_compare23(vyy300, vyy40, True, dg, dh, ea) → EQ
new_compare9(vyy301, vyy41) → new_primCmpInt(vyy301, vyy41)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Integer) → new_ltEs14(vyy3010, vyy410)
new_ltEs13(EQ, GT) → True
new_esEs15(LT, EQ) → False
new_esEs15(EQ, LT) → False
new_esEs20(vyy3011, vyy411, app(ty_[], gg)) → new_esEs18(vyy3011, vyy411, gg)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_@0) → new_esEs11(vyy3000, vyy400)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_compare0(vyy3000, vyy400, app(app(ty_@2, beb), bec)) → new_compare15(vyy3000, vyy400, beb, bec)
new_compare27(vyy300, vyy40, False, baa, bab) → new_compare110(vyy300, vyy40, new_ltEs5(vyy300, vyy40, baa, bab), baa, bab)
new_esEs21(vyy3010, vyy410, ty_Double) → new_esEs19(vyy3010, vyy410)
new_esEs15(EQ, GT) → False
new_esEs15(GT, EQ) → False
new_ltEs19(vyy951, vyy961, ty_Bool) → new_ltEs6(vyy951, vyy961)
new_esEs6(Left(vyy3000), Right(vyy400), baa, bab) → False
new_esEs6(Right(vyy3000), Left(vyy400), baa, bab) → False
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_Ratio, cfe)) → new_ltEs9(vyy3010, vyy410, cfe)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_lt5(vyy300, vyy40) → new_esEs15(new_compare35(vyy300, vyy40), LT)
new_lt20(vyy950, vyy960, app(ty_Ratio, dca)) → new_lt9(vyy950, vyy960, dca)
new_compare213(vyy300, vyy40, False) → new_compare113(vyy300, vyy40, new_ltEs13(vyy300, vyy40))
new_compare29(vyy3000, vyy400, vyy3001, vyy401) → new_primCmpInt(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt4(vyy300, vyy40) → new_esEs15(new_primCmpChar(vyy300, vyy40), LT)
new_esEs20(vyy3011, vyy411, ty_@0) → new_esEs11(vyy3011, vyy411)
new_esEs9(vyy3000, vyy400, app(ty_Ratio, cac)) → new_esEs14(vyy3000, vyy400, cac)
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_[], bbd), bae) → new_ltEs16(vyy3010, vyy410, bbd)
new_compare0(vyy3000, vyy400, ty_Int) → new_compare9(vyy3000, vyy400)
new_ltEs19(vyy951, vyy961, app(app(app(ty_@3, cg), da), db)) → new_ltEs4(vyy951, vyy961, cg, da, db)
new_primCompAux00(vyy164, vyy165, EQ, ty_Char) → new_compare8(vyy164, vyy165)
new_pePe(True, vyy133) → True
new_primEqNat0(Zero, Zero) → True
new_esEs8(vyy3001, vyy401, app(ty_Maybe, bhe)) → new_esEs7(vyy3001, vyy401, bhe)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_ltEs7(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, bd) → new_pePe(new_lt20(vyy950, vyy960, cd), new_asAs(new_esEs27(vyy950, vyy960, cd), new_ltEs19(vyy951, vyy961, bd)))
new_compare11(vyy300, vyy40, True, bgd) → LT
new_esEs25(vyy3001, vyy401, app(ty_[], dae)) → new_esEs18(vyy3001, vyy401, dae)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat1(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_compare111(vyy300, vyy40, False, h, ba) → GT
new_esEs24(vyy3002, vyy402, app(ty_[], chc)) → new_esEs18(vyy3002, vyy402, chc)
new_esEs20(vyy3011, vyy411, ty_Bool) → new_esEs13(vyy3011, vyy411)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Int, bae) → new_ltEs15(vyy3010, vyy410)
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(app(ty_Either, ced), cee)) → new_esEs6(vyy3000, vyy400, ced, cee)
new_ltEs19(vyy951, vyy961, ty_Float) → new_ltEs8(vyy951, vyy961)
new_compare0(vyy3000, vyy400, ty_Ordering) → new_compare7(vyy3000, vyy400)
new_lt12(vyy3010, vyy410, ty_Ordering) → new_lt18(vyy3010, vyy410)
new_compare110(vyy300, vyy40, False, baa, bab) → GT
new_compare35(vyy300, vyy40) → new_compare211(vyy300, vyy40, new_esEs13(vyy300, vyy40))
new_ltEs18(vyy3012, vyy412, ty_Char) → new_ltEs10(vyy3012, vyy412)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_compare0(vyy3000, vyy400, ty_Float) → new_compare16(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(app(ty_Either, bed), bee)) → new_esEs6(vyy3000, vyy400, bed, bee)
new_ltEs10(vyy301, vyy41) → new_not(new_esEs15(new_compare8(vyy301, vyy41), GT))
new_ltEs4(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, ee) → new_pePe(new_lt12(vyy3010, vyy410, ff), new_asAs(new_esEs21(vyy3010, vyy410, ff), new_pePe(new_lt13(vyy3011, vyy411, ed), new_asAs(new_esEs20(vyy3011, vyy411, ed), new_ltEs18(vyy3012, vyy412, ee)))))
new_ltEs19(vyy951, vyy961, ty_Char) → new_ltEs10(vyy951, vyy961)
new_compare0(vyy3000, vyy400, ty_@0) → new_compare14(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Bool) → new_ltEs6(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(app(ty_Either, he), hf)) → new_ltEs5(vyy3012, vyy412, he, hf)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Bool) → new_ltEs6(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs19(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs10(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs27(vyy950, vyy960, ty_Bool) → new_esEs13(vyy950, vyy960)
new_compare10(vyy300, vyy40, False, dg, dh, ea) → GT
new_compare0(vyy3000, vyy400, app(ty_[], bfb)) → new_compare26(vyy3000, vyy400, bfb)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Integer, bae) → new_ltEs14(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, app(ty_Maybe, fc)) → new_lt17(vyy3010, vyy410, fc)
new_compare26([], :(vyy410, vyy411), bdh) → LT
new_ltEs19(vyy951, vyy961, app(ty_Ratio, dcb)) → new_ltEs9(vyy951, vyy961, dcb)
new_ltEs13(LT, GT) → True
new_compare26(:(vyy3010, vyy3011), [], bdh) → GT
new_esEs21(vyy3010, vyy410, app(ty_[], fd)) → new_esEs18(vyy3010, vyy410, fd)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Double) → new_ltEs11(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_@0) → new_ltEs17(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Char) → new_ltEs10(vyy3010, vyy410)
new_compare7(vyy3000, vyy400) → new_compare33(vyy3000, vyy400)
new_ltEs11(vyy301, vyy41) → new_not(new_esEs15(new_compare19(vyy301, vyy41), GT))
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_lt20(vyy950, vyy960, ty_Integer) → new_lt11(vyy950, vyy960)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, cdd), bab) → new_esEs14(vyy3000, vyy400, cdd)
new_lt13(vyy3011, vyy411, ty_Double) → new_lt15(vyy3011, vyy411)
new_esEs21(vyy3010, vyy410, ty_Ordering) → new_esEs15(vyy3010, vyy410)
new_primPlusNat1(Zero, vyy40100) → Succ(vyy40100)
new_esEs4(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, ba) → new_asAs(new_esEs9(vyy3000, vyy400, h), new_esEs8(vyy3001, vyy401, ba))
new_ltEs9(vyy301, vyy41, cff) → new_not(new_esEs15(new_compare17(vyy301, vyy41, cff), GT))
new_esEs26(vyy3000, vyy400, app(ty_[], dbg)) → new_esEs18(vyy3000, vyy400, dbg)
new_compare0(vyy3000, vyy400, ty_Char) → new_compare8(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_lt20(vyy950, vyy960, app(app(app(ty_@3, be), bf), bg)) → new_lt6(vyy950, vyy960, be, bf, bg)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bae) → new_ltEs12(vyy3010, vyy410, bbc)
new_lt13(vyy3011, vyy411, ty_Float) → new_lt14(vyy3011, vyy411)
new_compare11(vyy300, vyy40, False, bgd) → GT
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Float) → new_ltEs8(vyy3010, vyy410)
new_compare112(vyy300, vyy40, True) → LT
new_ltEs13(GT, LT) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_lt12(vyy3010, vyy410, ty_Double) → new_lt15(vyy3010, vyy410)
new_compare27(vyy300, vyy40, True, baa, bab) → EQ
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(ty_Either, bba), bbb), bae) → new_ltEs5(vyy3010, vyy410, bba, bbb)
new_ltEs13(EQ, EQ) → True
new_ltEs18(vyy3012, vyy412, ty_Ordering) → new_ltEs13(vyy3012, vyy412)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, cde), cdf), cdg), bab) → new_esEs5(vyy3000, vyy400, cde, cdf, cdg)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs20(vyy3011, vyy411, ty_Int) → new_esEs10(vyy3011, vyy411)
new_lt7(@0, @0) → new_esEs15(EQ, LT)
new_ltEs6(False, True) → True
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Int) → new_compare9(new_sr(vyy3010, vyy411), new_sr(vyy410, vyy3011))
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(app(ty_@2, bbf), bbg)) → new_ltEs7(vyy3010, vyy410, bbf, bbg)
new_ltEs15(vyy301, vyy41) → new_not(new_esEs15(new_compare9(vyy301, vyy41), GT))
new_ltEs6(True, True) → True
new_lt9(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cce) → new_esEs15(new_compare28(vyy3000, vyy401, vyy400, vyy3001, cce), LT)
new_lt13(vyy3011, vyy411, app(ty_[], gg)) → new_lt19(vyy3011, vyy411, gg)
new_esEs20(vyy3011, vyy411, ty_Ordering) → new_esEs15(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, app(app(ty_Either, gd), ge)) → new_lt16(vyy3011, vyy411, gd, ge)
new_esEs9(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Ordering, bae) → new_ltEs13(vyy3010, vyy410)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, bab) → new_esEs16(vyy3000, vyy400)
new_primCompAux00(vyy164, vyy165, EQ, ty_Integer) → new_compare25(vyy164, vyy165)
new_esEs9(vyy3000, vyy400, app(app(ty_Either, caa), cab)) → new_esEs6(vyy3000, vyy400, caa, cab)
new_compare212(vyy300, vyy40, True, bgd) → EQ
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_esEs26(vyy3000, vyy400, app(app(ty_@2, daf), dag)) → new_esEs4(vyy3000, vyy400, daf, dag)
new_esEs27(vyy950, vyy960, app(app(app(ty_@3, be), bf), bg)) → new_esEs5(vyy950, vyy960, be, bf, bg)
new_esEs9(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_ltEs18(vyy3012, vyy412, ty_Double) → new_ltEs11(vyy3012, vyy412)
new_esEs7(Nothing, Nothing, bgd) → True
new_ltEs17(vyy301, vyy41) → new_not(new_esEs15(new_compare14(vyy301, vyy41), GT))
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_compare18(vyy3000, vyy400, bef, beg, beh) → new_compare36(vyy3000, vyy400, bef, beg, beh)
new_primPlusNat0(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat0(Succ(vyy17400), Zero) → Succ(vyy17400)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(ty_Maybe, cfb)) → new_esEs7(vyy3000, vyy400, cfb)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_lt20(vyy950, vyy960, ty_Bool) → new_lt5(vyy950, vyy960)
new_esEs8(vyy3001, vyy401, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs5(vyy3001, vyy401, bhb, bhc, bhd)
new_compare210(vyy300, vyy40, False, h, ba) → new_compare111(vyy300, vyy40, new_ltEs7(vyy300, vyy40, h, ba), h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs4(vyy3010, vyy410, bbh, bca, bcb)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Char, bae) → new_ltEs10(vyy3010, vyy410)
new_esEs8(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, app(ty_[], bhf)) → new_esEs18(vyy3001, vyy401, bhf)
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, bab) → new_esEs17(vyy3000, vyy400)
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_lt6(vyy300, vyy40, dg, dh, ea) → new_esEs15(new_compare36(vyy300, vyy40, dg, dh, ea), LT)
new_esEs25(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_lt20(vyy950, vyy960, app(ty_[], cc)) → new_lt19(vyy950, vyy960, cc)
new_esEs24(vyy3002, vyy402, app(app(ty_@2, cgb), cgc)) → new_esEs4(vyy3002, vyy402, cgb, cgc)
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_Maybe, bdf)) → new_ltEs12(vyy3010, vyy410, bdf)
new_esEs7(Just(vyy3000), Nothing, bgd) → False
new_esEs7(Nothing, Just(vyy400), bgd) → False
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Int) → new_ltEs15(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, app(ty_Ratio, cfg)) → new_lt9(vyy3010, vyy410, cfg)
new_compare37(vyy300, vyy40, baa, bab) → new_compare27(vyy300, vyy40, new_esEs6(vyy300, vyy40, baa, bab), baa, bab)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bda), bdb), bdc)) → new_ltEs4(vyy3010, vyy410, bda, bdb, bdc)
new_lt12(vyy3010, vyy410, ty_Float) → new_lt14(vyy3010, vyy410)
new_esEs8(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_ltEs13(GT, EQ) → False
new_ltEs13(EQ, LT) → False
new_lt12(vyy3010, vyy410, ty_Bool) → new_lt5(vyy3010, vyy410)
new_ltEs8(vyy301, vyy41) → new_not(new_esEs15(new_compare16(vyy301, vyy41), GT))
new_compare16(vyy301, vyy41) → new_primCmpFloat(vyy301, vyy41)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dbh)) → new_esEs14(vyy3000, vyy400, dbh)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_lt12(vyy3010, vyy410, ty_Integer) → new_lt11(vyy3010, vyy410)
new_compare113(vyy300, vyy40, True) → LT
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_not(False) → True
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, cdb), cdc), bab) → new_esEs6(vyy3000, vyy400, cdb, cdc)
new_compare210(vyy300, vyy40, True, h, ba) → EQ
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_esEs9(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(ty_@2, bcg), bch)) → new_ltEs7(vyy3010, vyy410, bcg, bch)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, dbb)) → new_esEs14(vyy3000, vyy400, dbb)
new_lt15(vyy300, vyy40) → new_esEs15(new_primCmpDouble(vyy300, vyy40), LT)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_@0, bae) → new_ltEs17(vyy3010, vyy410)
new_compare28(vyy3000, vyy401, vyy400, vyy3001, ty_Int) → new_compare29(vyy3000, vyy401, vyy400, vyy3001)
new_esEs24(vyy3002, vyy402, app(app(ty_Either, cgd), cge)) → new_esEs6(vyy3002, vyy402, cgd, cge)
new_compare113(vyy300, vyy40, False) → GT
new_ltEs18(vyy3012, vyy412, ty_@0) → new_ltEs17(vyy3012, vyy412)
new_lt13(vyy3011, vyy411, ty_Char) → new_lt4(vyy3011, vyy411)
new_compare0(vyy3000, vyy400, app(app(ty_Either, bed), bee)) → new_compare24(vyy3000, vyy400, bed, bee)
new_compare0(vyy3000, vyy400, app(app(app(ty_@3, bef), beg), beh)) → new_compare18(vyy3000, vyy400, bef, beg, beh)
new_lt20(vyy950, vyy960, app(app(ty_Either, bh), ca)) → new_lt16(vyy950, vyy960, bh, ca)
new_esEs24(vyy3002, vyy402, ty_Integer) → new_esEs12(vyy3002, vyy402)
new_lt20(vyy950, vyy960, app(ty_Maybe, cb)) → new_lt17(vyy950, vyy960, cb)
new_lt20(vyy950, vyy960, ty_Ordering) → new_lt18(vyy950, vyy960)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, bab) → new_esEs13(vyy3000, vyy400)
new_esEs27(vyy950, vyy960, app(app(ty_Either, bh), ca)) → new_esEs6(vyy950, vyy960, bh, ca)
new_esEs27(vyy950, vyy960, app(ty_[], cc)) → new_esEs18(vyy950, vyy960, cc)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Ordering) → new_ltEs13(vyy3010, vyy410)
new_lt13(vyy3011, vyy411, ty_Ordering) → new_lt18(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, app(ty_Ratio, cfh)) → new_lt9(vyy3011, vyy411, cfh)
new_lt12(vyy3010, vyy410, app(ty_[], fd)) → new_lt19(vyy3010, vyy410, fd)
new_esEs20(vyy3011, vyy411, app(app(app(ty_@3, ga), gb), gc)) → new_esEs5(vyy3011, vyy411, ga, gb, gc)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs28(vyy3000, vyy400, app(ty_Maybe, bfa)) → new_esEs7(vyy3000, vyy400, bfa)
new_esEs21(vyy3010, vyy410, app(app(app(ty_@3, ef), eg), eh)) → new_esEs5(vyy3010, vyy410, ef, eg, eh)
new_esEs21(vyy3010, vyy410, app(ty_Maybe, fc)) → new_esEs7(vyy3010, vyy410, fc)
new_ltEs19(vyy951, vyy961, app(ty_[], df)) → new_ltEs16(vyy951, vyy961, df)
new_primCompAux00(vyy164, vyy165, EQ, ty_Double) → new_compare19(vyy164, vyy165)
new_lt20(vyy950, vyy960, ty_Double) → new_lt15(vyy950, vyy960)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs21(vyy3010, vyy410, app(app(ty_@2, eb), ec)) → new_esEs4(vyy3010, vyy410, eb, ec)
new_ltEs14(vyy301, vyy41) → new_not(new_esEs15(new_compare25(vyy301, vyy41), GT))
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_lt19(:(vyy3000, vyy3001), :(vyy400, vyy401), bea) → new_esEs15(new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, bea), LT)
new_esEs27(vyy950, vyy960, ty_Char) → new_esEs17(vyy950, vyy960)
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_compare34(vyy300, vyy40, bgd) → new_compare212(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgd), bgd)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Double) → new_esEs19(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs19(vyy951, vyy961, app(app(ty_Either, dc), dd)) → new_ltEs5(vyy951, vyy961, dc, dd)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_esEs27(vyy950, vyy960, ty_@0) → new_esEs11(vyy950, vyy960)
new_primCompAux00(vyy164, vyy165, EQ, ty_Ordering) → new_compare7(vyy164, vyy165)
new_esEs9(vyy3000, vyy400, app(app(app(ty_@3, cad), cae), caf)) → new_esEs5(vyy3000, vyy400, cad, cae, caf)
new_esEs15(LT, GT) → False
new_esEs15(GT, LT) → False
new_esEs8(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_compare211(vyy300, vyy40, False) → new_compare112(vyy300, vyy40, new_ltEs6(vyy300, vyy40))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare12(vyy3000, vyy400, bfa) → new_compare34(vyy3000, vyy400, bfa)
new_lt12(vyy3010, vyy410, app(app(ty_Either, fa), fb)) → new_lt16(vyy3010, vyy410, fa, fb)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(ty_[], bcf)) → new_ltEs16(vyy3010, vyy410, bcf)
new_esEs15(LT, LT) → True
new_esEs11(@0, @0) → True
new_esEs25(vyy3001, vyy401, ty_@0) → new_esEs11(vyy3001, vyy401)
new_esEs20(vyy3011, vyy411, app(app(ty_Either, gd), ge)) → new_esEs6(vyy3011, vyy411, gd, ge)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Double) → new_ltEs11(vyy3010, vyy410)
new_esEs9(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy951, vyy961, ty_@0) → new_ltEs17(vyy951, vyy961)
new_primPlusNat1(Succ(vyy1740), vyy40100) → Succ(Succ(new_primPlusNat0(vyy1740, vyy40100)))
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], cea), bab) → new_esEs18(vyy3000, vyy400, cea)
new_esEs24(vyy3002, vyy402, ty_Double) → new_esEs19(vyy3002, vyy402)
new_compare0(vyy3000, vyy400, app(ty_Ratio, dbh)) → new_compare17(vyy3000, vyy400, dbh)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, bab) → new_esEs15(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, ty_Char) → new_esEs17(vyy3010, vyy410)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, cdh), bab) → new_esEs7(vyy3000, vyy400, cdh)
new_esEs25(vyy3001, vyy401, app(ty_Ratio, chh)) → new_esEs14(vyy3001, vyy401, chh)
new_compare33(vyy300, vyy40) → new_compare213(vyy300, vyy40, new_esEs15(vyy300, vyy40))
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(app(ty_@2, ceb), cec)) → new_esEs4(vyy3000, vyy400, ceb, cec)
new_lt13(vyy3011, vyy411, ty_Bool) → new_lt5(vyy3011, vyy411)
new_esEs8(vyy3001, vyy401, ty_Ordering) → new_esEs15(vyy3001, vyy401)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(ty_Either, bdd), bde)) → new_ltEs5(vyy3010, vyy410, bdd, bde)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Float) → new_ltEs8(vyy3010, vyy410)
new_esEs25(vyy3001, vyy401, app(ty_Maybe, dad)) → new_esEs7(vyy3001, vyy401, dad)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs5(vyy3000, vyy400, cbh, cca, ccb)
new_primCmpFloat(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_esEs9(vyy3000, vyy400, app(app(ty_@2, bhg), bhh)) → new_esEs4(vyy3000, vyy400, bhg, bhh)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Float, bae) → new_ltEs8(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, app(ty_[], bfb)) → new_esEs18(vyy3000, vyy400, bfb)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(vyy950, vyy960, app(ty_Ratio, dca)) → new_esEs14(vyy950, vyy960, dca)
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs11(vyy3000, vyy400)
new_compare8(vyy301, vyy41) → new_primCmpChar(vyy301, vyy41)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(ty_Ratio, ccg)) → new_ltEs9(vyy3010, vyy410, ccg)
new_esEs24(vyy3002, vyy402, ty_Int) → new_esEs10(vyy3002, vyy402)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], ccd)) → new_esEs18(vyy3000, vyy400, ccd)
new_ltEs13(GT, GT) → True
new_lt13(vyy3011, vyy411, ty_Int) → new_lt10(vyy3011, vyy411)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, beb), bec)) → new_esEs4(vyy3000, vyy400, beb, bec)
new_asAs(False, vyy159) → False
new_ltEs19(vyy951, vyy961, app(app(ty_@2, ce), cf)) → new_ltEs7(vyy951, vyy961, ce, cf)
new_lt17(vyy300, vyy40, bgd) → new_esEs15(new_compare34(vyy300, vyy40, bgd), LT)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, bab) → new_esEs11(vyy3000, vyy400)
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_lt18(vyy300, vyy40) → new_esEs15(new_compare33(vyy300, vyy40), LT)
new_compare0(vyy3000, vyy400, ty_Double) → new_compare19(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs18([], [], bea) → True
new_esEs21(vyy3010, vyy410, ty_Bool) → new_esEs13(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(app(ty_@2, gh), ha)) → new_ltEs7(vyy3012, vyy412, gh, ha)
new_primCompAux00(vyy164, vyy165, EQ, app(ty_Ratio, cbb)) → new_compare17(vyy164, vyy165, cbb)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, dbf)) → new_esEs7(vyy3000, vyy400, dbf)
new_esEs20(vyy3011, vyy411, ty_Float) → new_esEs16(vyy3011, vyy411)
new_esEs24(vyy3002, vyy402, ty_Ordering) → new_esEs15(vyy3002, vyy402)
new_ltEs18(vyy3012, vyy412, app(ty_Maybe, hg)) → new_ltEs12(vyy3012, vyy412, hg)
new_compare38(vyy300, vyy40, h, ba) → new_compare210(vyy300, vyy40, new_esEs4(vyy300, vyy40, h, ba), h, ba)
new_esEs13(False, False) → True
new_primCompAux00(vyy164, vyy165, LT, cba) → LT
new_primCompAux00(vyy164, vyy165, GT, cba) → GT
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Int) → new_esEs10(vyy3000, vyy400)
new_ltEs12(Nothing, Just(vyy410), cfd) → True
new_esEs20(vyy3011, vyy411, app(app(ty_@2, fg), fh)) → new_esEs4(vyy3011, vyy411, fg, fh)
new_esEs20(vyy3011, vyy411, ty_Integer) → new_esEs12(vyy3011, vyy411)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Ordering) → new_ltEs13(vyy3010, vyy410)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs27(vyy950, vyy960, app(app(ty_@2, bb), bc)) → new_esEs4(vyy950, vyy960, bb, bc)
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Integer) → new_compare25(new_sr0(vyy3010, vyy411), new_sr0(vyy410, vyy3011))
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_[], bdg)) → new_ltEs16(vyy3010, vyy410, bdg)
new_lt12(vyy3010, vyy410, app(app(app(ty_@3, ef), eg), eh)) → new_lt6(vyy3010, vyy410, ef, eg, eh)
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(ty_@2, bac), bad), bae) → new_ltEs7(vyy3010, vyy410, bac, bad)
new_esEs8(vyy3001, vyy401, app(ty_Ratio, bha)) → new_esEs14(vyy3001, vyy401, bha)
new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, bea) → new_primCompAux00(vyy3001, vyy401, new_compare0(vyy3000, vyy400, bea), app(ty_[], bea))
new_compare28(Integer(vyy30000), Integer(vyy4010), vyy400, vyy3001, ty_Integer) → new_compare25(Integer(new_primMulInt(vyy30000, vyy4010)), new_sr0(vyy400, vyy3001))
new_ltEs19(vyy951, vyy961, ty_Int) → new_ltEs15(vyy951, vyy961)
new_lt16(vyy300, vyy40, baa, bab) → new_esEs15(new_compare37(vyy300, vyy40, baa, bab), LT)
new_lt12(vyy3010, vyy410, app(app(ty_@2, eb), ec)) → new_lt8(vyy3010, vyy410, eb, ec)
new_primCompAux00(vyy164, vyy165, EQ, app(ty_Maybe, bgb)) → new_compare12(vyy164, vyy165, bgb)
new_esEs9(vyy3000, vyy400, app(ty_Maybe, cag)) → new_esEs7(vyy3000, vyy400, cag)
new_lt19([], [], bea) → new_esEs15(EQ, LT)
new_esEs25(vyy3001, vyy401, app(app(app(ty_@3, daa), dab), dac)) → new_esEs5(vyy3001, vyy401, daa, dab, dac)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_compare112(vyy300, vyy40, False) → GT
new_primCmpDouble(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_lt13(vyy3011, vyy411, ty_Integer) → new_lt11(vyy3011, vyy411)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_compare36(vyy300, vyy40, dg, dh, ea) → new_compare23(vyy300, vyy40, new_esEs5(vyy300, vyy40, dg, dh, ea), dg, dh, ea)
new_compare19(vyy301, vyy41) → new_primCmpDouble(vyy301, vyy41)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_ltEs13(LT, LT) → True
new_compare213(vyy300, vyy40, True) → EQ
new_esEs25(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(ty_[], cfc)) → new_esEs18(vyy3000, vyy400, cfc)
new_esEs20(vyy3011, vyy411, ty_Char) → new_esEs17(vyy3011, vyy411)
new_lt11(Integer(vyy3000), Integer(vyy400)) → new_esEs15(new_primCmpInt(vyy3000, vyy400), LT)
new_compare212(vyy300, vyy40, False, bgd) → new_compare11(vyy300, vyy40, new_ltEs12(vyy300, vyy40, bgd), bgd)
new_primPlusNat0(Succ(vyy17400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat0(vyy17400, vyy401000)))
new_esEs26(vyy3000, vyy400, app(app(ty_Either, dah), dba)) → new_esEs6(vyy3000, vyy400, dah, dba)
new_esEs21(vyy3010, vyy410, ty_@0) → new_esEs11(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(ty_[], hh)) → new_ltEs16(vyy3012, vyy412, hh)
new_compare111(vyy300, vyy40, True, h, ba) → LT
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(ty_Maybe, bce)) → new_ltEs12(vyy3010, vyy410, bce)
new_compare26(:(vyy3010, vyy3011), :(vyy410, vyy411), bdh) → new_primCompAux1(vyy3010, vyy410, vyy3011, vyy411, bdh)
new_lt12(vyy3010, vyy410, ty_@0) → new_lt7(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Int) → new_ltEs15(vyy3010, vyy410)
new_esEs24(vyy3002, vyy402, ty_Float) → new_esEs16(vyy3002, vyy402)
new_asAs(True, vyy159) → vyy159
new_primCmpChar(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_compare25(Integer(vyy3010), Integer(vyy410)) → new_primCmpInt(vyy3010, vyy410)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs5(vyy3000, vyy400, dbc, dbd, dbe)
new_esEs27(vyy950, vyy960, ty_Float) → new_esEs16(vyy950, vyy960)
new_esEs9(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs13(True, True) → True
new_lt13(vyy3011, vyy411, app(app(app(ty_@3, ga), gb), gc)) → new_lt6(vyy3011, vyy411, ga, gb, gc)
new_esEs8(vyy3001, vyy401, ty_@0) → new_esEs11(vyy3001, vyy401)
new_esEs27(vyy950, vyy960, ty_Int) → new_esEs10(vyy950, vyy960)
new_ltEs12(Just(vyy3010), Nothing, cfd) → False
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, ty_Int) → new_esEs10(vyy3010, vyy410)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Float) → new_esEs16(vyy3000, vyy400)
new_compare211(vyy300, vyy40, True) → EQ
new_lt13(vyy3011, vyy411, app(app(ty_@2, fg), fh)) → new_lt8(vyy3011, vyy411, fg, fh)
new_ltEs6(False, False) → True
new_esEs21(vyy3010, vyy410, ty_Integer) → new_esEs12(vyy3010, vyy410)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs15(GT, GT) → True
new_lt12(vyy3010, vyy410, ty_Int) → new_lt10(vyy3010, vyy410)
new_esEs8(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs10(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Bool, bae) → new_ltEs6(vyy3010, vyy410)
new_esEs25(vyy3001, vyy401, ty_Ordering) → new_esEs15(vyy3001, vyy401)
new_esEs21(vyy3010, vyy410, ty_Float) → new_esEs16(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, baf), bag), bah), bae) → new_ltEs4(vyy3010, vyy410, baf, bag, bah)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs5(vyy3000, vyy400, ceg, ceh, cfa)
new_primCompAux00(vyy164, vyy165, EQ, ty_Int) → new_compare9(vyy164, vyy165)
new_lt10(vyy300, vyy40) → new_esEs15(new_primCmpInt(vyy300, vyy40), LT)
new_ltEs18(vyy3012, vyy412, ty_Int) → new_ltEs15(vyy3012, vyy412)
new_compare13(vyy3000, vyy400) → new_compare35(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Double, bae) → new_ltEs11(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, bab) → new_esEs10(vyy3000, vyy400)
new_not(True) → False
new_ltEs19(vyy951, vyy961, ty_Ordering) → new_ltEs13(vyy951, vyy961)
new_esEs27(vyy950, vyy960, ty_Double) → new_esEs19(vyy950, vyy960)

The set Q consists of the following terms:

new_ltEs18(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_lt14(x0, x1)
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_compare213(x0, x1, False)
new_esEs9(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, x2, x3, ty_Int)
new_esEs25(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(x0, x1, ty_Char)
new_lt11(Integer(x0), Integer(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare110(x0, x1, False, x2, x3)
new_esEs7(Just(x0), Nothing, x1)
new_compare36(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, ty_@0)
new_primCompAux00(x0, x1, LT, x2)
new_lt19(:(x0, x1), :(x2, x3), x4)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_ltEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, ty_Float)
new_compare211(x0, x1, False)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Right(x0), Right(x1), x2, ty_Double)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_esEs28(x0, x1, ty_Int)
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_compare37(x0, x1, x2, x3)
new_compare7(x0, x1)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare0(x0, x1, ty_Char)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_primCompAux00(x0, x1, EQ, ty_@0)
new_esEs11(@0, @0)
new_lt5(x0, x1)
new_esEs8(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_compare26([], :(x0, x1), x2)
new_compare113(x0, x1, True)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_@0)
new_ltEs17(x0, x1)
new_compare26([], [], x0)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare26(:(x0, x1), :(x2, x3), x4)
new_esEs17(Char(x0), Char(x1))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare111(x0, x1, False, x2, x3)
new_lt12(x0, x1, app(ty_[], x2))
new_ltEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs16(x0, x1, x2)
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_primCompAux00(x0, x1, EQ, ty_Int)
new_ltEs6(True, True)
new_sr(x0, x1)
new_ltEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_ltEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_esEs7(Nothing, Nothing, x0)
new_ltEs5(Left(x0), Left(x1), ty_@0, x2)
new_lt12(x0, x1, ty_Char)
new_compare210(x0, x1, True, x2, x3)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Int)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare26(:(x0, x1), [], x2)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare212(x0, x1, True, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare11(x0, x1, True, x2)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare112(x0, x1, True)
new_primEqNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs18([], [], x0)
new_esEs23(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, x1, EQ, ty_Float)
new_ltEs13(EQ, EQ)
new_lt13(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, False, x2)
new_esEs13(False, False)
new_primMulNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt13(x0, x1, ty_Int)
new_primPlusNat0(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_@0)
new_ltEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_compare8(x0, x1)
new_compare23(x0, x1, False, x2, x3, x4)
new_primPlusNat1(Zero, x0)
new_esEs27(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare12(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, ty_Integer)
new_compare0(x0, x1, ty_@0)
new_primCompAux1(x0, x1, x2, x3, x4)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Bool)
new_ltEs13(LT, EQ)
new_ltEs13(EQ, LT)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare25(Integer(x0), Integer(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs18(x0, x1, ty_Integer)
new_esEs9(x0, x1, ty_Int)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare113(x0, x1, False)
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_ltEs14(x0, x1)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt13(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs8(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_@0)
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt13(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs9(x0, x1, ty_@0)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3, x4)
new_esEs26(x0, x1, ty_@0)
new_compare0(x0, x1, ty_Ordering)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_compare213(x0, x1, True)
new_ltEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs9(x0, x1, ty_Char)
new_compare0(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Integer)
new_primCmpChar(Char(x0), Char(x1))
new_lt19([], :(x0, x1), x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt19([], [], x0)
new_compare9(x0, x1)
new_ltEs19(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1, x2)
new_esEs25(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_lt12(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat0(Zero, Zero)
new_compare27(x0, x1, False, x2, x3)
new_lt12(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs5(Left(x0), Right(x1), x2, x3)
new_ltEs5(Right(x0), Left(x1), x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, ty_Double)
new_lt12(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_ltEs19(x0, x1, ty_Bool)
new_lt18(x0, x1)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs15(LT, LT)
new_esEs22(x0, x1, ty_Integer)
new_ltEs6(True, False)
new_ltEs6(False, True)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs10(x0, x1)
new_esEs18([], :(x0, x1), x2)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs15(EQ, GT)
new_esEs15(GT, EQ)
new_ltEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Double)
new_ltEs13(EQ, GT)
new_ltEs13(GT, EQ)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare19(x0, x1)
new_esEs21(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare212(x0, x1, False, x2)
new_compare10(x0, x1, True, x2, x3, x4)
new_lt20(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs12(Nothing, Just(x0), x1)
new_esEs22(x0, x1, ty_Int)
new_lt15(x0, x1)
new_ltEs13(LT, GT)
new_ltEs13(GT, LT)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs6(False, False)
new_ltEs19(x0, x1, ty_Double)
new_lt6(x0, x1, x2, x3, x4)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_compare10(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare14(@0, @0)
new_lt20(x0, x1, ty_Int)
new_lt10(x0, x1)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, ty_Integer)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_ltEs12(Nothing, Nothing, x0)
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_compare35(x0, x1)
new_pePe(False, x0)
new_primCompAux00(x0, x1, GT, x2)
new_compare0(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_@0)
new_esEs10(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, x2, x3)
new_primEqNat0(Zero, Succ(x0))
new_ltEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, ty_Float)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Float)
new_lt7(@0, @0)
new_lt20(x0, x1, ty_Double)
new_compare0(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), x1)
new_compare33(x0, x1)
new_primCmpNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs8(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(LT, LT)
new_esEs8(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_compare0(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs15(GT, GT)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_esEs9(x0, x1, ty_Double)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs15(GT, LT)
new_esEs15(LT, GT)
new_ltEs8(x0, x1)
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(GT, GT)
new_esEs13(False, True)
new_esEs13(True, False)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Double)
new_ltEs5(Right(x0), Right(x1), x2, ty_Bool)
new_compare27(x0, x1, True, x2, x3)
new_ltEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(x0, x1, ty_Integer)
new_compare18(x0, x1, x2, x3, x4)
new_primPlusNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_esEs25(x0, x1, ty_Double)
new_compare16(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_esEs16(Float(x0, x1), Float(x2, x3))
new_esEs13(True, True)
new_compare112(x0, x1, False)
new_esEs15(EQ, EQ)
new_compare38(x0, x1, x2, x3)
new_compare210(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_pePe(True, x0)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs18(:(x0, x1), [], x2)
new_compare111(x0, x1, True, x2, x3)
new_compare211(x0, x1, True)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs28(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare0(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt17(x0, x1, x2)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_lt9(:%(x0, x1), :%(x2, x3), x4)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt8(x0, x1, x2, x3)
new_asAs(False, x0)
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs12(Integer(x0), Integer(x1))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Nothing, x1)
new_asAs(True, x0)
new_compare28(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_lt13(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs15(LT, EQ)
new_esEs15(EQ, LT)
new_compare0(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs9(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Char)
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs5(Right(x0), Right(x1), x2, ty_Float)
new_compare15(x0, x1, x2, x3)
new_lt16(x0, x1, x2, x3)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_lt19(:(x0, x1), [], x2)
new_lt12(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(ty_[], x2))
new_esEs7(Nothing, Just(x0), x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Float)
new_ltEs5(Left(x0), Left(x1), ty_Char, x2)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Double)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Double)
new_compare34(x0, x1, x2)
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Float)
new_lt13(x0, x1, ty_@0)
new_compare13(x0, x1)

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

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

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

new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(ty_Maybe, bfa)) → new_compare32(vyy3000, vyy400, bfa)
new_ltEs1(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bae) → new_ltEs2(vyy3010, vyy410, bbc)
new_lt(vyy300, vyy40, h, ba) → new_compare2(vyy300, vyy40, new_esEs4(vyy300, vyy40, h, ba), h, ba)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_[], fd), ed, ee) → new_lt3(vyy3010, vyy410, fd)
new_compare2(vyy300, vyy40, False, h, ba) → new_ltEs(vyy300, vyy40, h, ba)
new_ltEs1(Left(vyy3010), Left(vyy410), app(app(ty_Either, bba), bbb), bae) → new_ltEs1(vyy3010, vyy410, bba, bbb)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs0(vyy3010, vyy410, bbh, bca, bcb)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(ty_Maybe, bce)) → new_ltEs2(vyy3010, vyy410, bce)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(app(ty_@3, ef), eg), eh), ed, ee) → new_lt0(vyy3010, vyy410, ef, eg, eh)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(ty_Maybe, de)) → new_ltEs2(vyy951, vyy961, de)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_Maybe, cb), bd) → new_lt2(vyy950, vyy960, cb)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(app(ty_@2, gh), ha)) → new_ltEs(vyy3012, vyy412, gh, ha)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(app(ty_@3, bef), beg), beh)) → new_compare30(vyy3000, vyy400, bef, beg, beh)
new_ltEs2(Just(vyy3010), Just(vyy410), app(ty_[], bdg)) → new_ltEs3(vyy3010, vyy410, bdg)
new_ltEs1(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, baf), bag), bah), bae) → new_ltEs0(vyy3010, vyy410, baf, bag, bah)
new_ltEs1(Left(vyy3010), Left(vyy410), app(app(ty_@2, bac), bad), bae) → new_ltEs(vyy3010, vyy410, bac, bad)
new_compare(:(vyy3010, vyy3011), :(vyy410, vyy411), bdh) → new_primCompAux(vyy3010, vyy410, vyy3011, vyy411, bdh)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(ty_Maybe, fc), ed, ee) → new_lt2(vyy3010, vyy410, fc)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(ty_[], hh)) → new_ltEs3(vyy3012, vyy412, hh)
new_compare31(vyy300, vyy40, baa, bab) → new_compare21(vyy300, vyy40, new_esEs6(vyy300, vyy40, baa, bab), baa, bab)
new_ltEs3(:(vyy3010, vyy3011), :(vyy410, vyy411), bdh) → new_primCompAux(vyy3010, vyy410, vyy3011, vyy411, bdh)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_[], bfb)) → new_compare(vyy3000, vyy400, bfb)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, bea) → new_primCompAux0(vyy3001, vyy401, new_compare0(vyy3000, vyy400, bea), app(ty_[], bea))
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_Either, fa), fb), ed, ee) → new_lt1(vyy3010, vyy410, fa, fb)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_@2, beb), bec)) → new_compare3(vyy3000, vyy400, beb, bec)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(ty_[], df)) → new_ltEs3(vyy951, vyy961, df)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(ty_@2, beb), bec)) → new_compare3(vyy3000, vyy400, beb, bec)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_@2, bb), bc), bd) → new_lt(vyy950, vyy960, bb, bc)
new_ltEs2(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bda), bdb), bdc)) → new_ltEs0(vyy3010, vyy410, bda, bdb, bdc)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(app(ty_@2, bbf), bbg)) → new_ltEs(vyy3010, vyy410, bbf, bbg)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(app(ty_@3, be), bf), bg), bd) → new_lt0(vyy950, vyy960, be, bf, bg)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(app(ty_Either, bed), bee)) → new_compare31(vyy3000, vyy400, bed, bee)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(ty_[], bcf)) → new_ltEs3(vyy3010, vyy410, bcf)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(app(app(ty_@3, ga), gb), gc), ee) → new_lt0(vyy3011, vyy411, ga, gb, gc)
new_compare30(vyy300, vyy40, dg, dh, ea) → new_compare20(vyy300, vyy40, new_esEs5(vyy300, vyy40, dg, dh, ea), dg, dh, ea)
new_compare21(vyy300, vyy40, False, baa, bab) → new_ltEs1(vyy300, vyy40, baa, bab)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(app(ty_@3, bef), beg), beh)) → new_compare30(vyy3000, vyy400, bef, beg, beh)
new_lt0(vyy300, vyy40, dg, dh, ea) → new_compare20(vyy300, vyy40, new_esEs5(vyy300, vyy40, dg, dh, ea), dg, dh, ea)
new_compare3(vyy300, vyy40, h, ba) → new_compare2(vyy300, vyy40, new_esEs4(vyy300, vyy40, h, ba), h, ba)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(app(ty_Either, bh), ca), bd) → new_lt1(vyy950, vyy960, bh, ca)
new_ltEs2(Just(vyy3010), Just(vyy410), app(app(ty_Either, bdd), bde)) → new_ltEs1(vyy3010, vyy410, bdd, bde)
new_lt1(vyy300, vyy40, baa, bab) → new_compare21(vyy300, vyy40, new_esEs6(vyy300, vyy40, baa, bab), baa, bab)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(ty_[], bfb)) → new_compare(vyy3000, vyy400, bfb)
new_lt2(vyy300, vyy40, bgd) → new_compare22(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgd), bgd)
new_primCompAux0(vyy164, vyy165, EQ, app(ty_[], bgc)) → new_compare(vyy164, vyy165, bgc)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(app(ty_Either, gd), ge), ee) → new_lt1(vyy3011, vyy411, gd, ge)
new_compare22(vyy300, vyy40, False, bgd) → new_ltEs2(vyy300, vyy40, bgd)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs0(vyy3012, vyy412, hb, hc, hd)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(app(ty_@2, fg), fh), ee) → new_lt(vyy3011, vyy411, fg, fh)
new_ltEs2(Just(vyy3010), Just(vyy410), app(app(ty_@2, bcg), bch)) → new_ltEs(vyy3010, vyy410, bcg, bch)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(ty_Maybe, hg)) → new_ltEs2(vyy3012, vyy412, hg)
new_ltEs2(Just(vyy3010), Just(vyy410), app(ty_Maybe, bdf)) → new_ltEs2(vyy3010, vyy410, bdf)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, app(app(ty_Either, he), hf)) → new_ltEs1(vyy3012, vyy412, he, hf)
new_ltEs1(Left(vyy3010), Left(vyy410), app(ty_[], bbd), bae) → new_ltEs3(vyy3010, vyy410, bbd)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(app(ty_@2, ce), cf)) → new_ltEs(vyy951, vyy961, ce, cf)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), app(ty_[], cc), bd) → new_lt3(vyy950, vyy960, cc)
new_ltEs1(Right(vyy3010), Right(vyy410), bbe, app(app(ty_Either, bcc), bcd)) → new_ltEs1(vyy3010, vyy410, bcc, bcd)
new_primCompAux(vyy3000, vyy400, vyy3001, vyy401, app(app(ty_Either, bed), bee)) → new_compare31(vyy3000, vyy400, bed, bee)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(ty_[], gg), ee) → new_lt3(vyy3011, vyy411, gg)
new_compare32(vyy300, vyy40, bgd) → new_compare22(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgd), bgd)
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, app(ty_Maybe, gf), ee) → new_lt2(vyy3011, vyy411, gf)
new_compare20(vyy300, vyy40, False, dg, dh, ea) → new_ltEs0(vyy300, vyy40, dg, dh, ea)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(app(ty_Either, dc), dd)) → new_ltEs1(vyy951, vyy961, dc, dd)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), app(ty_Maybe, bfa)) → new_compare32(vyy3000, vyy400, bfa)
new_ltEs(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, app(app(app(ty_@3, cg), da), db)) → new_ltEs0(vyy951, vyy961, cg, da, db)
new_lt3(:(vyy3000, vyy3001), :(vyy400, vyy401), bea) → new_primCompAux0(vyy3001, vyy401, new_compare0(vyy3000, vyy400, bea), app(ty_[], bea))
new_ltEs0(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), app(app(ty_@2, eb), ec), ed, ee) → new_lt(vyy3010, vyy410, eb, ec)

The TRS R consists of the following rules:

new_compare0(vyy3000, vyy400, ty_Integer) → new_compare25(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Bool) → new_compare13(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(ty_Maybe, bfa)) → new_compare12(vyy3000, vyy400, bfa)
new_compare0(vyy3000, vyy400, app(app(ty_@2, beb), bec)) → new_compare15(vyy3000, vyy400, beb, bec)
new_compare0(vyy3000, vyy400, ty_Int) → new_compare9(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Ordering) → new_compare7(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Float) → new_compare16(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_@0) → new_compare14(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(ty_[], bfb)) → new_compare26(vyy3000, vyy400, bfb)
new_compare0(vyy3000, vyy400, ty_Char) → new_compare8(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(app(ty_Either, bed), bee)) → new_compare24(vyy3000, vyy400, bed, bee)
new_compare0(vyy3000, vyy400, app(app(app(ty_@3, bef), beg), beh)) → new_compare18(vyy3000, vyy400, bef, beg, beh)
new_compare0(vyy3000, vyy400, app(ty_Ratio, dbh)) → new_compare17(vyy3000, vyy400, dbh)
new_compare0(vyy3000, vyy400, ty_Double) → new_compare19(vyy3000, vyy400)
new_compare19(vyy301, vyy41) → new_primCmpDouble(vyy301, vyy41)
new_primCmpDouble(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_compare29(vyy3000, vyy400, vyy3001, vyy401) → new_primCmpInt(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat1(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primPlusNat1(Zero, vyy40100) → Succ(vyy40100)
new_primPlusNat1(Succ(vyy1740), vyy40100) → Succ(Succ(new_primPlusNat0(vyy1740, vyy40100)))
new_primPlusNat0(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat0(Succ(vyy17400), Zero) → Succ(vyy17400)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(vyy17400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat0(vyy17400, vyy401000)))
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Int) → new_compare9(new_sr(vyy3010, vyy411), new_sr(vyy410, vyy3011))
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Integer) → new_compare25(new_sr0(vyy3010, vyy411), new_sr0(vyy410, vyy3011))
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_compare25(Integer(vyy3010), Integer(vyy410)) → new_primCmpInt(vyy3010, vyy410)
new_compare9(vyy301, vyy41) → new_primCmpInt(vyy301, vyy41)
new_compare18(vyy3000, vyy400, bef, beg, beh) → new_compare36(vyy3000, vyy400, bef, beg, beh)
new_compare36(vyy300, vyy40, dg, dh, ea) → new_compare23(vyy300, vyy40, new_esEs5(vyy300, vyy40, dg, dh, ea), dg, dh, ea)
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), dg, dh, ea) → new_asAs(new_esEs26(vyy3000, vyy400, dg), new_asAs(new_esEs25(vyy3001, vyy401, dh), new_esEs24(vyy3002, vyy402, ea)))
new_compare23(vyy300, vyy40, False, dg, dh, ea) → new_compare10(vyy300, vyy40, new_ltEs4(vyy300, vyy40, dg, dh, ea), dg, dh, ea)
new_compare23(vyy300, vyy40, True, dg, dh, ea) → EQ
new_ltEs4(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), ff, ed, ee) → new_pePe(new_lt12(vyy3010, vyy410, ff), new_asAs(new_esEs21(vyy3010, vyy410, ff), new_pePe(new_lt13(vyy3011, vyy411, ed), new_asAs(new_esEs20(vyy3011, vyy411, ed), new_ltEs18(vyy3012, vyy412, ee)))))
new_compare10(vyy300, vyy40, True, dg, dh, ea) → LT
new_compare10(vyy300, vyy40, False, dg, dh, ea) → GT
new_lt12(vyy3010, vyy410, ty_Char) → new_lt4(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, ty_Ordering) → new_lt18(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, app(ty_Maybe, fc)) → new_lt17(vyy3010, vyy410, fc)
new_lt12(vyy3010, vyy410, ty_Double) → new_lt15(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, app(ty_Ratio, cfg)) → new_lt9(vyy3010, vyy410, cfg)
new_lt12(vyy3010, vyy410, ty_Float) → new_lt14(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, ty_Bool) → new_lt5(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, ty_Integer) → new_lt11(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, app(ty_[], fd)) → new_lt19(vyy3010, vyy410, fd)
new_lt12(vyy3010, vyy410, app(app(ty_Either, fa), fb)) → new_lt16(vyy3010, vyy410, fa, fb)
new_lt12(vyy3010, vyy410, app(app(app(ty_@3, ef), eg), eh)) → new_lt6(vyy3010, vyy410, ef, eg, eh)
new_lt12(vyy3010, vyy410, app(app(ty_@2, eb), ec)) → new_lt8(vyy3010, vyy410, eb, ec)
new_lt12(vyy3010, vyy410, ty_@0) → new_lt7(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, ty_Int) → new_lt10(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, app(ty_Ratio, cfg)) → new_esEs14(vyy3010, vyy410, cfg)
new_esEs21(vyy3010, vyy410, app(app(ty_Either, fa), fb)) → new_esEs6(vyy3010, vyy410, fa, fb)
new_esEs21(vyy3010, vyy410, ty_Double) → new_esEs19(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, app(ty_[], fd)) → new_esEs18(vyy3010, vyy410, fd)
new_esEs21(vyy3010, vyy410, ty_Ordering) → new_esEs15(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, app(app(app(ty_@3, ef), eg), eh)) → new_esEs5(vyy3010, vyy410, ef, eg, eh)
new_esEs21(vyy3010, vyy410, app(ty_Maybe, fc)) → new_esEs7(vyy3010, vyy410, fc)
new_esEs21(vyy3010, vyy410, app(app(ty_@2, eb), ec)) → new_esEs4(vyy3010, vyy410, eb, ec)
new_esEs21(vyy3010, vyy410, ty_Char) → new_esEs17(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, ty_Bool) → new_esEs13(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, ty_@0) → new_esEs11(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, ty_Int) → new_esEs10(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, ty_Integer) → new_esEs12(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, ty_Float) → new_esEs16(vyy3010, vyy410)
new_lt13(vyy3011, vyy411, ty_@0) → new_lt7(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, app(ty_Maybe, gf)) → new_lt17(vyy3011, vyy411, gf)
new_lt13(vyy3011, vyy411, ty_Double) → new_lt15(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, ty_Float) → new_lt14(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, app(ty_[], gg)) → new_lt19(vyy3011, vyy411, gg)
new_lt13(vyy3011, vyy411, app(app(ty_Either, gd), ge)) → new_lt16(vyy3011, vyy411, gd, ge)
new_lt13(vyy3011, vyy411, ty_Char) → new_lt4(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, ty_Ordering) → new_lt18(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, app(ty_Ratio, cfh)) → new_lt9(vyy3011, vyy411, cfh)
new_lt13(vyy3011, vyy411, ty_Bool) → new_lt5(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, ty_Int) → new_lt10(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, ty_Integer) → new_lt11(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, app(app(app(ty_@3, ga), gb), gc)) → new_lt6(vyy3011, vyy411, ga, gb, gc)
new_lt13(vyy3011, vyy411, app(app(ty_@2, fg), fh)) → new_lt8(vyy3011, vyy411, fg, fh)
new_esEs20(vyy3011, vyy411, app(ty_Maybe, gf)) → new_esEs7(vyy3011, vyy411, gf)
new_esEs20(vyy3011, vyy411, ty_Double) → new_esEs19(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, app(ty_Ratio, cfh)) → new_esEs14(vyy3011, vyy411, cfh)
new_esEs20(vyy3011, vyy411, app(ty_[], gg)) → new_esEs18(vyy3011, vyy411, gg)
new_esEs20(vyy3011, vyy411, ty_@0) → new_esEs11(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, ty_Bool) → new_esEs13(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, ty_Int) → new_esEs10(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, ty_Ordering) → new_esEs15(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, app(app(app(ty_@3, ga), gb), gc)) → new_esEs5(vyy3011, vyy411, ga, gb, gc)
new_esEs20(vyy3011, vyy411, app(app(ty_Either, gd), ge)) → new_esEs6(vyy3011, vyy411, gd, ge)
new_esEs20(vyy3011, vyy411, ty_Float) → new_esEs16(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, app(app(ty_@2, fg), fh)) → new_esEs4(vyy3011, vyy411, fg, fh)
new_esEs20(vyy3011, vyy411, ty_Integer) → new_esEs12(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, ty_Char) → new_esEs17(vyy3011, vyy411)
new_ltEs18(vyy3012, vyy412, ty_Float) → new_ltEs8(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Integer) → new_ltEs14(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Bool) → new_ltEs6(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, app(ty_Ratio, cga)) → new_ltEs9(vyy3012, vyy412, cga)
new_ltEs18(vyy3012, vyy412, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs4(vyy3012, vyy412, hb, hc, hd)
new_ltEs18(vyy3012, vyy412, ty_Char) → new_ltEs10(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, app(app(ty_Either, he), hf)) → new_ltEs5(vyy3012, vyy412, he, hf)
new_ltEs18(vyy3012, vyy412, ty_Ordering) → new_ltEs13(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Double) → new_ltEs11(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_@0) → new_ltEs17(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, app(app(ty_@2, gh), ha)) → new_ltEs7(vyy3012, vyy412, gh, ha)
new_ltEs18(vyy3012, vyy412, app(ty_Maybe, hg)) → new_ltEs12(vyy3012, vyy412, hg)
new_ltEs18(vyy3012, vyy412, app(ty_[], hh)) → new_ltEs16(vyy3012, vyy412, hh)
new_ltEs18(vyy3012, vyy412, ty_Int) → new_ltEs15(vyy3012, vyy412)
new_asAs(False, vyy159) → False
new_asAs(True, vyy159) → vyy159
new_pePe(False, vyy133) → vyy133
new_pePe(True, vyy133) → True
new_ltEs15(vyy301, vyy41) → new_not(new_esEs15(new_compare9(vyy301, vyy41), GT))
new_esEs15(EQ, GT) → False
new_esEs15(LT, GT) → False
new_esEs15(GT, GT) → True
new_not(False) → True
new_not(True) → False
new_ltEs16(vyy301, vyy41, bdh) → new_not(new_esEs15(new_compare26(vyy301, vyy41, bdh), GT))
new_compare26([], [], bdh) → EQ
new_compare26([], :(vyy410, vyy411), bdh) → LT
new_compare26(:(vyy3010, vyy3011), [], bdh) → GT
new_primCompAux00(vyy164, vyy165, EQ, app(ty_[], bgc)) → new_compare26(vyy164, vyy165, bgc)
new_compare26(:(vyy3010, vyy3011), :(vyy410, vyy411), bdh) → new_primCompAux1(vyy3010, vyy410, vyy3011, vyy411, bdh)
new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, bea) → new_primCompAux00(vyy3001, vyy401, new_compare0(vyy3000, vyy400, bea), app(ty_[], bea))
new_primCompAux00(vyy164, vyy165, LT, cba) → LT
new_primCompAux00(vyy164, vyy165, GT, cba) → GT
new_ltEs12(Nothing, Nothing, cfd) → True
new_ltEs12(Just(vyy3010), Just(vyy410), ty_@0) → new_ltEs17(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Integer) → new_ltEs14(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_Ratio, cfe)) → new_ltEs9(vyy3010, vyy410, cfe)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Bool) → new_ltEs6(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Char) → new_ltEs10(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bda), bdb), bdc)) → new_ltEs4(vyy3010, vyy410, bda, bdb, bdc)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(ty_@2, bcg), bch)) → new_ltEs7(vyy3010, vyy410, bcg, bch)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Double) → new_ltEs11(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Float) → new_ltEs8(vyy3010, vyy410)
new_ltEs12(Nothing, Just(vyy410), cfd) → True
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Ordering) → new_ltEs13(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_[], bdg)) → new_ltEs16(vyy3010, vyy410, bdg)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Int) → new_ltEs15(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Nothing, cfd) → False
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_Maybe, bbc), bae) → new_ltEs12(vyy3010, vyy410, bbc)
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(ty_Either, bba), bbb), bae) → new_ltEs5(vyy3010, vyy410, bba, bbb)
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_Maybe, bdf)) → new_ltEs12(vyy3010, vyy410, bdf)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(ty_Either, bdd), bde)) → new_ltEs5(vyy3010, vyy410, bdd, bde)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(app(ty_Either, bcc), bcd)) → new_ltEs5(vyy3010, vyy410, bcc, bcd)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(ty_Maybe, bce)) → new_ltEs12(vyy3010, vyy410, bce)
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_Ratio, ccf), bae) → new_ltEs9(vyy3010, vyy410, ccf)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Integer) → new_ltEs14(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Right(vyy410), bbe, bae) → True
new_ltEs5(Right(vyy3010), Left(vyy410), bbe, bae) → False
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Char) → new_ltEs10(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_[], bbd), bae) → new_ltEs16(vyy3010, vyy410, bbd)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Int, bae) → new_ltEs15(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Bool) → new_ltEs6(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Integer, bae) → new_ltEs14(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Double) → new_ltEs11(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_@0) → new_ltEs17(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Float) → new_ltEs8(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(app(ty_@2, bbf), bbg)) → new_ltEs7(vyy3010, vyy410, bbf, bbg)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Ordering, bae) → new_ltEs13(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs4(vyy3010, vyy410, bbh, bca, bcb)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Char, bae) → new_ltEs10(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Int) → new_ltEs15(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_@0, bae) → new_ltEs17(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, ty_Ordering) → new_ltEs13(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(ty_[], bcf)) → new_ltEs16(vyy3010, vyy410, bcf)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Float, bae) → new_ltEs8(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), bbe, app(ty_Ratio, ccg)) → new_ltEs9(vyy3010, vyy410, ccg)
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(ty_@2, bac), bad), bae) → new_ltEs7(vyy3010, vyy410, bac, bad)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Bool, bae) → new_ltEs6(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, baf), bag), bah), bae) → new_ltEs4(vyy3010, vyy410, baf, bag, bah)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Double, bae) → new_ltEs11(vyy3010, vyy410)
new_ltEs11(vyy301, vyy41) → new_not(new_esEs15(new_compare19(vyy301, vyy41), GT))
new_ltEs6(True, False) → False
new_ltEs6(False, True) → True
new_ltEs6(True, True) → True
new_ltEs6(False, False) → True
new_ltEs7(@2(vyy950, vyy951), @2(vyy960, vyy961), cd, bd) → new_pePe(new_lt20(vyy950, vyy960, cd), new_asAs(new_esEs27(vyy950, vyy960, cd), new_ltEs19(vyy951, vyy961, bd)))
new_lt20(vyy950, vyy960, ty_Int) → new_lt10(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_Float) → new_lt14(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_@0) → new_lt7(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(app(ty_@2, bb), bc)) → new_lt8(vyy950, vyy960, bb, bc)
new_lt20(vyy950, vyy960, ty_Char) → new_lt4(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(ty_Ratio, dca)) → new_lt9(vyy950, vyy960, dca)
new_lt20(vyy950, vyy960, ty_Integer) → new_lt11(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(app(app(ty_@3, be), bf), bg)) → new_lt6(vyy950, vyy960, be, bf, bg)
new_lt20(vyy950, vyy960, ty_Bool) → new_lt5(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(ty_[], cc)) → new_lt19(vyy950, vyy960, cc)
new_lt20(vyy950, vyy960, app(app(ty_Either, bh), ca)) → new_lt16(vyy950, vyy960, bh, ca)
new_lt20(vyy950, vyy960, app(ty_Maybe, cb)) → new_lt17(vyy950, vyy960, cb)
new_lt20(vyy950, vyy960, ty_Ordering) → new_lt18(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_Double) → new_lt15(vyy950, vyy960)
new_esEs27(vyy950, vyy960, app(ty_Maybe, cb)) → new_esEs7(vyy950, vyy960, cb)
new_esEs27(vyy950, vyy960, ty_Integer) → new_esEs12(vyy950, vyy960)
new_esEs27(vyy950, vyy960, ty_Ordering) → new_esEs15(vyy950, vyy960)
new_esEs27(vyy950, vyy960, ty_Bool) → new_esEs13(vyy950, vyy960)
new_esEs27(vyy950, vyy960, app(app(app(ty_@3, be), bf), bg)) → new_esEs5(vyy950, vyy960, be, bf, bg)
new_esEs27(vyy950, vyy960, app(app(ty_Either, bh), ca)) → new_esEs6(vyy950, vyy960, bh, ca)
new_esEs27(vyy950, vyy960, app(ty_[], cc)) → new_esEs18(vyy950, vyy960, cc)
new_esEs27(vyy950, vyy960, ty_Char) → new_esEs17(vyy950, vyy960)
new_esEs27(vyy950, vyy960, ty_@0) → new_esEs11(vyy950, vyy960)
new_esEs27(vyy950, vyy960, app(ty_Ratio, dca)) → new_esEs14(vyy950, vyy960, dca)
new_esEs27(vyy950, vyy960, app(app(ty_@2, bb), bc)) → new_esEs4(vyy950, vyy960, bb, bc)
new_esEs27(vyy950, vyy960, ty_Float) → new_esEs16(vyy950, vyy960)
new_esEs27(vyy950, vyy960, ty_Int) → new_esEs10(vyy950, vyy960)
new_esEs27(vyy950, vyy960, ty_Double) → new_esEs19(vyy950, vyy960)
new_ltEs19(vyy951, vyy961, ty_Double) → new_ltEs11(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Integer) → new_ltEs14(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, app(ty_Maybe, de)) → new_ltEs12(vyy951, vyy961, de)
new_ltEs19(vyy951, vyy961, ty_Bool) → new_ltEs6(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, app(app(app(ty_@3, cg), da), db)) → new_ltEs4(vyy951, vyy961, cg, da, db)
new_ltEs19(vyy951, vyy961, ty_Float) → new_ltEs8(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Char) → new_ltEs10(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, app(ty_Ratio, dcb)) → new_ltEs9(vyy951, vyy961, dcb)
new_ltEs19(vyy951, vyy961, app(ty_[], df)) → new_ltEs16(vyy951, vyy961, df)
new_ltEs19(vyy951, vyy961, app(app(ty_Either, dc), dd)) → new_ltEs5(vyy951, vyy961, dc, dd)
new_ltEs19(vyy951, vyy961, ty_@0) → new_ltEs17(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, app(app(ty_@2, ce), cf)) → new_ltEs7(vyy951, vyy961, ce, cf)
new_ltEs19(vyy951, vyy961, ty_Int) → new_ltEs15(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Ordering) → new_ltEs13(vyy951, vyy961)
new_ltEs13(LT, EQ) → True
new_ltEs13(EQ, GT) → True
new_ltEs13(LT, GT) → True
new_ltEs13(GT, LT) → False
new_ltEs13(EQ, EQ) → True
new_ltEs13(GT, EQ) → False
new_ltEs13(EQ, LT) → False
new_ltEs13(GT, GT) → True
new_ltEs13(LT, LT) → True
new_ltEs17(vyy301, vyy41) → new_not(new_esEs15(new_compare14(vyy301, vyy41), GT))
new_compare14(@0, @0) → EQ
new_ltEs9(vyy301, vyy41, cff) → new_not(new_esEs15(new_compare17(vyy301, vyy41, cff), GT))
new_ltEs10(vyy301, vyy41) → new_not(new_esEs15(new_compare8(vyy301, vyy41), GT))
new_compare8(vyy301, vyy41) → new_primCmpChar(vyy301, vyy41)
new_primCmpChar(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_ltEs8(vyy301, vyy41) → new_not(new_esEs15(new_compare16(vyy301, vyy41), GT))
new_compare16(vyy301, vyy41) → new_primCmpFloat(vyy301, vyy41)
new_primCmpFloat(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_ltEs14(vyy301, vyy41) → new_not(new_esEs15(new_compare25(vyy301, vyy41), GT))
new_esEs19(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs10(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs10(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_esEs16(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs10(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs4(@2(vyy3000, vyy3001), @2(vyy400, vyy401), h, ba) → new_asAs(new_esEs9(vyy3000, vyy400, h), new_esEs8(vyy3001, vyy401, ba))
new_esEs9(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, app(ty_[], cah)) → new_esEs18(vyy3000, vyy400, cah)
new_esEs9(vyy3000, vyy400, app(ty_Ratio, cac)) → new_esEs14(vyy3000, vyy400, cac)
new_esEs9(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, app(app(ty_Either, caa), cab)) → new_esEs6(vyy3000, vyy400, caa, cab)
new_esEs9(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, app(app(app(ty_@3, cad), cae), caf)) → new_esEs5(vyy3000, vyy400, cad, cae, caf)
new_esEs9(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, app(app(ty_@2, bhg), bhh)) → new_esEs4(vyy3000, vyy400, bhg, bhh)
new_esEs9(vyy3000, vyy400, app(ty_Maybe, cag)) → new_esEs7(vyy3000, vyy400, cag)
new_esEs9(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs8(vyy3001, vyy401, app(app(ty_Either, bgg), bgh)) → new_esEs6(vyy3001, vyy401, bgg, bgh)
new_esEs8(vyy3001, vyy401, app(app(ty_@2, bge), bgf)) → new_esEs4(vyy3001, vyy401, bge, bgf)
new_esEs8(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, app(ty_Maybe, bhe)) → new_esEs7(vyy3001, vyy401, bhe)
new_esEs8(vyy3001, vyy401, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs5(vyy3001, vyy401, bhb, bhc, bhd)
new_esEs8(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, app(ty_[], bhf)) → new_esEs18(vyy3001, vyy401, bhf)
new_esEs8(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, ty_Ordering) → new_esEs15(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, app(ty_Ratio, bha)) → new_esEs14(vyy3001, vyy401, bha)
new_esEs8(vyy3001, vyy401, ty_@0) → new_esEs11(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs11(@0, @0) → True
new_esEs14(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cce) → new_asAs(new_esEs23(vyy3000, vyy400, cce), new_esEs22(vyy3001, vyy401, cce))
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_esEs12(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs15(EQ, EQ) → True
new_esEs15(LT, EQ) → False
new_esEs15(EQ, LT) → False
new_esEs15(GT, EQ) → False
new_esEs15(GT, LT) → False
new_esEs15(LT, LT) → True
new_esEs17(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs18(:(vyy3000, vyy3001), :(vyy400, vyy401), bea) → new_asAs(new_esEs28(vyy3000, vyy400, bea), new_esEs18(vyy3001, vyy401, bea))
new_esEs18(:(vyy3000, vyy3001), [], bea) → False
new_esEs18([], :(vyy400, vyy401), bea) → False
new_esEs18([], [], bea) → True
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, bef), beg), beh)) → new_esEs5(vyy3000, vyy400, bef, beg, beh)
new_esEs28(vyy3000, vyy400, app(app(ty_Either, bed), bee)) → new_esEs6(vyy3000, vyy400, bed, bee)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dbh)) → new_esEs14(vyy3000, vyy400, dbh)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, bfa)) → new_esEs7(vyy3000, vyy400, bfa)
new_esEs28(vyy3000, vyy400, app(ty_[], bfb)) → new_esEs18(vyy3000, vyy400, bfb)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, beb), bec)) → new_esEs4(vyy3000, vyy400, beb, bec)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_esEs13(True, False) → False
new_esEs13(False, True) → False
new_esEs13(False, False) → True
new_esEs13(True, True) → True
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, cdh), bab) → new_esEs7(vyy3000, vyy400, cdh)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, ccc)) → new_esEs7(vyy3000, vyy400, ccc)
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(ty_Maybe, cfb)) → new_esEs7(vyy3000, vyy400, cfb)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, cdb), cdc), bab) → new_esEs6(vyy3000, vyy400, cdb, cdc)
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(app(ty_Either, ced), cee)) → new_esEs6(vyy3000, vyy400, ced, cee)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, cbe), cbf)) → new_esEs6(vyy3000, vyy400, cbe, cbf)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, cbc), cbd)) → new_esEs4(vyy3000, vyy400, cbc, cbd)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, cbg)) → new_esEs14(vyy3000, vyy400, cbg)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs7(Nothing, Nothing, bgd) → True
new_esEs7(Just(vyy3000), Nothing, bgd) → False
new_esEs7(Nothing, Just(vyy400), bgd) → False
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs5(vyy3000, vyy400, cbh, cca, ccb)
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs11(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], ccd)) → new_esEs18(vyy3000, vyy400, ccd)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, bab) → new_esEs19(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, bab) → new_esEs12(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, cch), cda), bab) → new_esEs4(vyy3000, vyy400, cch, cda)
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(ty_Ratio, cef)) → new_esEs14(vyy3000, vyy400, cef)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_@0) → new_esEs11(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Right(vyy400), baa, bab) → False
new_esEs6(Right(vyy3000), Left(vyy400), baa, bab) → False
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, cdd), bab) → new_esEs14(vyy3000, vyy400, cdd)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, cde), cdf), cdg), bab) → new_esEs5(vyy3000, vyy400, cde, cdf, cdg)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, bab) → new_esEs16(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, bab) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, bab) → new_esEs13(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], cea), bab) → new_esEs18(vyy3000, vyy400, cea)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, bab) → new_esEs15(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(app(ty_@2, ceb), cec)) → new_esEs4(vyy3000, vyy400, ceb, cec)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, bab) → new_esEs11(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(ty_[], cfc)) → new_esEs18(vyy3000, vyy400, cfc)
new_esEs6(Right(vyy3000), Right(vyy400), baa, ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), baa, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs5(vyy3000, vyy400, ceg, ceh, cfa)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, bab) → new_esEs10(vyy3000, vyy400)
new_lt15(vyy300, vyy40) → new_esEs15(new_primCmpDouble(vyy300, vyy40), LT)
new_lt18(vyy300, vyy40) → new_esEs15(new_compare33(vyy300, vyy40), LT)
new_compare33(vyy300, vyy40) → new_compare213(vyy300, vyy40, new_esEs15(vyy300, vyy40))
new_compare213(vyy300, vyy40, False) → new_compare113(vyy300, vyy40, new_ltEs13(vyy300, vyy40))
new_compare213(vyy300, vyy40, True) → EQ
new_compare113(vyy300, vyy40, True) → LT
new_compare113(vyy300, vyy40, False) → GT
new_lt17(vyy300, vyy40, bgd) → new_esEs15(new_compare34(vyy300, vyy40, bgd), LT)
new_compare34(vyy300, vyy40, bgd) → new_compare212(vyy300, vyy40, new_esEs7(vyy300, vyy40, bgd), bgd)
new_compare212(vyy300, vyy40, True, bgd) → EQ
new_compare212(vyy300, vyy40, False, bgd) → new_compare11(vyy300, vyy40, new_ltEs12(vyy300, vyy40, bgd), bgd)
new_compare11(vyy300, vyy40, True, bgd) → LT
new_compare11(vyy300, vyy40, False, bgd) → GT
new_lt16(vyy300, vyy40, baa, bab) → new_esEs15(new_compare37(vyy300, vyy40, baa, bab), LT)
new_compare37(vyy300, vyy40, baa, bab) → new_compare27(vyy300, vyy40, new_esEs6(vyy300, vyy40, baa, bab), baa, bab)
new_compare27(vyy300, vyy40, False, baa, bab) → new_compare110(vyy300, vyy40, new_ltEs5(vyy300, vyy40, baa, bab), baa, bab)
new_compare27(vyy300, vyy40, True, baa, bab) → EQ
new_compare110(vyy300, vyy40, True, baa, bab) → LT
new_compare110(vyy300, vyy40, False, baa, bab) → GT
new_lt19([], :(vyy400, vyy401), bea) → new_esEs15(LT, LT)
new_lt19(:(vyy3000, vyy3001), [], bea) → new_esEs15(GT, LT)
new_lt19(:(vyy3000, vyy3001), :(vyy400, vyy401), bea) → new_esEs15(new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, bea), LT)
new_lt19([], [], bea) → new_esEs15(EQ, LT)
new_lt5(vyy300, vyy40) → new_esEs15(new_compare35(vyy300, vyy40), LT)
new_compare35(vyy300, vyy40) → new_compare211(vyy300, vyy40, new_esEs13(vyy300, vyy40))
new_compare211(vyy300, vyy40, False) → new_compare112(vyy300, vyy40, new_ltEs6(vyy300, vyy40))
new_compare211(vyy300, vyy40, True) → EQ
new_compare112(vyy300, vyy40, True) → LT
new_compare112(vyy300, vyy40, False) → GT
new_lt6(vyy300, vyy40, dg, dh, ea) → new_esEs15(new_compare36(vyy300, vyy40, dg, dh, ea), LT)
new_lt11(Integer(vyy3000), Integer(vyy400)) → new_esEs15(new_primCmpInt(vyy3000, vyy400), LT)
new_lt9(:%(vyy3000, vyy3001), :%(vyy400, vyy401), cce) → new_esEs15(new_compare28(vyy3000, vyy401, vyy400, vyy3001, cce), LT)
new_compare28(vyy3000, vyy401, vyy400, vyy3001, ty_Int) → new_compare29(vyy3000, vyy401, vyy400, vyy3001)
new_compare28(Integer(vyy30000), Integer(vyy4010), vyy400, vyy3001, ty_Integer) → new_compare25(Integer(new_primMulInt(vyy30000, vyy4010)), new_sr0(vyy400, vyy3001))
new_lt4(vyy300, vyy40) → new_esEs15(new_primCmpChar(vyy300, vyy40), LT)
new_lt8(vyy300, vyy40, h, ba) → new_esEs15(new_compare38(vyy300, vyy40, h, ba), LT)
new_compare38(vyy300, vyy40, h, ba) → new_compare210(vyy300, vyy40, new_esEs4(vyy300, vyy40, h, ba), h, ba)
new_compare210(vyy300, vyy40, False, h, ba) → new_compare111(vyy300, vyy40, new_ltEs7(vyy300, vyy40, h, ba), h, ba)
new_compare210(vyy300, vyy40, True, h, ba) → EQ
new_compare111(vyy300, vyy40, False, h, ba) → GT
new_compare111(vyy300, vyy40, True, h, ba) → LT
new_lt7(@0, @0) → new_esEs15(EQ, LT)
new_lt14(vyy300, vyy40) → new_esEs15(new_primCmpFloat(vyy300, vyy40), LT)
new_lt10(vyy300, vyy40) → new_esEs15(new_primCmpInt(vyy300, vyy40), LT)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_[], dbg)) → new_esEs18(vyy3000, vyy400, dbg)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, daf), dag)) → new_esEs4(vyy3000, vyy400, daf, dag)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, dbb)) → new_esEs14(vyy3000, vyy400, dbb)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, dbf)) → new_esEs7(vyy3000, vyy400, dbf)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, dah), dba)) → new_esEs6(vyy3000, vyy400, dah, dba)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs5(vyy3000, vyy400, dbc, dbd, dbe)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, app(app(ty_Either, chf), chg)) → new_esEs6(vyy3001, vyy401, chf, chg)
new_esEs25(vyy3001, vyy401, app(app(ty_@2, chd), che)) → new_esEs4(vyy3001, vyy401, chd, che)
new_esEs25(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, app(ty_[], dae)) → new_esEs18(vyy3001, vyy401, dae)
new_esEs25(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, ty_@0) → new_esEs11(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, app(ty_Ratio, chh)) → new_esEs14(vyy3001, vyy401, chh)
new_esEs25(vyy3001, vyy401, app(ty_Maybe, dad)) → new_esEs7(vyy3001, vyy401, dad)
new_esEs25(vyy3001, vyy401, app(app(app(ty_@3, daa), dab), dac)) → new_esEs5(vyy3001, vyy401, daa, dab, dac)
new_esEs25(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, ty_Ordering) → new_esEs15(vyy3001, vyy401)
new_esEs24(vyy3002, vyy402, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs5(vyy3002, vyy402, cgg, cgh, cha)
new_esEs24(vyy3002, vyy402, ty_Char) → new_esEs17(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, ty_Bool) → new_esEs13(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, app(ty_Ratio, cgf)) → new_esEs14(vyy3002, vyy402, cgf)
new_esEs24(vyy3002, vyy402, app(ty_Maybe, chb)) → new_esEs7(vyy3002, vyy402, chb)
new_esEs24(vyy3002, vyy402, ty_@0) → new_esEs11(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, app(ty_[], chc)) → new_esEs18(vyy3002, vyy402, chc)
new_esEs24(vyy3002, vyy402, app(app(ty_@2, cgb), cgc)) → new_esEs4(vyy3002, vyy402, cgb, cgc)
new_esEs24(vyy3002, vyy402, app(app(ty_Either, cgd), cge)) → new_esEs6(vyy3002, vyy402, cgd, cge)
new_esEs24(vyy3002, vyy402, ty_Integer) → new_esEs12(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, ty_Double) → new_esEs19(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, ty_Int) → new_esEs10(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, ty_Ordering) → new_esEs15(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, ty_Float) → new_esEs16(vyy3002, vyy402)
new_compare24(vyy3000, vyy400, bed, bee) → new_compare37(vyy3000, vyy400, bed, bee)
new_compare7(vyy3000, vyy400) → new_compare33(vyy3000, vyy400)
new_compare15(vyy3000, vyy400, beb, bec) → new_compare38(vyy3000, vyy400, beb, bec)
new_compare12(vyy3000, vyy400, bfa) → new_compare34(vyy3000, vyy400, bfa)
new_compare13(vyy3000, vyy400) → new_compare35(vyy3000, vyy400)

The set Q consists of the following terms:

new_ltEs18(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_lt14(x0, x1)
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_compare213(x0, x1, False)
new_esEs9(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, x2, x3, ty_Int)
new_esEs25(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(x0, x1, ty_Char)
new_lt11(Integer(x0), Integer(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare110(x0, x1, False, x2, x3)
new_esEs7(Just(x0), Nothing, x1)
new_compare36(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, ty_@0)
new_primCompAux00(x0, x1, LT, x2)
new_lt19(:(x0, x1), :(x2, x3), x4)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_ltEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, ty_Float)
new_compare211(x0, x1, False)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Right(x0), Right(x1), x2, ty_Double)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_esEs28(x0, x1, ty_Int)
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_compare37(x0, x1, x2, x3)
new_compare7(x0, x1)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare0(x0, x1, ty_Char)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_primCompAux00(x0, x1, EQ, ty_@0)
new_esEs11(@0, @0)
new_lt5(x0, x1)
new_esEs8(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_compare26([], :(x0, x1), x2)
new_compare113(x0, x1, True)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_@0)
new_ltEs17(x0, x1)
new_compare26([], [], x0)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare26(:(x0, x1), :(x2, x3), x4)
new_esEs17(Char(x0), Char(x1))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare111(x0, x1, False, x2, x3)
new_lt12(x0, x1, app(ty_[], x2))
new_ltEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs16(x0, x1, x2)
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_primCompAux00(x0, x1, EQ, ty_Int)
new_ltEs6(True, True)
new_sr(x0, x1)
new_ltEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_ltEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_esEs7(Nothing, Nothing, x0)
new_ltEs5(Left(x0), Left(x1), ty_@0, x2)
new_lt12(x0, x1, ty_Char)
new_compare210(x0, x1, True, x2, x3)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Int)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare26(:(x0, x1), [], x2)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare212(x0, x1, True, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare11(x0, x1, True, x2)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare112(x0, x1, True)
new_primEqNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs18([], [], x0)
new_esEs23(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, x1, EQ, ty_Float)
new_ltEs13(EQ, EQ)
new_lt13(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, False, x2)
new_esEs13(False, False)
new_primMulNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt13(x0, x1, ty_Int)
new_primPlusNat0(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_@0)
new_ltEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_compare8(x0, x1)
new_compare23(x0, x1, False, x2, x3, x4)
new_primPlusNat1(Zero, x0)
new_esEs27(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare12(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, ty_Integer)
new_compare0(x0, x1, ty_@0)
new_primCompAux1(x0, x1, x2, x3, x4)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Bool)
new_ltEs13(LT, EQ)
new_ltEs13(EQ, LT)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare25(Integer(x0), Integer(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs18(x0, x1, ty_Integer)
new_esEs9(x0, x1, ty_Int)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare113(x0, x1, False)
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_ltEs14(x0, x1)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt13(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs8(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_@0)
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt13(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs9(x0, x1, ty_@0)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3, x4)
new_esEs26(x0, x1, ty_@0)
new_compare0(x0, x1, ty_Ordering)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_compare213(x0, x1, True)
new_ltEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs9(x0, x1, ty_Char)
new_compare0(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Integer)
new_primCmpChar(Char(x0), Char(x1))
new_lt19([], :(x0, x1), x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt19([], [], x0)
new_compare9(x0, x1)
new_ltEs19(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1, x2)
new_esEs25(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_lt12(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat0(Zero, Zero)
new_compare27(x0, x1, False, x2, x3)
new_lt12(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs5(Left(x0), Right(x1), x2, x3)
new_ltEs5(Right(x0), Left(x1), x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, ty_Double)
new_lt12(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_ltEs19(x0, x1, ty_Bool)
new_lt18(x0, x1)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs15(LT, LT)
new_esEs22(x0, x1, ty_Integer)
new_ltEs6(True, False)
new_ltEs6(False, True)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs10(x0, x1)
new_esEs18([], :(x0, x1), x2)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs15(EQ, GT)
new_esEs15(GT, EQ)
new_ltEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Double)
new_ltEs13(EQ, GT)
new_ltEs13(GT, EQ)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare19(x0, x1)
new_esEs21(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare212(x0, x1, False, x2)
new_compare10(x0, x1, True, x2, x3, x4)
new_lt20(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs12(Nothing, Just(x0), x1)
new_esEs22(x0, x1, ty_Int)
new_lt15(x0, x1)
new_ltEs13(LT, GT)
new_ltEs13(GT, LT)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs6(False, False)
new_ltEs19(x0, x1, ty_Double)
new_lt6(x0, x1, x2, x3, x4)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_compare10(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare14(@0, @0)
new_lt20(x0, x1, ty_Int)
new_lt10(x0, x1)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs28(x0, x1, ty_Integer)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_ltEs12(Nothing, Nothing, x0)
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_compare35(x0, x1)
new_pePe(False, x0)
new_primCompAux00(x0, x1, GT, x2)
new_compare0(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_@0)
new_esEs10(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, x2, x3)
new_primEqNat0(Zero, Succ(x0))
new_ltEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, ty_Float)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Float)
new_lt7(@0, @0)
new_lt20(x0, x1, ty_Double)
new_compare0(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), x1)
new_compare33(x0, x1)
new_primCmpNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs8(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(LT, LT)
new_esEs8(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_compare0(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs15(GT, GT)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_esEs9(x0, x1, ty_Double)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs15(GT, LT)
new_esEs15(LT, GT)
new_ltEs8(x0, x1)
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(GT, GT)
new_esEs13(False, True)
new_esEs13(True, False)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Double)
new_ltEs5(Right(x0), Right(x1), x2, ty_Bool)
new_compare27(x0, x1, True, x2, x3)
new_ltEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(x0, x1, ty_Integer)
new_compare18(x0, x1, x2, x3, x4)
new_primPlusNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_esEs25(x0, x1, ty_Double)
new_compare16(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_esEs16(Float(x0, x1), Float(x2, x3))
new_esEs13(True, True)
new_compare112(x0, x1, False)
new_esEs15(EQ, EQ)
new_compare38(x0, x1, x2, x3)
new_compare210(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_pePe(True, x0)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs18(:(x0, x1), [], x2)
new_compare111(x0, x1, True, x2, x3)
new_compare211(x0, x1, True)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs28(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare0(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt17(x0, x1, x2)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_lt9(:%(x0, x1), :%(x2, x3), x4)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt8(x0, x1, x2, x3)
new_asAs(False, x0)
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs12(Integer(x0), Integer(x1))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Nothing, x1)
new_asAs(True, x0)
new_compare28(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_lt13(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs15(LT, EQ)
new_esEs15(EQ, LT)
new_compare0(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs9(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Char)
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs5(Right(x0), Right(x1), x2, ty_Float)
new_compare15(x0, x1, x2, x3)
new_lt16(x0, x1, x2, x3)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_lt19(:(x0, x1), [], x2)
new_lt12(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(ty_[], x2))
new_esEs7(Nothing, Just(x0), x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Float)
new_ltEs5(Left(x0), Left(x1), ty_Char, x2)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Double)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Double)
new_compare34(x0, x1, x2)
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Float)
new_lt13(x0, x1, ty_@0)
new_compare13(x0, x1)

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

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



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

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_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_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_ltEs7(vyy6130, @2(vyy54, vyy55), h, ba), 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_ltEs7(vyy6130, @2(vyy54, vyy55), h, ba), 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_fmToList_LE0(vyy610, vyy611, vyy105, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, new_ltEs7(vyy6140, @2(vyy54, vyy55), h, ba), h, ba, bb)

The TRS R consists of the following rules:

new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, ec)) → new_esEs7(vyy3000, vyy400, ec)
new_esEs20(vyy3011, vyy411, app(ty_Maybe, bgf)) → new_esEs7(vyy3011, vyy411, bgf)
new_compare0(vyy3000, vyy400, ty_Integer) → new_compare25(vyy3000, vyy400)
new_ltEs16(vyy301, vyy41, bce) → new_not(new_esEs15(new_compare26(vyy301, vyy41, bce), GT))
new_ltEs18(vyy3012, vyy412, ty_Float) → new_ltEs8(vyy3012, vyy412)
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bc, bd, be) → new_asAs(new_esEs26(vyy3000, vyy400, bc), new_asAs(new_esEs25(vyy3001, vyy401, bd), new_esEs24(vyy3002, vyy402, be)))
new_esEs25(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_compare10(vyy300, vyy40, True, bc, bd, be) → LT
new_esEs16(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs10(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs20(vyy3011, vyy411, ty_Double) → new_esEs19(vyy3011, vyy411)
new_esEs24(vyy3002, vyy402, app(app(app(ty_@3, che), chf), chg)) → new_esEs5(vyy3002, vyy402, che, chf, chg)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs13(False, True) → False
new_esEs13(True, False) → False
new_esEs18(:(vyy3000, vyy3001), :(vyy400, vyy401), cdb) → new_asAs(new_esEs28(vyy3000, vyy400, cdb), new_esEs18(vyy3001, vyy401, cdb))
new_compare15(vyy3000, vyy400, cab, cac) → new_compare38(vyy3000, vyy400, cab, cac)
new_ltEs18(vyy3012, vyy412, ty_Integer) → new_ltEs14(vyy3012, vyy412)
new_primCompAux00(vyy164, vyy165, EQ, app(ty_[], db)) → new_compare26(vyy164, vyy165, db)
new_esEs17(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_primCompAux00(vyy164, vyy165, EQ, ty_Float) → new_compare16(vyy164, vyy165)
new_lt20(vyy950, vyy960, ty_Int) → new_lt10(vyy950, vyy960)
new_esEs24(vyy3002, vyy402, ty_Char) → new_esEs17(vyy3002, vyy402)
new_compare110(vyy300, vyy40, True, eg, eh) → LT
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_ltEs7(vyy6130, @2(vyy54, vyy55), h, ba), h, ba, bb)
new_compare23(vyy300, vyy40, False, bc, bd, be) → new_compare10(vyy300, vyy40, new_ltEs4(vyy300, vyy40, bc, bd, be), bc, bd, be)
new_lt20(vyy950, vyy960, ty_Float) → new_lt14(vyy950, vyy960)
new_esEs15(EQ, EQ) → True
new_esEs27(vyy950, vyy960, app(ty_Maybe, cbf)) → new_esEs7(vyy950, vyy960, cbf)
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Char) → new_esEs17(vyy3000, vyy400)
new_lt19([], :(vyy400, vyy401), cdb) → new_esEs15(LT, LT)
new_ltEs19(vyy951, vyy961, ty_Double) → new_ltEs11(vyy951, vyy961)
new_esEs25(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
new_fmToList_LE0(vyy610, vyy611, vyy104, h, ba, bb) → :(@2(vyy610, vyy611), vyy104)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs19(vyy3000, vyy400)
new_ltEs6(True, False) → False
new_ltEs12(Nothing, Nothing, bcf) → True
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, de), df)) → new_esEs6(vyy3000, vyy400, de, df)
new_primMulNat0(Zero, Zero) → Zero
new_lt13(vyy3011, vyy411, ty_@0) → new_lt7(vyy3011, vyy411)
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_Ratio, ff), fd) → new_ltEs9(vyy3010, vyy410, ff)
new_lt20(vyy950, vyy960, ty_@0) → new_lt7(vyy950, vyy960)
new_ltEs18(vyy3012, vyy412, ty_Bool) → new_ltEs6(vyy3012, vyy412)
new_esEs25(vyy3001, vyy401, app(app(ty_Either, dad), dae)) → new_esEs6(vyy3001, vyy401, dad, dae)
new_esEs25(vyy3001, vyy401, app(app(ty_@2, dab), dac)) → new_esEs4(vyy3001, vyy401, dab, dac)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, eh) → new_esEs19(vyy3000, vyy400)
new_ltEs19(vyy951, vyy961, ty_Integer) → new_ltEs14(vyy951, vyy961)
new_lt13(vyy3011, vyy411, app(ty_Maybe, bgf)) → new_lt17(vyy3011, vyy411, bgf)
new_lt20(vyy950, vyy960, app(app(ty_@2, caf), cag)) → new_lt8(vyy950, vyy960, caf, cag)
new_lt12(vyy3010, vyy410, ty_Char) → new_lt4(vyy3010, vyy410)
new_esEs27(vyy950, vyy960, ty_Integer) → new_esEs12(vyy950, vyy960)
new_primCompAux00(vyy164, vyy165, EQ, ty_Bool) → new_compare13(vyy164, vyy165)
new_esEs24(vyy3002, vyy402, ty_Bool) → new_esEs13(vyy3002, vyy402)
new_esEs20(vyy3011, vyy411, app(ty_Ratio, bfh)) → new_esEs14(vyy3011, vyy411, bfh)
new_compare24(vyy3000, vyy400, cdc, cdd) → new_compare37(vyy3000, vyy400, cdc, cdd)
new_ltEs18(vyy3012, vyy412, app(ty_Ratio, bhb)) → new_ltEs9(vyy3012, vyy412, bhb)
new_ltEs18(vyy3012, vyy412, app(app(app(ty_@3, bhc), bhd), bhe)) → new_ltEs4(vyy3012, vyy412, bhc, bhd, bhe)
new_ltEs13(LT, EQ) → True
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Integer) → new_ltEs14(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Right(vyy410), gf, fd) → True
new_ltEs12(Just(vyy3010), Just(vyy410), ty_@0) → new_ltEs17(vyy3010, vyy410)
new_esEs9(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Bool) → new_compare13(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, app(ty_Ratio, bef)) → new_esEs14(vyy3010, vyy410, bef)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, dc), dd)) → new_esEs4(vyy3000, vyy400, dc, dd)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, app(app(ty_Either, he), hf)) → new_ltEs5(vyy3010, vyy410, he, hf)
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, app(app(ty_Either, bfb), bfc)) → new_esEs6(vyy3010, vyy410, bfb, bfc)
new_esEs12(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs8(vyy3001, vyy401, app(app(ty_Either, cee), cef)) → new_esEs6(vyy3001, vyy401, cee, cef)
new_lt19(:(vyy3000, vyy3001), [], cdb) → new_esEs15(GT, LT)
new_esEs9(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_ltEs19(vyy951, vyy961, app(ty_Maybe, cch)) → new_ltEs12(vyy951, vyy961, cch)
new_primCompAux00(vyy164, vyy165, EQ, app(app(app(ty_@3, cc), cd), ce)) → new_compare18(vyy164, vyy165, cc, cd, ce)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, dg)) → new_esEs14(vyy3000, vyy400, dg)
new_esEs8(vyy3001, vyy401, app(app(ty_@2, cec), ced)) → new_esEs4(vyy3001, vyy401, cec, ced)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs5(vyy3000, vyy400, cdf, cdg, cdh)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, eh) → new_esEs12(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_compare26([], [], bce) → EQ
new_ltEs5(Right(vyy3010), Left(vyy410), gf, fd) → False
new_lt8(vyy300, vyy40, ee, ef) → new_esEs15(new_compare38(vyy300, vyy40, ee, ef), LT)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Char) → new_ltEs10(vyy3010, vyy410)
new_lt20(vyy950, vyy960, ty_Char) → new_lt4(vyy950, vyy960)
new_esEs9(vyy3000, vyy400, app(ty_[], cgf)) → new_esEs18(vyy3000, vyy400, cgf)
new_esEs8(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_compare0(vyy3000, vyy400, app(ty_Maybe, cea)) → new_compare12(vyy3000, vyy400, cea)
new_pePe(False, vyy133) → vyy133
new_primCompAux00(vyy164, vyy165, EQ, ty_@0) → new_compare14(vyy164, vyy165)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs10(vyy3000, vyy400)
new_primCompAux00(vyy164, vyy165, EQ, app(app(ty_Either, cf), cg)) → new_compare24(vyy164, vyy165, cf, cg)
new_esEs24(vyy3002, vyy402, app(ty_Ratio, chd)) → new_esEs14(vyy3002, vyy402, chd)
new_primCompAux00(vyy164, vyy165, EQ, app(app(ty_@2, bh), ca)) → new_compare15(vyy164, vyy165, bh, ca)
new_esEs18([], :(vyy400, vyy401), cdb) → False
new_esEs18(:(vyy3000, vyy3001), [], cdb) → False
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, baa), bab), eh) → new_esEs4(vyy3000, vyy400, baa, bab)
new_esEs6(Right(vyy3000), Right(vyy400), eg, app(ty_Ratio, bbg)) → new_esEs14(vyy3000, vyy400, bbg)
new_esEs14(:%(vyy3000, vyy3001), :%(vyy400, vyy401), fa) → new_asAs(new_esEs23(vyy3000, vyy400, fa), new_esEs22(vyy3001, vyy401, fa))
new_esEs8(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_esEs27(vyy950, vyy960, ty_Ordering) → new_esEs15(vyy950, vyy960)
new_esEs24(vyy3002, vyy402, app(ty_Maybe, chh)) → new_esEs7(vyy3002, vyy402, chh)
new_compare14(@0, @0) → EQ
new_esEs24(vyy3002, vyy402, ty_@0) → new_esEs11(vyy3002, vyy402)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
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_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_lt14(vyy300, vyy40) → new_esEs15(new_primCmpFloat(vyy300, vyy40), LT)
new_compare23(vyy300, vyy40, True, bc, bd, be) → EQ
new_compare9(vyy301, vyy41) → new_primCmpInt(vyy301, vyy41)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Integer) → new_ltEs14(vyy3010, vyy410)
new_ltEs13(EQ, GT) → True
new_esEs15(LT, EQ) → False
new_esEs15(EQ, LT) → False
new_esEs20(vyy3011, vyy411, app(ty_[], bgg)) → new_esEs18(vyy3011, vyy411, bgg)
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_esEs6(Right(vyy3000), Right(vyy400), eg, ty_@0) → new_esEs11(vyy3000, vyy400)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_compare0(vyy3000, vyy400, app(app(ty_@2, cab), cac)) → new_compare15(vyy3000, vyy400, cab, cac)
new_compare27(vyy300, vyy40, False, eg, eh) → new_compare110(vyy300, vyy40, new_ltEs5(vyy300, vyy40, eg, eh), eg, eh)
new_esEs21(vyy3010, vyy410, ty_Double) → new_esEs19(vyy3010, vyy410)
new_esEs15(EQ, GT) → False
new_esEs15(GT, EQ) → False
new_ltEs19(vyy951, vyy961, ty_Bool) → new_ltEs6(vyy951, vyy961)
new_esEs6(Left(vyy3000), Right(vyy400), eg, eh) → False
new_esEs6(Right(vyy3000), Left(vyy400), eg, eh) → False
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_Ratio, bda)) → new_ltEs9(vyy3010, vyy410, bda)
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_compare213(vyy300, vyy40, False) → new_compare113(vyy300, vyy40, new_ltEs13(vyy300, vyy40))
new_lt20(vyy950, vyy960, app(ty_Ratio, cah)) → new_lt9(vyy950, vyy960, cah)
new_lt5(vyy300, vyy40) → new_esEs15(new_compare35(vyy300, vyy40), LT)
new_compare29(vyy3000, vyy400, vyy3001, vyy401) → new_primCmpInt(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt4(vyy300, vyy40) → new_esEs15(new_primCmpChar(vyy300, vyy40), LT)
new_esEs9(vyy3000, vyy400, app(ty_Ratio, cga)) → new_esEs14(vyy3000, vyy400, cga)
new_esEs20(vyy3011, vyy411, ty_@0) → new_esEs11(vyy3011, vyy411)
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_[], ge), fd) → new_ltEs16(vyy3010, vyy410, ge)
new_ltEs19(vyy951, vyy961, app(app(app(ty_@3, ccc), ccd), cce)) → new_ltEs4(vyy951, vyy961, ccc, ccd, cce)
new_compare0(vyy3000, vyy400, ty_Int) → new_compare9(vyy3000, vyy400)
new_primCompAux00(vyy164, vyy165, EQ, ty_Char) → new_compare8(vyy164, vyy165)
new_pePe(True, vyy133) → True
new_primEqNat0(Zero, Zero) → True
new_esEs8(vyy3001, vyy401, app(ty_Maybe, cfc)) → new_esEs7(vyy3001, vyy401, cfc)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_ltEs7(@2(vyy950, vyy951), @2(vyy960, vyy961), cad, cae) → new_pePe(new_lt20(vyy950, vyy960, cad), new_asAs(new_esEs27(vyy950, vyy960, cad), new_ltEs19(vyy951, vyy961, cae)))
new_compare11(vyy300, vyy40, True, bf) → LT
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat1(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs25(vyy3001, vyy401, app(ty_[], dbc)) → new_esEs18(vyy3001, vyy401, dbc)
new_compare111(vyy300, vyy40, False, ee, ef) → GT
new_esEs24(vyy3002, vyy402, app(ty_[], daa)) → new_esEs18(vyy3002, vyy402, daa)
new_esEs20(vyy3011, vyy411, ty_Bool) → new_esEs13(vyy3011, vyy411)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Int, fd) → new_ltEs15(vyy3010, vyy410)
new_ltEs19(vyy951, vyy961, ty_Float) → new_ltEs8(vyy951, vyy961)
new_esEs6(Right(vyy3000), Right(vyy400), eg, app(app(ty_Either, bbe), bbf)) → new_esEs6(vyy3000, vyy400, bbe, bbf)
new_compare0(vyy3000, vyy400, ty_Ordering) → new_compare7(vyy3000, vyy400)
new_lt12(vyy3010, vyy410, ty_Ordering) → new_lt18(vyy3010, vyy410)
new_compare110(vyy300, vyy40, False, eg, eh) → GT
new_compare35(vyy300, vyy40) → new_compare211(vyy300, vyy40, new_esEs13(vyy300, vyy40))
new_ltEs18(vyy3012, vyy412, ty_Char) → new_ltEs10(vyy3012, vyy412)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_compare0(vyy3000, vyy400, ty_Float) → new_compare16(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(app(ty_Either, cdc), cdd)) → new_esEs6(vyy3000, vyy400, cdc, cdd)
new_ltEs10(vyy301, vyy41) → new_not(new_esEs15(new_compare8(vyy301, vyy41), GT))
new_ltEs4(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), bea, beb, bec) → new_pePe(new_lt12(vyy3010, vyy410, bea), new_asAs(new_esEs21(vyy3010, vyy410, bea), new_pePe(new_lt13(vyy3011, vyy411, beb), new_asAs(new_esEs20(vyy3011, vyy411, beb), new_ltEs18(vyy3012, vyy412, bec)))))
new_ltEs19(vyy951, vyy961, ty_Char) → new_ltEs10(vyy951, vyy961)
new_compare0(vyy3000, vyy400, ty_@0) → new_compare14(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Bool) → new_ltEs6(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(app(ty_Either, bhf), bhg)) → new_ltEs5(vyy3012, vyy412, bhf, bhg)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs12(vyy3000, vyy400)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Bool) → new_ltEs6(vyy3010, vyy410)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs19(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs10(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs27(vyy950, vyy960, ty_Bool) → new_esEs13(vyy950, vyy960)
new_compare10(vyy300, vyy40, False, bc, bd, be) → GT
new_compare0(vyy3000, vyy400, app(ty_[], ceb)) → new_compare26(vyy3000, vyy400, ceb)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Integer, fd) → new_ltEs14(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, app(ty_Maybe, bfd)) → new_lt17(vyy3010, vyy410, bfd)
new_ltEs19(vyy951, vyy961, app(ty_Ratio, ccb)) → new_ltEs9(vyy951, vyy961, ccb)
new_compare26([], :(vyy410, vyy411), bce) → LT
new_ltEs13(LT, GT) → True
new_compare26(:(vyy3010, vyy3011), [], bce) → GT
new_esEs21(vyy3010, vyy410, app(ty_[], bfe)) → new_esEs18(vyy3010, vyy410, bfe)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Double) → new_ltEs11(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_@0) → new_ltEs17(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Char) → new_ltEs10(vyy3010, vyy410)
new_compare7(vyy3000, vyy400) → new_compare33(vyy3000, vyy400)
new_ltEs11(vyy301, vyy41) → new_not(new_esEs15(new_compare19(vyy301, vyy41), GT))
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_lt20(vyy950, vyy960, ty_Integer) → new_lt11(vyy950, vyy960)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, bae), eh) → new_esEs14(vyy3000, vyy400, bae)
new_lt13(vyy3011, vyy411, ty_Double) → new_lt15(vyy3011, vyy411)
new_primPlusNat1(Zero, vyy40100) → Succ(vyy40100)
new_esEs21(vyy3010, vyy410, ty_Ordering) → new_esEs15(vyy3010, vyy410)
new_esEs4(@2(vyy3000, vyy3001), @2(vyy400, vyy401), ee, ef) → new_asAs(new_esEs9(vyy3000, vyy400, ee), new_esEs8(vyy3001, vyy401, ef))
new_ltEs9(vyy301, vyy41, cgg) → new_not(new_esEs15(new_compare17(vyy301, vyy41, cgg), GT))
new_esEs26(vyy3000, vyy400, app(ty_[], dce)) → new_esEs18(vyy3000, vyy400, dce)
new_compare0(vyy3000, vyy400, ty_Char) → new_compare8(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_lt20(vyy950, vyy960, app(app(app(ty_@3, cba), cbb), cbc)) → new_lt6(vyy950, vyy960, cba, cbb, cbc)
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_Maybe, gd), fd) → new_ltEs12(vyy3010, vyy410, gd)
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_lt13(vyy3011, vyy411, ty_Float) → new_lt14(vyy3011, vyy411)
new_compare112(vyy300, vyy40, True) → LT
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Float) → new_ltEs8(vyy3010, vyy410)
new_compare11(vyy300, vyy40, False, bf) → GT
new_ltEs13(GT, LT) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_lt12(vyy3010, vyy410, ty_Double) → new_lt15(vyy3010, vyy410)
new_compare27(vyy300, vyy40, True, eg, eh) → EQ
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(ty_Either, gb), gc), fd) → new_ltEs5(vyy3010, vyy410, gb, gc)
new_ltEs13(EQ, EQ) → True
new_ltEs18(vyy3012, vyy412, ty_Ordering) → new_ltEs13(vyy3012, vyy412)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, baf), bag), bah), eh) → new_esEs5(vyy3000, vyy400, baf, bag, bah)
new_ltEs6(False, True) → True
new_lt7(@0, @0) → new_esEs15(EQ, LT)
new_esEs20(vyy3011, vyy411, ty_Int) → new_esEs10(vyy3011, vyy411)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_foldFM_LE3(vyy610, vyy611, vyy104, vyy54, vyy55, h, ba, bb) → new_fmToList_LE0(vyy610, vyy611, vyy104, h, ba, bb)
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Int) → new_compare9(new_sr(vyy3010, vyy411), new_sr(vyy410, vyy3011))
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, app(app(ty_@2, gg), gh)) → new_ltEs7(vyy3010, vyy410, gg, gh)
new_ltEs15(vyy301, vyy41) → new_not(new_esEs15(new_compare9(vyy301, vyy41), GT))
new_ltEs6(True, True) → True
new_lt9(:%(vyy3000, vyy3001), :%(vyy400, vyy401), fa) → new_esEs15(new_compare28(vyy3000, vyy401, vyy400, vyy3001, fa), LT)
new_lt13(vyy3011, vyy411, app(ty_[], bgg)) → new_lt19(vyy3011, vyy411, bgg)
new_esEs20(vyy3011, vyy411, ty_Ordering) → new_esEs15(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, app(app(ty_Either, bgd), bge)) → new_lt16(vyy3011, vyy411, bgd, bge)
new_esEs9(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Ordering, fd) → new_ltEs13(vyy3010, vyy410)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, eh) → new_esEs16(vyy3000, vyy400)
new_primCompAux00(vyy164, vyy165, EQ, ty_Integer) → new_compare25(vyy164, vyy165)
new_esEs9(vyy3000, vyy400, app(app(ty_Either, cfg), cfh)) → new_esEs6(vyy3000, vyy400, cfg, cfh)
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_compare212(vyy300, vyy40, True, bf) → EQ
new_esEs27(vyy950, vyy960, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs5(vyy950, vyy960, cba, cbb, cbc)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, dbd), dbe)) → new_esEs4(vyy3000, vyy400, dbd, dbe)
new_esEs9(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_ltEs18(vyy3012, vyy412, ty_Double) → new_ltEs11(vyy3012, vyy412)
new_esEs7(Nothing, Nothing, bf) → True
new_ltEs17(vyy301, vyy41) → new_not(new_esEs15(new_compare14(vyy301, vyy41), GT))
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_compare18(vyy3000, vyy400, cdf, cdg, cdh) → new_compare36(vyy3000, vyy400, cdf, cdg, cdh)
new_foldFM_LE20(vyy610, vyy611, vyy105, vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb) → new_foldFM_LE10(new_fmToList_LE0(vyy610, vyy611, vyy105, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, new_ltEs7(vyy6140, @2(vyy54, vyy55), h, ba), h, ba, bb)
new_primPlusNat0(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat0(Succ(vyy17400), Zero) → Succ(vyy17400)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), eg, app(ty_Maybe, bcc)) → new_esEs7(vyy3000, vyy400, bcc)
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_lt20(vyy950, vyy960, ty_Bool) → new_lt5(vyy950, vyy960)
new_esEs8(vyy3001, vyy401, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs5(vyy3001, vyy401, ceh, cfa, cfb)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_compare210(vyy300, vyy40, False, ee, ef) → new_compare111(vyy300, vyy40, new_ltEs7(vyy300, vyy40, ee, ef), ee, ef)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs4(vyy3010, vyy410, hb, hc, hd)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Char, fd) → new_ltEs10(vyy3010, vyy410)
new_esEs8(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, app(ty_[], cfd)) → new_esEs18(vyy3001, vyy401, cfd)
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, eh) → new_esEs17(vyy3000, vyy400)
new_lt6(vyy300, vyy40, bc, bd, be) → new_esEs15(new_compare36(vyy300, vyy40, bc, bd, be), LT)
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_esEs25(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_lt20(vyy950, vyy960, app(ty_[], cbg)) → new_lt19(vyy950, vyy960, cbg)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Int) → new_ltEs15(vyy3010, vyy410)
new_esEs7(Nothing, Just(vyy400), bf) → False
new_esEs7(Just(vyy3000), Nothing, bf) → False
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_Maybe, bdg)) → new_ltEs12(vyy3010, vyy410, bdg)
new_esEs24(vyy3002, vyy402, app(app(ty_@2, cgh), cha)) → new_esEs4(vyy3002, vyy402, cgh, cha)
new_lt12(vyy3010, vyy410, app(ty_Ratio, bef)) → new_lt9(vyy3010, vyy410, bef)
new_compare37(vyy300, vyy40, eg, eh) → new_compare27(vyy300, vyy40, new_esEs6(vyy300, vyy40, eg, eh), eg, eh)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs4(vyy3010, vyy410, bdb, bdc, bdd)
new_lt12(vyy3010, vyy410, ty_Float) → new_lt14(vyy3010, vyy410)
new_esEs8(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_ltEs13(GT, EQ) → False
new_ltEs13(EQ, LT) → False
new_lt12(vyy3010, vyy410, ty_Bool) → new_lt5(vyy3010, vyy410)
new_ltEs8(vyy301, vyy41) → new_not(new_esEs15(new_compare16(vyy301, vyy41), GT))
new_compare16(vyy301, vyy41) → new_primCmpFloat(vyy301, vyy41)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, cde)) → new_esEs14(vyy3000, vyy400, cde)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_lt12(vyy3010, vyy410, ty_Integer) → new_lt11(vyy3010, vyy410)
new_compare113(vyy300, vyy40, True) → LT
new_not(False) → True
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, bac), bad), eh) → new_esEs6(vyy3000, vyy400, bac, bad)
new_esEs9(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(ty_@2, bcg), bch)) → new_ltEs7(vyy3010, vyy410, bcg, bch)
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_compare210(vyy300, vyy40, True, ee, ef) → EQ
new_esEs26(vyy3000, vyy400, app(ty_Ratio, dbh)) → new_esEs14(vyy3000, vyy400, dbh)
new_lt15(vyy300, vyy40) → new_esEs15(new_primCmpDouble(vyy300, vyy40), LT)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_@0, fd) → new_ltEs17(vyy3010, vyy410)
new_compare28(vyy3000, vyy401, vyy400, vyy3001, ty_Int) → new_compare29(vyy3000, vyy401, vyy400, vyy3001)
new_esEs24(vyy3002, vyy402, app(app(ty_Either, chb), chc)) → new_esEs6(vyy3002, vyy402, chb, chc)
new_compare113(vyy300, vyy40, False) → GT
new_ltEs18(vyy3012, vyy412, ty_@0) → new_ltEs17(vyy3012, vyy412)
new_lt13(vyy3011, vyy411, ty_Char) → new_lt4(vyy3011, vyy411)
new_compare0(vyy3000, vyy400, app(app(ty_Either, cdc), cdd)) → new_compare24(vyy3000, vyy400, cdc, cdd)
new_lt20(vyy950, vyy960, app(app(ty_Either, cbd), cbe)) → new_lt16(vyy950, vyy960, cbd, cbe)
new_compare0(vyy3000, vyy400, app(app(app(ty_@3, cdf), cdg), cdh)) → new_compare18(vyy3000, vyy400, cdf, cdg, cdh)
new_lt20(vyy950, vyy960, app(ty_Maybe, cbf)) → new_lt17(vyy950, vyy960, cbf)
new_esEs24(vyy3002, vyy402, ty_Integer) → new_esEs12(vyy3002, vyy402)
new_lt20(vyy950, vyy960, ty_Ordering) → new_lt18(vyy950, vyy960)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, eh) → new_esEs13(vyy3000, vyy400)
new_esEs27(vyy950, vyy960, app(ty_[], cbg)) → new_esEs18(vyy950, vyy960, cbg)
new_esEs27(vyy950, vyy960, app(app(ty_Either, cbd), cbe)) → new_esEs6(vyy950, vyy960, cbd, cbe)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Ordering) → new_ltEs13(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, app(ty_[], bfe)) → new_lt19(vyy3010, vyy410, bfe)
new_lt13(vyy3011, vyy411, app(ty_Ratio, bfh)) → new_lt9(vyy3011, vyy411, bfh)
new_lt13(vyy3011, vyy411, ty_Ordering) → new_lt18(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, app(app(app(ty_@3, bga), bgb), bgc)) → new_esEs5(vyy3011, vyy411, bga, bgb, bgc)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_esEs28(vyy3000, vyy400, app(ty_Maybe, cea)) → new_esEs7(vyy3000, vyy400, cea)
new_esEs21(vyy3010, vyy410, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs5(vyy3010, vyy410, beg, beh, bfa)
new_ltEs19(vyy951, vyy961, app(ty_[], cda)) → new_ltEs16(vyy951, vyy961, cda)
new_esEs21(vyy3010, vyy410, app(ty_Maybe, bfd)) → new_esEs7(vyy3010, vyy410, bfd)
new_lt20(vyy950, vyy960, ty_Double) → new_lt15(vyy950, vyy960)
new_primCompAux00(vyy164, vyy165, EQ, ty_Double) → new_compare19(vyy164, vyy165)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_esEs21(vyy3010, vyy410, app(app(ty_@2, bed), bee)) → new_esEs4(vyy3010, vyy410, bed, bee)
new_ltEs14(vyy301, vyy41) → new_not(new_esEs15(new_compare25(vyy301, vyy41), GT))
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_lt19(:(vyy3000, vyy3001), :(vyy400, vyy401), cdb) → new_esEs15(new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, cdb), LT)
new_esEs27(vyy950, vyy960, ty_Char) → new_esEs17(vyy950, vyy960)
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_compare34(vyy300, vyy40, bf) → new_compare212(vyy300, vyy40, new_esEs7(vyy300, vyy40, bf), bf)
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Double) → new_esEs19(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs19(vyy951, vyy961, app(app(ty_Either, ccf), ccg)) → new_ltEs5(vyy951, vyy961, ccf, ccg)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_esEs27(vyy950, vyy960, ty_@0) → new_esEs11(vyy950, vyy960)
new_esEs9(vyy3000, vyy400, app(app(app(ty_@3, cgb), cgc), cgd)) → new_esEs5(vyy3000, vyy400, cgb, cgc, cgd)
new_primCompAux00(vyy164, vyy165, EQ, ty_Ordering) → new_compare7(vyy164, vyy165)
new_esEs15(LT, GT) → False
new_esEs15(GT, LT) → False
new_esEs8(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_compare211(vyy300, vyy40, False) → new_compare112(vyy300, vyy40, new_ltEs6(vyy300, vyy40))
new_compare12(vyy3000, vyy400, cea) → new_compare34(vyy3000, vyy400, cea)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt12(vyy3010, vyy410, app(app(ty_Either, bfb), bfc)) → new_lt16(vyy3010, vyy410, bfb, bfc)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, app(ty_[], hh)) → new_ltEs16(vyy3010, vyy410, hh)
new_esEs15(LT, LT) → True
new_esEs11(@0, @0) → True
new_esEs20(vyy3011, vyy411, app(app(ty_Either, bgd), bge)) → new_esEs6(vyy3011, vyy411, bgd, bge)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Double) → new_ltEs11(vyy3010, vyy410)
new_esEs25(vyy3001, vyy401, ty_@0) → new_esEs11(vyy3001, vyy401)
new_esEs9(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_ltEs19(vyy951, vyy961, ty_@0) → new_ltEs17(vyy951, vyy961)
new_primPlusNat1(Succ(vyy1740), vyy40100) → Succ(Succ(new_primPlusNat0(vyy1740, vyy40100)))
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], bbb), eh) → new_esEs18(vyy3000, vyy400, bbb)
new_esEs24(vyy3002, vyy402, ty_Double) → new_esEs19(vyy3002, vyy402)
new_compare0(vyy3000, vyy400, app(ty_Ratio, cde)) → new_compare17(vyy3000, vyy400, cde)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, eh) → new_esEs15(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, ty_Char) → new_esEs17(vyy3010, vyy410)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, bba), eh) → new_esEs7(vyy3000, vyy400, bba)
new_esEs25(vyy3001, vyy401, app(ty_Ratio, daf)) → new_esEs14(vyy3001, vyy401, daf)
new_compare33(vyy300, vyy40) → new_compare213(vyy300, vyy40, new_esEs15(vyy300, vyy40))
new_esEs6(Right(vyy3000), Right(vyy400), eg, app(app(ty_@2, bbc), bbd)) → new_esEs4(vyy3000, vyy400, bbc, bbd)
new_lt13(vyy3011, vyy411, ty_Bool) → new_lt5(vyy3011, vyy411)
new_esEs8(vyy3001, vyy401, ty_Ordering) → new_esEs15(vyy3001, vyy401)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(ty_Either, bde), bdf)) → new_ltEs5(vyy3010, vyy410, bde, bdf)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Float) → new_ltEs8(vyy3010, vyy410)
new_esEs25(vyy3001, vyy401, app(ty_Maybe, dbb)) → new_esEs7(vyy3001, vyy401, dbb)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, dh), ea), eb)) → new_esEs5(vyy3000, vyy400, dh, ea, eb)
new_primCmpFloat(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_esEs9(vyy3000, vyy400, app(app(ty_@2, cfe), cff)) → new_esEs4(vyy3000, vyy400, cfe, cff)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Float, fd) → new_ltEs8(vyy3010, vyy410)
new_esEs28(vyy3000, vyy400, app(ty_[], ceb)) → new_esEs18(vyy3000, vyy400, ceb)
new_esEs27(vyy950, vyy960, app(ty_Ratio, cah)) → new_esEs14(vyy950, vyy960, cah)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs11(vyy3000, vyy400)
new_compare8(vyy301, vyy41) → new_primCmpChar(vyy301, vyy41)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, app(ty_Ratio, ha)) → new_ltEs9(vyy3010, vyy410, ha)
new_esEs24(vyy3002, vyy402, ty_Int) → new_esEs10(vyy3002, vyy402)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], ed)) → new_esEs18(vyy3000, vyy400, ed)
new_ltEs13(GT, GT) → True
new_lt13(vyy3011, vyy411, ty_Int) → new_lt10(vyy3011, vyy411)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, cab), cac)) → new_esEs4(vyy3000, vyy400, cab, cac)
new_lt17(vyy300, vyy40, bf) → new_esEs15(new_compare34(vyy300, vyy40, bf), LT)
new_ltEs19(vyy951, vyy961, app(app(ty_@2, cbh), cca)) → new_ltEs7(vyy951, vyy961, cbh, cca)
new_asAs(False, vyy159) → False
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, eh) → new_esEs11(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_lt18(vyy300, vyy40) → new_esEs15(new_compare33(vyy300, vyy40), LT)
new_compare0(vyy3000, vyy400, ty_Double) → new_compare19(vyy3000, vyy400)
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_esEs18([], [], cdb) → True
new_esEs21(vyy3010, vyy410, ty_Bool) → new_esEs13(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(app(ty_@2, bgh), bha)) → new_ltEs7(vyy3012, vyy412, bgh, bha)
new_primCompAux00(vyy164, vyy165, EQ, app(ty_Ratio, cb)) → new_compare17(vyy164, vyy165, cb)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, dcd)) → new_esEs7(vyy3000, vyy400, dcd)
new_esEs20(vyy3011, vyy411, ty_Float) → new_esEs16(vyy3011, vyy411)
new_esEs24(vyy3002, vyy402, ty_Ordering) → new_esEs15(vyy3002, vyy402)
new_ltEs18(vyy3012, vyy412, app(ty_Maybe, bhh)) → new_ltEs12(vyy3012, vyy412, bhh)
new_compare38(vyy300, vyy40, ee, ef) → new_compare210(vyy300, vyy40, new_esEs4(vyy300, vyy40, ee, ef), ee, ef)
new_primCompAux00(vyy164, vyy165, LT, bg) → LT
new_esEs13(False, False) → True
new_primCompAux00(vyy164, vyy165, GT, bg) → GT
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Int) → new_esEs10(vyy3000, vyy400)
new_ltEs12(Nothing, Just(vyy410), bcf) → True
new_esEs20(vyy3011, vyy411, app(app(ty_@2, bff), bfg)) → new_esEs4(vyy3011, vyy411, bff, bfg)
new_esEs20(vyy3011, vyy411, ty_Integer) → new_esEs12(vyy3011, vyy411)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Ordering) → new_ltEs13(vyy3010, vyy410)
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(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs17(vyy3000, vyy400)
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Integer) → new_compare25(new_sr0(vyy3010, vyy411), new_sr0(vyy410, vyy3011))
new_esEs27(vyy950, vyy960, app(app(ty_@2, caf), cag)) → new_esEs4(vyy950, vyy960, caf, cag)
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_[], bdh)) → new_ltEs16(vyy3010, vyy410, bdh)
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(ty_@2, fb), fc), fd) → new_ltEs7(vyy3010, vyy410, fb, fc)
new_lt12(vyy3010, vyy410, app(app(app(ty_@3, beg), beh), bfa)) → new_lt6(vyy3010, vyy410, beg, beh, bfa)
new_esEs8(vyy3001, vyy401, app(ty_Ratio, ceg)) → new_esEs14(vyy3001, vyy401, ceg)
new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, cdb) → new_primCompAux00(vyy3001, vyy401, new_compare0(vyy3000, vyy400, cdb), app(ty_[], cdb))
new_compare28(Integer(vyy30000), Integer(vyy4010), vyy400, vyy3001, ty_Integer) → new_compare25(Integer(new_primMulInt(vyy30000, vyy4010)), new_sr0(vyy400, vyy3001))
new_ltEs19(vyy951, vyy961, ty_Int) → new_ltEs15(vyy951, vyy961)
new_lt16(vyy300, vyy40, eg, eh) → new_esEs15(new_compare37(vyy300, vyy40, eg, eh), LT)
new_esEs9(vyy3000, vyy400, app(ty_Maybe, cge)) → new_esEs7(vyy3000, vyy400, cge)
new_primCompAux00(vyy164, vyy165, EQ, app(ty_Maybe, da)) → new_compare12(vyy164, vyy165, da)
new_lt12(vyy3010, vyy410, app(app(ty_@2, bed), bee)) → new_lt8(vyy3010, vyy410, bed, bee)
new_lt19([], [], cdb) → new_esEs15(EQ, LT)
new_esEs25(vyy3001, vyy401, app(app(app(ty_@3, dag), dah), dba)) → new_esEs5(vyy3001, vyy401, dag, dah, dba)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_compare112(vyy300, vyy40, False) → GT
new_primCmpDouble(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_lt13(vyy3011, vyy411, ty_Integer) → new_lt11(vyy3011, vyy411)
new_compare19(vyy301, vyy41) → new_primCmpDouble(vyy301, vyy41)
new_compare36(vyy300, vyy40, bc, bd, be) → new_compare23(vyy300, vyy40, new_esEs5(vyy300, vyy40, bc, bd, be), bc, bd, be)
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_compare213(vyy300, vyy40, True) → EQ
new_ltEs13(LT, LT) → True
new_esEs6(Right(vyy3000), Right(vyy400), eg, app(ty_[], bcd)) → new_esEs18(vyy3000, vyy400, bcd)
new_esEs25(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs20(vyy3011, vyy411, ty_Char) → new_esEs17(vyy3011, vyy411)
new_lt11(Integer(vyy3000), Integer(vyy400)) → new_esEs15(new_primCmpInt(vyy3000, vyy400), LT)
new_primPlusNat0(Succ(vyy17400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat0(vyy17400, vyy401000)))
new_compare212(vyy300, vyy40, False, bf) → new_compare11(vyy300, vyy40, new_ltEs12(vyy300, vyy40, bf), bf)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, dbf), dbg)) → new_esEs6(vyy3000, vyy400, dbf, dbg)
new_esEs21(vyy3010, vyy410, ty_@0) → new_esEs11(vyy3010, vyy410)
new_ltEs18(vyy3012, vyy412, app(ty_[], caa)) → new_ltEs16(vyy3012, vyy412, caa)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, app(ty_Maybe, hg)) → new_ltEs12(vyy3010, vyy410, hg)
new_compare111(vyy300, vyy40, True, ee, ef) → LT
new_compare26(:(vyy3010, vyy3011), :(vyy410, vyy411), bce) → new_primCompAux1(vyy3010, vyy410, vyy3011, vyy411, bce)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Int) → new_ltEs15(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, ty_@0) → new_lt7(vyy3010, vyy410)
new_primCmpChar(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_asAs(True, vyy159) → vyy159
new_esEs24(vyy3002, vyy402, ty_Float) → new_esEs16(vyy3002, vyy402)
new_compare25(Integer(vyy3010), Integer(vyy410)) → new_primCmpInt(vyy3010, vyy410)
new_esEs27(vyy950, vyy960, ty_Float) → new_esEs16(vyy950, vyy960)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, dca), dcb), dcc)) → new_esEs5(vyy3000, vyy400, dca, dcb, dcc)
new_esEs9(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_lt13(vyy3011, vyy411, app(app(app(ty_@3, bga), bgb), bgc)) → new_lt6(vyy3011, vyy411, bga, bgb, bgc)
new_esEs13(True, True) → True
new_esEs8(vyy3001, vyy401, ty_@0) → new_esEs11(vyy3001, vyy401)
new_esEs27(vyy950, vyy960, ty_Int) → new_esEs10(vyy950, vyy960)
new_ltEs12(Just(vyy3010), Nothing, bcf) → False
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs21(vyy3010, vyy410, ty_Int) → new_esEs10(vyy3010, vyy410)
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Float) → new_esEs16(vyy3000, vyy400)
new_compare211(vyy300, vyy40, True) → EQ
new_lt13(vyy3011, vyy411, app(app(ty_@2, bff), bfg)) → new_lt8(vyy3011, vyy411, bff, bfg)
new_ltEs6(False, False) → True
new_esEs21(vyy3010, vyy410, ty_Integer) → new_esEs12(vyy3010, vyy410)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs15(GT, GT) → True
new_lt12(vyy3010, vyy410, ty_Int) → new_lt10(vyy3010, vyy410)
new_esEs8(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs10(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Bool, fd) → new_ltEs6(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, ty_Float) → new_esEs16(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, fg), fh), ga), fd) → new_ltEs4(vyy3010, vyy410, fg, fh, ga)
new_esEs25(vyy3001, vyy401, ty_Ordering) → new_esEs15(vyy3001, vyy401)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), eg, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs5(vyy3000, vyy400, bbh, bca, bcb)
new_primCompAux00(vyy164, vyy165, EQ, ty_Int) → new_compare9(vyy164, vyy165)
new_lt10(vyy300, vyy40) → new_esEs15(new_primCmpInt(vyy300, vyy40), LT)
new_ltEs18(vyy3012, vyy412, ty_Int) → new_ltEs15(vyy3012, vyy412)
new_compare13(vyy3000, vyy400) → new_compare35(vyy3000, vyy400)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Double, fd) → new_ltEs11(vyy3010, vyy410)
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, eh) → new_esEs10(vyy3000, vyy400)
new_not(True) → False
new_ltEs19(vyy951, vyy961, ty_Ordering) → new_ltEs13(vyy951, vyy961)
new_foldFM_LE0(vyy84, vyy54, vyy55, EmptyFM, h, ba, bb) → vyy84
new_esEs27(vyy950, vyy960, ty_Double) → new_esEs19(vyy950, vyy960)

The set Q consists of the following terms:

new_ltEs18(x0, x1, ty_Int)
new_lt13(x0, x1, app(ty_[], x2))
new_ltEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Ordering)
new_lt14(x0, x1)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_compare213(x0, x1, False)
new_compare28(x0, x1, x2, x3, ty_Int)
new_esEs25(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_lt11(Integer(x0), Integer(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_@0)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, EmptyFM, True, x7, x8, x9)
new_ltEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt19([], :(x0, x1), x2)
new_ltEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare211(x0, x1, False)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Int)
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_compare7(x0, x1)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare0(x0, x1, ty_Char)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_compare0(x0, x1, app(ty_[], x2))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_foldFM_LE3(x0, x1, x2, x3, x4, x5, x6, x7)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_primCompAux00(x0, x1, EQ, ty_@0)
new_esEs11(@0, @0)
new_foldFM_LE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_lt5(x0, x1)
new_ltEs18(x0, x1, ty_Float)
new_compare113(x0, x1, True)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs15(x0, x1)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_@0)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare23(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Just(x0), Nothing, x1)
new_compare0(x0, x1, app(ty_Maybe, x2))
new_ltEs17(x0, x1)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_foldFM_LE0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10)
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, ty_Ordering)
new_fmToList_LE0(x0, x1, x2, x3, x4, x5)
new_esEs17(Char(x0), Char(x1))
new_ltEs12(Nothing, Nothing, x0)
new_ltEs9(x0, x1, x2)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, x1, EQ, ty_Int)
new_ltEs6(True, True)
new_sr(x0, x1)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_lt6(x0, x1, x2, x3, x4)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare112(x0, x1, True)
new_primEqNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Char)
new_lt9(:%(x0, x1), :%(x2, x3), x4)
new_ltEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs23(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare111(x0, x1, False, x2, x3)
new_compare110(x0, x1, False, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCompAux00(x0, x1, EQ, ty_Float)
new_ltEs13(EQ, EQ)
new_lt13(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_ltEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs13(False, False)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primMulNat0(Zero, Zero)
new_lt19(:(x0, x1), [], x2)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_primMulInt(Pos(x0), Pos(x1))
new_lt13(x0, x1, ty_Int)
new_compare11(x0, x1, True, x2)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat0(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_@0)
new_compare8(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_primPlusNat1(Zero, x0)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_compare27(x0, x1, True, x2, x3)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, ty_Integer)
new_compare0(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Bool)
new_compare210(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs13(LT, EQ)
new_ltEs13(EQ, LT)
new_esEs21(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, False, x2, x3)
new_ltEs5(Left(x0), Right(x1), x2, x3)
new_ltEs5(Right(x0), Left(x1), x2, x3)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Succ(x1))
new_compare25(Integer(x0), Integer(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt17(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs18(x0, x1, ty_Integer)
new_esEs9(x0, x1, ty_Int)
new_esEs18([], [], x0)
new_esEs27(x0, x1, ty_Char)
new_compare212(x0, x1, True, x2)
new_compare0(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1, x2, x3)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare113(x0, x1, False)
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_ltEs14(x0, x1)
new_lt13(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs8(x0, x1, ty_@0)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1, ty_@0)
new_lt13(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_@0)
new_compare0(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_compare213(x0, x1, True)
new_esEs9(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Integer)
new_esEs8(x0, x1, app(ty_[], x2))
new_primCmpChar(Char(x0), Char(x1))
new_compare18(x0, x1, x2, x3, x4)
new_compare26(:(x0, x1), :(x2, x3), x4)
new_compare9(x0, x1)
new_compare24(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_@0)
new_ltEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs24(x0, x1, ty_Double)
new_lt12(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_compare110(x0, x1, True, x2, x3)
new_esEs18(:(x0, x1), [], x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Bool)
new_compare34(x0, x1, x2)
new_esEs20(x0, x1, app(ty_[], x2))
new_compare12(x0, x1, x2)
new_lt18(x0, x1)
new_esEs24(x0, x1, ty_Int)
new_ltEs5(Left(x0), Left(x1), ty_Bool, x2)
new_compare37(x0, x1, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs15(LT, LT)
new_esEs22(x0, x1, ty_Integer)
new_ltEs6(True, False)
new_ltEs6(False, True)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs5(Right(x0), Right(x1), x2, ty_Float)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs7(Just(x0), Nothing, x1)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(x0, x1)
new_compare111(x0, x1, True, x2, x3)
new_esEs15(EQ, GT)
new_esEs15(GT, EQ)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs13(EQ, GT)
new_ltEs13(GT, EQ)
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs8(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Left(x0), Left(x1), ty_Char, x2)
new_compare19(x0, x1)
new_esEs21(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Int)
new_primCompAux00(x0, x1, LT, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_lt15(x0, x1)
new_ltEs13(LT, GT)
new_ltEs13(GT, LT)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare10(x0, x1, False, x2, x3, x4)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs6(False, False)
new_ltEs19(x0, x1, ty_Double)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare14(@0, @0)
new_lt20(x0, x1, ty_Int)
new_lt10(x0, x1)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs28(x0, x1, ty_Integer)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_primCompAux1(x0, x1, x2, x3, x4)
new_ltEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_compare35(x0, x1)
new_pePe(False, x0)
new_compare0(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_esEs28(x0, x1, ty_@0)
new_ltEs16(x0, x1, x2)
new_esEs10(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_compare29(x0, x1, x2, x3)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_compare23(x0, x1, False, x2, x3, x4)
new_ltEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs25(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt12(x0, x1, ty_Float)
new_lt7(@0, @0)
new_lt20(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare0(x0, x1, ty_Integer)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, ty_Double)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Right(x0), Right(x1), x2, ty_Bool)
new_compare15(x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), x1)
new_compare33(x0, x1)
new_primCmpNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs8(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt13(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_ltEs13(LT, LT)
new_esEs8(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_compare0(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Bool)
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs15(GT, GT)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_esEs9(x0, x1, ty_Double)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_lt19(:(x0, x1), :(x2, x3), x4)
new_lt16(x0, x1, x2, x3)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs15(GT, LT)
new_esEs15(LT, GT)
new_ltEs8(x0, x1)
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs13(GT, GT)
new_esEs13(False, True)
new_esEs13(True, False)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, x1, EQ, ty_Double)
new_esEs8(x0, x1, ty_Integer)
new_primPlusNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_esEs25(x0, x1, ty_Double)
new_compare16(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_esEs16(Float(x0, x1), Float(x2, x3))
new_esEs13(True, True)
new_compare112(x0, x1, False)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs15(EQ, EQ)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare26(:(x0, x1), [], x2)
new_compare11(x0, x1, False, x2)
new_foldFM_LE0(x0, x1, x2, EmptyFM, x3, x4, x5)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_pePe(True, x0)
new_esEs7(Nothing, Just(x0), x1)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs18([], :(x0, x1), x2)
new_compare211(x0, x1, True)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, x7, False, x8, x9, x10)
new_esEs28(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare0(x0, x1, ty_Int)
new_ltEs12(Nothing, Just(x0), x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2, x3, x4)
new_esEs7(Nothing, Nothing, x0)
new_compare212(x0, x1, False, x2)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(False, x0)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs12(Integer(x0), Integer(x1))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), True, x12, x13, x14)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux00(x0, x1, GT, x2)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare36(x0, x1, x2, x3, x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_asAs(True, x0)
new_compare28(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_compare38(x0, x1, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_compare210(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_sr0(Integer(x0), Integer(x1))
new_primEqNat0(Succ(x0), Zero)
new_ltEs5(Left(x0), Left(x1), ty_Float, x2)
new_lt13(x0, x1, ty_Double)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs15(LT, EQ)
new_esEs15(EQ, LT)
new_compare0(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs9(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Left(x0), Left(x1), ty_Integer, x2)
new_compare26([], :(x0, x1), x2)
new_lt19([], [], x0)
new_primMulInt(Neg(x0), Neg(x1))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Float)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs8(x0, x1, ty_Char)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs28(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Int)
new_compare26([], [], x0)
new_ltEs18(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Float)
new_ltEs5(Right(x0), Right(x1), x2, ty_@0)
new_lt13(x0, x1, ty_@0)
new_compare13(x0, x1)

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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_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_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_ltEs7(vyy6130, @2(vyy54, vyy55), h, ba), 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_ltEs7(vyy6130, @2(vyy54, vyy55), h, ba), 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_fmToList_LE0(vyy610, vyy611, vyy105, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, new_ltEs7(vyy6140, @2(vyy54, vyy55), h, ba), h, ba, bb)

The TRS R consists of the following rules:

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_ltEs7(vyy6130, @2(vyy54, vyy55), h, ba), h, ba, bb)
new_foldFM_LE20(vyy610, vyy611, vyy105, vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, h, ba, bb) → new_foldFM_LE10(new_fmToList_LE0(vyy610, vyy611, vyy105, h, ba, bb), vyy54, vyy55, vyy6140, vyy6141, vyy6142, vyy6143, vyy6144, new_ltEs7(vyy6140, @2(vyy54, vyy55), h, ba), h, ba, bb)
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_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_foldFM_LE0(vyy84, vyy54, vyy55, EmptyFM, h, ba, bb) → vyy84
new_fmToList_LE0(vyy610, vyy611, vyy104, h, ba, bb) → :(@2(vyy610, vyy611), vyy104)
new_ltEs7(@2(vyy950, vyy951), @2(vyy960, vyy961), cad, cae) → new_pePe(new_lt20(vyy950, vyy960, cad), new_asAs(new_esEs27(vyy950, vyy960, cad), new_ltEs19(vyy951, vyy961, cae)))
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_foldFM_LE3(vyy610, vyy611, vyy104, vyy54, vyy55, h, ba, bb) → new_fmToList_LE0(vyy610, vyy611, vyy104, h, ba, bb)
new_lt20(vyy950, vyy960, ty_Int) → new_lt10(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_Float) → new_lt14(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_@0) → new_lt7(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(app(ty_@2, caf), cag)) → new_lt8(vyy950, vyy960, caf, cag)
new_lt20(vyy950, vyy960, ty_Char) → new_lt4(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(ty_Ratio, cah)) → new_lt9(vyy950, vyy960, cah)
new_lt20(vyy950, vyy960, ty_Integer) → new_lt11(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(app(app(ty_@3, cba), cbb), cbc)) → new_lt6(vyy950, vyy960, cba, cbb, cbc)
new_lt20(vyy950, vyy960, ty_Bool) → new_lt5(vyy950, vyy960)
new_lt20(vyy950, vyy960, app(ty_[], cbg)) → new_lt19(vyy950, vyy960, cbg)
new_lt20(vyy950, vyy960, app(app(ty_Either, cbd), cbe)) → new_lt16(vyy950, vyy960, cbd, cbe)
new_lt20(vyy950, vyy960, app(ty_Maybe, cbf)) → new_lt17(vyy950, vyy960, cbf)
new_lt20(vyy950, vyy960, ty_Ordering) → new_lt18(vyy950, vyy960)
new_lt20(vyy950, vyy960, ty_Double) → new_lt15(vyy950, vyy960)
new_esEs27(vyy950, vyy960, app(ty_Maybe, cbf)) → new_esEs7(vyy950, vyy960, cbf)
new_esEs27(vyy950, vyy960, ty_Integer) → new_esEs12(vyy950, vyy960)
new_esEs27(vyy950, vyy960, ty_Ordering) → new_esEs15(vyy950, vyy960)
new_esEs27(vyy950, vyy960, ty_Bool) → new_esEs13(vyy950, vyy960)
new_esEs27(vyy950, vyy960, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs5(vyy950, vyy960, cba, cbb, cbc)
new_esEs27(vyy950, vyy960, app(ty_[], cbg)) → new_esEs18(vyy950, vyy960, cbg)
new_esEs27(vyy950, vyy960, app(app(ty_Either, cbd), cbe)) → new_esEs6(vyy950, vyy960, cbd, cbe)
new_esEs27(vyy950, vyy960, ty_Char) → new_esEs17(vyy950, vyy960)
new_esEs27(vyy950, vyy960, ty_@0) → new_esEs11(vyy950, vyy960)
new_esEs27(vyy950, vyy960, app(ty_Ratio, cah)) → new_esEs14(vyy950, vyy960, cah)
new_esEs27(vyy950, vyy960, app(app(ty_@2, caf), cag)) → new_esEs4(vyy950, vyy960, caf, cag)
new_esEs27(vyy950, vyy960, ty_Float) → new_esEs16(vyy950, vyy960)
new_esEs27(vyy950, vyy960, ty_Int) → new_esEs10(vyy950, vyy960)
new_esEs27(vyy950, vyy960, ty_Double) → new_esEs19(vyy950, vyy960)
new_ltEs19(vyy951, vyy961, ty_Double) → new_ltEs11(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Integer) → new_ltEs14(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, app(ty_Maybe, cch)) → new_ltEs12(vyy951, vyy961, cch)
new_ltEs19(vyy951, vyy961, ty_Bool) → new_ltEs6(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, app(app(app(ty_@3, ccc), ccd), cce)) → new_ltEs4(vyy951, vyy961, ccc, ccd, cce)
new_ltEs19(vyy951, vyy961, ty_Float) → new_ltEs8(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Char) → new_ltEs10(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, app(ty_Ratio, ccb)) → new_ltEs9(vyy951, vyy961, ccb)
new_ltEs19(vyy951, vyy961, app(ty_[], cda)) → new_ltEs16(vyy951, vyy961, cda)
new_ltEs19(vyy951, vyy961, app(app(ty_Either, ccf), ccg)) → new_ltEs5(vyy951, vyy961, ccf, ccg)
new_ltEs19(vyy951, vyy961, ty_@0) → new_ltEs17(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, app(app(ty_@2, cbh), cca)) → new_ltEs7(vyy951, vyy961, cbh, cca)
new_ltEs19(vyy951, vyy961, ty_Int) → new_ltEs15(vyy951, vyy961)
new_ltEs19(vyy951, vyy961, ty_Ordering) → new_ltEs13(vyy951, vyy961)
new_asAs(False, vyy159) → False
new_asAs(True, vyy159) → vyy159
new_pePe(False, vyy133) → vyy133
new_pePe(True, vyy133) → True
new_ltEs13(LT, EQ) → True
new_ltEs13(EQ, GT) → True
new_ltEs13(LT, GT) → True
new_ltEs13(GT, LT) → False
new_ltEs13(EQ, EQ) → True
new_ltEs13(GT, EQ) → False
new_ltEs13(EQ, LT) → False
new_ltEs13(GT, GT) → True
new_ltEs13(LT, LT) → True
new_ltEs15(vyy301, vyy41) → new_not(new_esEs15(new_compare9(vyy301, vyy41), GT))
new_compare9(vyy301, vyy41) → new_primCmpInt(vyy301, vyy41)
new_esEs15(EQ, GT) → False
new_esEs15(LT, GT) → False
new_esEs15(GT, GT) → True
new_not(False) → True
new_not(True) → False
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(vyy30000)), Neg(vyy400)) → new_primCmpNat0(vyy400, Succ(vyy30000))
new_primCmpInt(Neg(Zero), Pos(Succ(vyy4000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(vyy4000))) → new_primCmpNat0(Zero, Succ(vyy4000))
new_primCmpInt(Pos(Succ(vyy30000)), Pos(vyy400)) → new_primCmpNat0(Succ(vyy30000), vyy400)
new_primCmpInt(Pos(Succ(vyy30000)), Neg(vyy400)) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(vyy4000))) → new_primCmpNat0(Succ(vyy4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy4000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(vyy30000)), Pos(vyy400)) → LT
new_primCmpNat0(Succ(vyy30000), Zero) → GT
new_primCmpNat0(Succ(vyy30000), Succ(vyy4000)) → new_primCmpNat0(vyy30000, vyy4000)
new_primCmpNat0(Zero, Succ(vyy4000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs17(vyy301, vyy41) → new_not(new_esEs15(new_compare14(vyy301, vyy41), GT))
new_compare14(@0, @0) → EQ
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_Ratio, ff), fd) → new_ltEs9(vyy3010, vyy410, ff)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Integer) → new_ltEs14(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Right(vyy410), gf, fd) → True
new_ltEs5(Right(vyy3010), Left(vyy410), gf, fd) → False
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Char) → new_ltEs10(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_[], ge), fd) → new_ltEs16(vyy3010, vyy410, ge)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Int, fd) → new_ltEs15(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Bool) → new_ltEs6(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Integer, fd) → new_ltEs14(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Double) → new_ltEs11(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_@0) → new_ltEs17(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Left(vyy410), app(ty_Maybe, gd), fd) → new_ltEs12(vyy3010, vyy410, gd)
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(ty_Either, gb), gc), fd) → new_ltEs5(vyy3010, vyy410, gb, gc)
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_Maybe, bdg)) → new_ltEs12(vyy3010, vyy410, bdg)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(ty_Either, bde), bdf)) → new_ltEs5(vyy3010, vyy410, bde, bdf)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, app(app(ty_Either, he), hf)) → new_ltEs5(vyy3010, vyy410, he, hf)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, app(ty_Maybe, hg)) → new_ltEs12(vyy3010, vyy410, hg)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Float) → new_ltEs8(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, app(app(ty_@2, gg), gh)) → new_ltEs7(vyy3010, vyy410, gg, gh)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Ordering, fd) → new_ltEs13(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs4(vyy3010, vyy410, hb, hc, hd)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Char, fd) → new_ltEs10(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Int) → new_ltEs15(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_@0, fd) → new_ltEs17(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, ty_Ordering) → new_ltEs13(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, app(ty_[], hh)) → new_ltEs16(vyy3010, vyy410, hh)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Float, fd) → new_ltEs8(vyy3010, vyy410)
new_ltEs5(Right(vyy3010), Right(vyy410), gf, app(ty_Ratio, ha)) → new_ltEs9(vyy3010, vyy410, ha)
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(ty_@2, fb), fc), fd) → new_ltEs7(vyy3010, vyy410, fb, fc)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Bool, fd) → new_ltEs6(vyy3010, vyy410)
new_ltEs5(Left(vyy3010), Left(vyy410), app(app(app(ty_@3, fg), fh), ga), fd) → new_ltEs4(vyy3010, vyy410, fg, fh, ga)
new_ltEs5(Left(vyy3010), Left(vyy410), ty_Double, fd) → new_ltEs11(vyy3010, vyy410)
new_ltEs11(vyy301, vyy41) → new_not(new_esEs15(new_compare19(vyy301, vyy41), GT))
new_compare19(vyy301, vyy41) → new_primCmpDouble(vyy301, vyy41)
new_primCmpDouble(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_compare29(vyy3000, vyy400, vyy3001, vyy401) → new_primCmpInt(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat1(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primPlusNat1(Zero, vyy40100) → Succ(vyy40100)
new_primPlusNat1(Succ(vyy1740), vyy40100) → Succ(Succ(new_primPlusNat0(vyy1740, vyy40100)))
new_primPlusNat0(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat0(Succ(vyy17400), Zero) → Succ(vyy17400)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(vyy17400), Succ(vyy401000)) → Succ(Succ(new_primPlusNat0(vyy17400, vyy401000)))
new_ltEs4(@3(vyy3010, vyy3011, vyy3012), @3(vyy410, vyy411, vyy412), bea, beb, bec) → new_pePe(new_lt12(vyy3010, vyy410, bea), new_asAs(new_esEs21(vyy3010, vyy410, bea), new_pePe(new_lt13(vyy3011, vyy411, beb), new_asAs(new_esEs20(vyy3011, vyy411, beb), new_ltEs18(vyy3012, vyy412, bec)))))
new_lt12(vyy3010, vyy410, ty_Char) → new_lt4(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, ty_Ordering) → new_lt18(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, app(ty_Maybe, bfd)) → new_lt17(vyy3010, vyy410, bfd)
new_lt12(vyy3010, vyy410, ty_Double) → new_lt15(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, app(ty_Ratio, bef)) → new_lt9(vyy3010, vyy410, bef)
new_lt12(vyy3010, vyy410, ty_Float) → new_lt14(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, ty_Bool) → new_lt5(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, ty_Integer) → new_lt11(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, app(ty_[], bfe)) → new_lt19(vyy3010, vyy410, bfe)
new_lt12(vyy3010, vyy410, app(app(ty_Either, bfb), bfc)) → new_lt16(vyy3010, vyy410, bfb, bfc)
new_lt12(vyy3010, vyy410, app(app(app(ty_@3, beg), beh), bfa)) → new_lt6(vyy3010, vyy410, beg, beh, bfa)
new_lt12(vyy3010, vyy410, app(app(ty_@2, bed), bee)) → new_lt8(vyy3010, vyy410, bed, bee)
new_lt12(vyy3010, vyy410, ty_@0) → new_lt7(vyy3010, vyy410)
new_lt12(vyy3010, vyy410, ty_Int) → new_lt10(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, app(ty_Ratio, bef)) → new_esEs14(vyy3010, vyy410, bef)
new_esEs21(vyy3010, vyy410, app(app(ty_Either, bfb), bfc)) → new_esEs6(vyy3010, vyy410, bfb, bfc)
new_esEs21(vyy3010, vyy410, ty_Double) → new_esEs19(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, app(ty_[], bfe)) → new_esEs18(vyy3010, vyy410, bfe)
new_esEs21(vyy3010, vyy410, ty_Ordering) → new_esEs15(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs5(vyy3010, vyy410, beg, beh, bfa)
new_esEs21(vyy3010, vyy410, app(ty_Maybe, bfd)) → new_esEs7(vyy3010, vyy410, bfd)
new_esEs21(vyy3010, vyy410, app(app(ty_@2, bed), bee)) → new_esEs4(vyy3010, vyy410, bed, bee)
new_esEs21(vyy3010, vyy410, ty_Char) → new_esEs17(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, ty_Bool) → new_esEs13(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, ty_@0) → new_esEs11(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, ty_Int) → new_esEs10(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, ty_Integer) → new_esEs12(vyy3010, vyy410)
new_esEs21(vyy3010, vyy410, ty_Float) → new_esEs16(vyy3010, vyy410)
new_lt13(vyy3011, vyy411, ty_@0) → new_lt7(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, app(ty_Maybe, bgf)) → new_lt17(vyy3011, vyy411, bgf)
new_lt13(vyy3011, vyy411, ty_Double) → new_lt15(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, ty_Float) → new_lt14(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, app(ty_[], bgg)) → new_lt19(vyy3011, vyy411, bgg)
new_lt13(vyy3011, vyy411, app(app(ty_Either, bgd), bge)) → new_lt16(vyy3011, vyy411, bgd, bge)
new_lt13(vyy3011, vyy411, ty_Char) → new_lt4(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, app(ty_Ratio, bfh)) → new_lt9(vyy3011, vyy411, bfh)
new_lt13(vyy3011, vyy411, ty_Ordering) → new_lt18(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, ty_Bool) → new_lt5(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, ty_Int) → new_lt10(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, ty_Integer) → new_lt11(vyy3011, vyy411)
new_lt13(vyy3011, vyy411, app(app(app(ty_@3, bga), bgb), bgc)) → new_lt6(vyy3011, vyy411, bga, bgb, bgc)
new_lt13(vyy3011, vyy411, app(app(ty_@2, bff), bfg)) → new_lt8(vyy3011, vyy411, bff, bfg)
new_esEs20(vyy3011, vyy411, app(ty_Maybe, bgf)) → new_esEs7(vyy3011, vyy411, bgf)
new_esEs20(vyy3011, vyy411, ty_Double) → new_esEs19(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, app(ty_Ratio, bfh)) → new_esEs14(vyy3011, vyy411, bfh)
new_esEs20(vyy3011, vyy411, app(ty_[], bgg)) → new_esEs18(vyy3011, vyy411, bgg)
new_esEs20(vyy3011, vyy411, ty_@0) → new_esEs11(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, ty_Bool) → new_esEs13(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, ty_Int) → new_esEs10(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, ty_Ordering) → new_esEs15(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, app(app(app(ty_@3, bga), bgb), bgc)) → new_esEs5(vyy3011, vyy411, bga, bgb, bgc)
new_esEs20(vyy3011, vyy411, app(app(ty_Either, bgd), bge)) → new_esEs6(vyy3011, vyy411, bgd, bge)
new_esEs20(vyy3011, vyy411, ty_Float) → new_esEs16(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, app(app(ty_@2, bff), bfg)) → new_esEs4(vyy3011, vyy411, bff, bfg)
new_esEs20(vyy3011, vyy411, ty_Integer) → new_esEs12(vyy3011, vyy411)
new_esEs20(vyy3011, vyy411, ty_Char) → new_esEs17(vyy3011, vyy411)
new_ltEs18(vyy3012, vyy412, ty_Float) → new_ltEs8(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Integer) → new_ltEs14(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Bool) → new_ltEs6(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, app(ty_Ratio, bhb)) → new_ltEs9(vyy3012, vyy412, bhb)
new_ltEs18(vyy3012, vyy412, app(app(app(ty_@3, bhc), bhd), bhe)) → new_ltEs4(vyy3012, vyy412, bhc, bhd, bhe)
new_ltEs18(vyy3012, vyy412, ty_Char) → new_ltEs10(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, app(app(ty_Either, bhf), bhg)) → new_ltEs5(vyy3012, vyy412, bhf, bhg)
new_ltEs18(vyy3012, vyy412, ty_Ordering) → new_ltEs13(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_Double) → new_ltEs11(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, ty_@0) → new_ltEs17(vyy3012, vyy412)
new_ltEs18(vyy3012, vyy412, app(app(ty_@2, bgh), bha)) → new_ltEs7(vyy3012, vyy412, bgh, bha)
new_ltEs18(vyy3012, vyy412, app(ty_Maybe, bhh)) → new_ltEs12(vyy3012, vyy412, bhh)
new_ltEs18(vyy3012, vyy412, app(ty_[], caa)) → new_ltEs16(vyy3012, vyy412, caa)
new_ltEs18(vyy3012, vyy412, ty_Int) → new_ltEs15(vyy3012, vyy412)
new_ltEs16(vyy301, vyy41, bce) → new_not(new_esEs15(new_compare26(vyy301, vyy41, bce), GT))
new_compare26([], [], bce) → EQ
new_compare26([], :(vyy410, vyy411), bce) → LT
new_compare26(:(vyy3010, vyy3011), [], bce) → GT
new_primCompAux00(vyy164, vyy165, EQ, app(ty_[], db)) → new_compare26(vyy164, vyy165, db)
new_compare26(:(vyy3010, vyy3011), :(vyy410, vyy411), bce) → new_primCompAux1(vyy3010, vyy410, vyy3011, vyy411, bce)
new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, cdb) → new_primCompAux00(vyy3001, vyy401, new_compare0(vyy3000, vyy400, cdb), app(ty_[], cdb))
new_compare0(vyy3000, vyy400, ty_Integer) → new_compare25(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Bool) → new_compare13(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(ty_Maybe, cea)) → new_compare12(vyy3000, vyy400, cea)
new_compare0(vyy3000, vyy400, app(app(ty_@2, cab), cac)) → new_compare15(vyy3000, vyy400, cab, cac)
new_compare0(vyy3000, vyy400, ty_Int) → new_compare9(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Ordering) → new_compare7(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_Float) → new_compare16(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, ty_@0) → new_compare14(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(ty_[], ceb)) → new_compare26(vyy3000, vyy400, ceb)
new_compare0(vyy3000, vyy400, ty_Char) → new_compare8(vyy3000, vyy400)
new_compare0(vyy3000, vyy400, app(app(ty_Either, cdc), cdd)) → new_compare24(vyy3000, vyy400, cdc, cdd)
new_compare0(vyy3000, vyy400, app(app(app(ty_@3, cdf), cdg), cdh)) → new_compare18(vyy3000, vyy400, cdf, cdg, cdh)
new_compare0(vyy3000, vyy400, app(ty_Ratio, cde)) → new_compare17(vyy3000, vyy400, cde)
new_compare0(vyy3000, vyy400, ty_Double) → new_compare19(vyy3000, vyy400)
new_primCompAux00(vyy164, vyy165, LT, bg) → LT
new_primCompAux00(vyy164, vyy165, GT, bg) → GT
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Int) → new_compare9(new_sr(vyy3010, vyy411), new_sr(vyy410, vyy3011))
new_compare17(:%(vyy3010, vyy3011), :%(vyy410, vyy411), ty_Integer) → new_compare25(new_sr0(vyy3010, vyy411), new_sr0(vyy410, vyy3011))
new_sr0(Integer(vyy4000), Integer(vyy30010)) → Integer(new_primMulInt(vyy4000, vyy30010))
new_compare25(Integer(vyy3010), Integer(vyy410)) → new_primCmpInt(vyy3010, vyy410)
new_compare18(vyy3000, vyy400, cdf, cdg, cdh) → new_compare36(vyy3000, vyy400, cdf, cdg, cdh)
new_compare36(vyy300, vyy40, bc, bd, be) → new_compare23(vyy300, vyy40, new_esEs5(vyy300, vyy40, bc, bd, be), bc, bd, be)
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bc, bd, be) → new_asAs(new_esEs26(vyy3000, vyy400, bc), new_asAs(new_esEs25(vyy3001, vyy401, bd), new_esEs24(vyy3002, vyy402, be)))
new_compare23(vyy300, vyy40, False, bc, bd, be) → new_compare10(vyy300, vyy40, new_ltEs4(vyy300, vyy40, bc, bd, be), bc, bd, be)
new_compare23(vyy300, vyy40, True, bc, bd, be) → EQ
new_compare10(vyy300, vyy40, True, bc, bd, be) → LT
new_compare10(vyy300, vyy40, False, bc, bd, be) → GT
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_[], dce)) → new_esEs18(vyy3000, vyy400, dce)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, dbd), dbe)) → new_esEs4(vyy3000, vyy400, dbd, dbe)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, dbh)) → new_esEs14(vyy3000, vyy400, dbh)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, dcd)) → new_esEs7(vyy3000, vyy400, dcd)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, dbf), dbg)) → new_esEs6(vyy3000, vyy400, dbf, dbg)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, dca), dcb), dcc)) → new_esEs5(vyy3000, vyy400, dca, dcb, dcc)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs25(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, app(app(ty_Either, dad), dae)) → new_esEs6(vyy3001, vyy401, dad, dae)
new_esEs25(vyy3001, vyy401, app(app(ty_@2, dab), dac)) → new_esEs4(vyy3001, vyy401, dab, dac)
new_esEs25(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, app(ty_[], dbc)) → new_esEs18(vyy3001, vyy401, dbc)
new_esEs25(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, ty_@0) → new_esEs11(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, app(ty_Ratio, daf)) → new_esEs14(vyy3001, vyy401, daf)
new_esEs25(vyy3001, vyy401, app(ty_Maybe, dbb)) → new_esEs7(vyy3001, vyy401, dbb)
new_esEs25(vyy3001, vyy401, app(app(app(ty_@3, dag), dah), dba)) → new_esEs5(vyy3001, vyy401, dag, dah, dba)
new_esEs25(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs25(vyy3001, vyy401, ty_Ordering) → new_esEs15(vyy3001, vyy401)
new_esEs24(vyy3002, vyy402, app(app(app(ty_@3, che), chf), chg)) → new_esEs5(vyy3002, vyy402, che, chf, chg)
new_esEs24(vyy3002, vyy402, ty_Char) → new_esEs17(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, ty_Bool) → new_esEs13(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, app(ty_Ratio, chd)) → new_esEs14(vyy3002, vyy402, chd)
new_esEs24(vyy3002, vyy402, app(ty_Maybe, chh)) → new_esEs7(vyy3002, vyy402, chh)
new_esEs24(vyy3002, vyy402, ty_@0) → new_esEs11(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, app(ty_[], daa)) → new_esEs18(vyy3002, vyy402, daa)
new_esEs24(vyy3002, vyy402, app(app(ty_@2, cgh), cha)) → new_esEs4(vyy3002, vyy402, cgh, cha)
new_esEs24(vyy3002, vyy402, app(app(ty_Either, chb), chc)) → new_esEs6(vyy3002, vyy402, chb, chc)
new_esEs24(vyy3002, vyy402, ty_Integer) → new_esEs12(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, ty_Double) → new_esEs19(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, ty_Int) → new_esEs10(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, ty_Ordering) → new_esEs15(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, ty_Float) → new_esEs16(vyy3002, vyy402)
new_esEs16(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs10(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs10(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_esEs15(EQ, EQ) → True
new_esEs15(LT, EQ) → False
new_esEs15(EQ, LT) → False
new_esEs15(GT, EQ) → False
new_esEs15(GT, LT) → False
new_esEs15(LT, LT) → True
new_esEs19(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs10(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_esEs12(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, eh) → new_esEs19(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, eh) → new_esEs12(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, baa), bab), eh) → new_esEs4(vyy3000, vyy400, baa, bab)
new_esEs6(Right(vyy3000), Right(vyy400), eg, app(ty_Ratio, bbg)) → new_esEs14(vyy3000, vyy400, bbg)
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_@0) → new_esEs11(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Right(vyy400), eg, eh) → False
new_esEs6(Right(vyy3000), Left(vyy400), eg, eh) → False
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, bae), eh) → new_esEs14(vyy3000, vyy400, bae)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, baf), bag), bah), eh) → new_esEs5(vyy3000, vyy400, baf, bag, bah)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, eh) → new_esEs16(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, eh) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, eh) → new_esEs13(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], bbb), eh) → new_esEs18(vyy3000, vyy400, bbb)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, eh) → new_esEs15(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), eg, app(app(ty_@2, bbc), bbd)) → new_esEs4(vyy3000, vyy400, bbc, bbd)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, eh) → new_esEs11(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), eg, app(ty_[], bcd)) → new_esEs18(vyy3000, vyy400, bcd)
new_esEs6(Right(vyy3000), Right(vyy400), eg, ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), eg, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs5(vyy3000, vyy400, bbh, bca, bcb)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, eh) → new_esEs10(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, bba), eh) → new_esEs7(vyy3000, vyy400, bba)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Maybe, ec)) → new_esEs7(vyy3000, vyy400, ec)
new_esEs6(Right(vyy3000), Right(vyy400), eg, app(ty_Maybe, bcc)) → new_esEs7(vyy3000, vyy400, bcc)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, bac), bad), eh) → new_esEs6(vyy3000, vyy400, bac, bad)
new_esEs6(Right(vyy3000), Right(vyy400), eg, app(app(ty_Either, bbe), bbf)) → new_esEs6(vyy3000, vyy400, bbe, bbf)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_Either, de), df)) → new_esEs6(vyy3000, vyy400, de, df)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(ty_@2, dc), dd)) → new_esEs4(vyy3000, vyy400, dc, dd)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_Ratio, dg)) → new_esEs14(vyy3000, vyy400, dg)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs7(Nothing, Nothing, bf) → True
new_esEs7(Nothing, Just(vyy400), bf) → False
new_esEs7(Just(vyy3000), Nothing, bf) → False
new_esEs7(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, dh), ea), eb)) → new_esEs5(vyy3000, vyy400, dh, ea, eb)
new_esEs7(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs11(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), app(ty_[], ed)) → new_esEs18(vyy3000, vyy400, ed)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs7(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs13(False, True) → False
new_esEs13(True, False) → False
new_esEs13(False, False) → True
new_esEs13(True, True) → True
new_esEs17(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs18(:(vyy3000, vyy3001), :(vyy400, vyy401), cdb) → new_asAs(new_esEs28(vyy3000, vyy400, cdb), new_esEs18(vyy3001, vyy401, cdb))
new_esEs18([], :(vyy400, vyy401), cdb) → False
new_esEs18(:(vyy3000, vyy3001), [], cdb) → False
new_esEs18([], [], cdb) → True
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs5(vyy3000, vyy400, cdf, cdg, cdh)
new_esEs28(vyy3000, vyy400, app(app(ty_Either, cdc), cdd)) → new_esEs6(vyy3000, vyy400, cdc, cdd)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, cde)) → new_esEs14(vyy3000, vyy400, cde)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, cea)) → new_esEs7(vyy3000, vyy400, cea)
new_esEs28(vyy3000, vyy400, app(ty_[], ceb)) → new_esEs18(vyy3000, vyy400, ceb)
new_esEs28(vyy3000, vyy400, app(app(ty_@2, cab), cac)) → new_esEs4(vyy3000, vyy400, cab, cac)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_esEs11(@0, @0) → True
new_esEs4(@2(vyy3000, vyy3001), @2(vyy400, vyy401), ee, ef) → new_asAs(new_esEs9(vyy3000, vyy400, ee), new_esEs8(vyy3001, vyy401, ef))
new_esEs9(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, ty_Ordering) → new_esEs15(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, app(ty_[], cgf)) → new_esEs18(vyy3000, vyy400, cgf)
new_esEs9(vyy3000, vyy400, app(ty_Ratio, cga)) → new_esEs14(vyy3000, vyy400, cga)
new_esEs9(vyy3000, vyy400, ty_@0) → new_esEs11(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, app(app(ty_Either, cfg), cfh)) → new_esEs6(vyy3000, vyy400, cfg, cfh)
new_esEs9(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, app(app(app(ty_@3, cgb), cgc), cgd)) → new_esEs5(vyy3000, vyy400, cgb, cgc, cgd)
new_esEs9(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs9(vyy3000, vyy400, app(app(ty_@2, cfe), cff)) → new_esEs4(vyy3000, vyy400, cfe, cff)
new_esEs9(vyy3000, vyy400, app(ty_Maybe, cge)) → new_esEs7(vyy3000, vyy400, cge)
new_esEs9(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs8(vyy3001, vyy401, app(app(ty_Either, cee), cef)) → new_esEs6(vyy3001, vyy401, cee, cef)
new_esEs8(vyy3001, vyy401, app(app(ty_@2, cec), ced)) → new_esEs4(vyy3001, vyy401, cec, ced)
new_esEs8(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, app(ty_Maybe, cfc)) → new_esEs7(vyy3001, vyy401, cfc)
new_esEs8(vyy3001, vyy401, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs5(vyy3001, vyy401, ceh, cfa, cfb)
new_esEs8(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, app(ty_[], cfd)) → new_esEs18(vyy3001, vyy401, cfd)
new_esEs8(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, ty_Ordering) → new_esEs15(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, app(ty_Ratio, ceg)) → new_esEs14(vyy3001, vyy401, ceg)
new_esEs8(vyy3001, vyy401, ty_@0) → new_esEs11(vyy3001, vyy401)
new_esEs8(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs14(:%(vyy3000, vyy3001), :%(vyy400, vyy401), fa) → new_asAs(new_esEs23(vyy3000, vyy400, fa), new_esEs22(vyy3001, vyy401, fa))
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs12(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs10(vyy3000, vyy400)
new_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs12(vyy3001, vyy401)
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs10(vyy3001, vyy401)
new_compare24(vyy3000, vyy400, cdc, cdd) → new_compare37(vyy3000, vyy400, cdc, cdd)
new_compare37(vyy300, vyy40, eg, eh) → new_compare27(vyy300, vyy40, new_esEs6(vyy300, vyy40, eg, eh), eg, eh)
new_compare27(vyy300, vyy40, False, eg, eh) → new_compare110(vyy300, vyy40, new_ltEs5(vyy300, vyy40, eg, eh), eg, eh)
new_compare27(vyy300, vyy40, True, eg, eh) → EQ
new_compare110(vyy300, vyy40, True, eg, eh) → LT
new_compare110(vyy300, vyy40, False, eg, eh) → GT
new_compare8(vyy301, vyy41) → new_primCmpChar(vyy301, vyy41)
new_primCmpChar(Char(vyy3000), Char(vyy400)) → new_primCmpNat0(vyy3000, vyy400)
new_compare16(vyy301, vyy41) → new_primCmpFloat(vyy301, vyy41)
new_primCmpFloat(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_compare29(vyy3000, vyy400, vyy3001, vyy401)
new_compare7(vyy3000, vyy400) → new_compare33(vyy3000, vyy400)
new_compare33(vyy300, vyy40) → new_compare213(vyy300, vyy40, new_esEs15(vyy300, vyy40))
new_compare213(vyy300, vyy40, False) → new_compare113(vyy300, vyy40, new_ltEs13(vyy300, vyy40))
new_compare213(vyy300, vyy40, True) → EQ
new_compare113(vyy300, vyy40, True) → LT
new_compare113(vyy300, vyy40, False) → GT
new_compare15(vyy3000, vyy400, cab, cac) → new_compare38(vyy3000, vyy400, cab, cac)
new_compare38(vyy300, vyy40, ee, ef) → new_compare210(vyy300, vyy40, new_esEs4(vyy300, vyy40, ee, ef), ee, ef)
new_compare210(vyy300, vyy40, False, ee, ef) → new_compare111(vyy300, vyy40, new_ltEs7(vyy300, vyy40, ee, ef), ee, ef)
new_compare210(vyy300, vyy40, True, ee, ef) → EQ
new_compare111(vyy300, vyy40, False, ee, ef) → GT
new_compare111(vyy300, vyy40, True, ee, ef) → LT
new_compare12(vyy3000, vyy400, cea) → new_compare34(vyy3000, vyy400, cea)
new_compare34(vyy300, vyy40, bf) → new_compare212(vyy300, vyy40, new_esEs7(vyy300, vyy40, bf), bf)
new_compare212(vyy300, vyy40, True, bf) → EQ
new_compare212(vyy300, vyy40, False, bf) → new_compare11(vyy300, vyy40, new_ltEs12(vyy300, vyy40, bf), bf)
new_ltEs12(Nothing, Nothing, bcf) → True
new_ltEs12(Just(vyy3010), Just(vyy410), ty_@0) → new_ltEs17(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Integer) → new_ltEs14(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_Ratio, bda)) → new_ltEs9(vyy3010, vyy410, bda)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Bool) → new_ltEs6(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Char) → new_ltEs10(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs4(vyy3010, vyy410, bdb, bdc, bdd)
new_ltEs12(Just(vyy3010), Just(vyy410), app(app(ty_@2, bcg), bch)) → new_ltEs7(vyy3010, vyy410, bcg, bch)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Double) → new_ltEs11(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Float) → new_ltEs8(vyy3010, vyy410)
new_ltEs12(Nothing, Just(vyy410), bcf) → True
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Ordering) → new_ltEs13(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Just(vyy410), app(ty_[], bdh)) → new_ltEs16(vyy3010, vyy410, bdh)
new_ltEs12(Just(vyy3010), Just(vyy410), ty_Int) → new_ltEs15(vyy3010, vyy410)
new_ltEs12(Just(vyy3010), Nothing, bcf) → False
new_compare11(vyy300, vyy40, True, bf) → LT
new_compare11(vyy300, vyy40, False, bf) → GT
new_ltEs8(vyy301, vyy41) → new_not(new_esEs15(new_compare16(vyy301, vyy41), GT))
new_ltEs10(vyy301, vyy41) → new_not(new_esEs15(new_compare8(vyy301, vyy41), GT))
new_ltEs6(True, False) → False
new_ltEs6(False, True) → True
new_ltEs6(True, True) → True
new_ltEs6(False, False) → True
new_ltEs9(vyy301, vyy41, cgg) → new_not(new_esEs15(new_compare17(vyy301, vyy41, cgg), GT))
new_ltEs14(vyy301, vyy41) → new_not(new_esEs15(new_compare25(vyy301, vyy41), GT))
new_compare13(vyy3000, vyy400) → new_compare35(vyy3000, vyy400)
new_compare35(vyy300, vyy40) → new_compare211(vyy300, vyy40, new_esEs13(vyy300, vyy40))
new_compare211(vyy300, vyy40, False) → new_compare112(vyy300, vyy40, new_ltEs6(vyy300, vyy40))
new_compare211(vyy300, vyy40, True) → EQ
new_compare112(vyy300, vyy40, True) → LT
new_compare112(vyy300, vyy40, False) → GT
new_lt8(vyy300, vyy40, ee, ef) → new_esEs15(new_compare38(vyy300, vyy40, ee, ef), LT)
new_lt6(vyy300, vyy40, bc, bd, be) → new_esEs15(new_compare36(vyy300, vyy40, bc, bd, be), LT)
new_lt11(Integer(vyy3000), Integer(vyy400)) → new_esEs15(new_primCmpInt(vyy3000, vyy400), LT)
new_lt10(vyy300, vyy40) → new_esEs15(new_primCmpInt(vyy300, vyy40), LT)
new_lt5(vyy300, vyy40) → new_esEs15(new_compare35(vyy300, vyy40), LT)
new_lt18(vyy300, vyy40) → new_esEs15(new_compare33(vyy300, vyy40), LT)
new_lt9(:%(vyy3000, vyy3001), :%(vyy400, vyy401), fa) → new_esEs15(new_compare28(vyy3000, vyy401, vyy400, vyy3001, fa), LT)
new_compare28(vyy3000, vyy401, vyy400, vyy3001, ty_Int) → new_compare29(vyy3000, vyy401, vyy400, vyy3001)
new_compare28(Integer(vyy30000), Integer(vyy4010), vyy400, vyy3001, ty_Integer) → new_compare25(Integer(new_primMulInt(vyy30000, vyy4010)), new_sr0(vyy400, vyy3001))
new_lt4(vyy300, vyy40) → new_esEs15(new_primCmpChar(vyy300, vyy40), LT)
new_lt16(vyy300, vyy40, eg, eh) → new_esEs15(new_compare37(vyy300, vyy40, eg, eh), LT)
new_lt19([], :(vyy400, vyy401), cdb) → new_esEs15(LT, LT)
new_lt19(:(vyy3000, vyy3001), [], cdb) → new_esEs15(GT, LT)
new_lt19(:(vyy3000, vyy3001), :(vyy400, vyy401), cdb) → new_esEs15(new_primCompAux1(vyy3000, vyy400, vyy3001, vyy401, cdb), LT)
new_lt19([], [], cdb) → new_esEs15(EQ, LT)
new_lt14(vyy300, vyy40) → new_esEs15(new_primCmpFloat(vyy300, vyy40), LT)
new_lt15(vyy300, vyy40) → new_esEs15(new_primCmpDouble(vyy300, vyy40), LT)
new_lt17(vyy300, vyy40, bf) → new_esEs15(new_compare34(vyy300, vyy40, bf), LT)
new_lt7(@0, @0) → new_esEs15(EQ, LT)

The set Q consists of the following terms:

new_ltEs18(x0, x1, ty_Int)
new_lt13(x0, x1, app(ty_[], x2))
new_ltEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Ordering)
new_lt14(x0, x1)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_compare213(x0, x1, False)
new_compare28(x0, x1, x2, x3, ty_Int)
new_esEs25(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_lt11(Integer(x0), Integer(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_@0)
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, EmptyFM, True, x7, x8, x9)
new_ltEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt19([], :(x0, x1), x2)
new_ltEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare211(x0, x1, False)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Int)
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_compare7(x0, x1)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare0(x0, x1, ty_Char)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpNat0(Succ(x0), Zero)
new_esEs26(x0, x1, ty_Bool)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_compare0(x0, x1, app(ty_[], x2))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_foldFM_LE3(x0, x1, x2, x3, x4, x5, x6, x7)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_primCompAux00(x0, x1, EQ, ty_@0)
new_esEs11(@0, @0)
new_foldFM_LE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_lt5(x0, x1)
new_ltEs18(x0, x1, ty_Float)
new_compare113(x0, x1, True)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs15(x0, x1)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_@0)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare23(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Just(x0), Nothing, x1)
new_compare0(x0, x1, app(ty_Maybe, x2))
new_ltEs17(x0, x1)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_foldFM_LE0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10)
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, ty_Ordering)
new_fmToList_LE0(x0, x1, x2, x3, x4, x5)
new_esEs17(Char(x0), Char(x1))
new_ltEs12(Nothing, Nothing, x0)
new_ltEs9(x0, x1, x2)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, x1, EQ, ty_Int)
new_ltEs6(True, True)
new_sr(x0, x1)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_lt6(x0, x1, x2, x3, x4)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare112(x0, x1, True)
new_primEqNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Char)
new_lt9(:%(x0, x1), :%(x2, x3), x4)
new_ltEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs23(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare111(x0, x1, False, x2, x3)
new_compare110(x0, x1, False, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCompAux00(x0, x1, EQ, ty_Float)
new_ltEs13(EQ, EQ)
new_lt13(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_ltEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs13(False, False)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primMulNat0(Zero, Zero)
new_lt19(:(x0, x1), [], x2)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_primMulInt(Pos(x0), Pos(x1))
new_lt13(x0, x1, ty_Int)
new_compare11(x0, x1, True, x2)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat0(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_@0)
new_compare8(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_primPlusNat1(Zero, x0)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_compare27(x0, x1, True, x2, x3)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, ty_Integer)
new_compare0(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Bool)
new_compare210(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs13(LT, EQ)
new_ltEs13(EQ, LT)
new_esEs21(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, False, x2, x3)
new_ltEs5(Left(x0), Right(x1), x2, x3)
new_ltEs5(Right(x0), Left(x1), x2, x3)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Succ(x1))
new_compare25(Integer(x0), Integer(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt17(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs18(x0, x1, ty_Integer)
new_esEs9(x0, x1, ty_Int)
new_esEs18([], [], x0)
new_esEs27(x0, x1, ty_Char)
new_compare212(x0, x1, True, x2)
new_compare0(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1, x2, x3)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare113(x0, x1, False)
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_ltEs14(x0, x1)
new_lt13(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs8(x0, x1, ty_@0)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1, ty_@0)
new_lt13(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_@0)
new_compare0(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_compare213(x0, x1, True)
new_esEs9(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Integer)
new_esEs8(x0, x1, app(ty_[], x2))
new_primCmpChar(Char(x0), Char(x1))
new_compare18(x0, x1, x2, x3, x4)
new_compare26(:(x0, x1), :(x2, x3), x4)
new_compare9(x0, x1)
new_compare24(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_@0)
new_ltEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs24(x0, x1, ty_Double)
new_lt12(x0, x1, ty_Ordering)
new_lt4(x0, x1)
new_compare110(x0, x1, True, x2, x3)
new_esEs18(:(x0, x1), [], x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Bool)
new_compare34(x0, x1, x2)
new_esEs20(x0, x1, app(ty_[], x2))
new_compare12(x0, x1, x2)
new_lt18(x0, x1)
new_esEs24(x0, x1, ty_Int)
new_ltEs5(Left(x0), Left(x1), ty_Bool, x2)
new_compare37(x0, x1, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs15(LT, LT)
new_esEs22(x0, x1, ty_Integer)
new_ltEs6(True, False)
new_ltEs6(False, True)
new_compare17(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs5(Right(x0), Right(x1), x2, ty_Float)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs7(Just(x0), Nothing, x1)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(x0, x1)
new_compare111(x0, x1, True, x2, x3)
new_esEs15(EQ, GT)
new_esEs15(GT, EQ)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs13(EQ, GT)
new_ltEs13(GT, EQ)
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs8(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Left(x0), Left(x1), ty_Char, x2)
new_compare19(x0, x1)
new_esEs21(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Int)
new_primCompAux00(x0, x1, LT, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_lt15(x0, x1)
new_ltEs13(LT, GT)
new_ltEs13(GT, LT)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare10(x0, x1, False, x2, x3, x4)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs6(False, False)
new_ltEs19(x0, x1, ty_Double)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare14(@0, @0)
new_lt20(x0, x1, ty_Int)
new_lt10(x0, x1)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs28(x0, x1, ty_Integer)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_primCompAux1(x0, x1, x2, x3, x4)
new_ltEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_compare35(x0, x1)
new_pePe(False, x0)
new_compare0(x0, x1, ty_Double)
new_ltEs11(x0, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_esEs28(x0, x1, ty_@0)
new_ltEs16(x0, x1, x2)
new_esEs10(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_compare29(x0, x1, x2, x3)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_compare23(x0, x1, False, x2, x3, x4)
new_ltEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs25(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt12(x0, x1, ty_Float)
new_lt7(@0, @0)
new_lt20(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare0(x0, x1, ty_Integer)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, ty_Double)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Right(x0), Right(x1), x2, ty_Bool)
new_compare15(x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), x1)
new_compare33(x0, x1)
new_primCmpNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs8(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt13(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_ltEs13(LT, LT)
new_esEs8(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_compare0(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Bool)
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs15(GT, GT)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_esEs9(x0, x1, ty_Double)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_lt19(:(x0, x1), :(x2, x3), x4)
new_lt16(x0, x1, x2, x3)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs15(GT, LT)
new_esEs15(LT, GT)
new_ltEs8(x0, x1)
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs13(GT, GT)
new_esEs13(False, True)
new_esEs13(True, False)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, x1, EQ, ty_Double)
new_esEs8(x0, x1, ty_Integer)
new_primPlusNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_esEs25(x0, x1, ty_Double)
new_compare16(x0, x1)
new_not(True)
new_lt20(x0, x1, ty_Float)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_esEs16(Float(x0, x1), Float(x2, x3))
new_esEs13(True, True)
new_compare112(x0, x1, False)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs15(EQ, EQ)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare26(:(x0, x1), [], x2)
new_compare11(x0, x1, False, x2)
new_foldFM_LE0(x0, x1, x2, EmptyFM, x3, x4, x5)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_pePe(True, x0)
new_esEs7(Nothing, Just(x0), x1)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs18([], :(x0, x1), x2)
new_compare211(x0, x1, True)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, x7, False, x8, x9, x10)
new_esEs28(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare0(x0, x1, ty_Int)
new_ltEs12(Nothing, Just(x0), x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2, x3, x4)
new_esEs7(Nothing, Nothing, x0)
new_compare212(x0, x1, False, x2)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(False, x0)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs12(Integer(x0), Integer(x1))
new_foldFM_LE10(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), True, x12, x13, x14)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux00(x0, x1, GT, x2)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare36(x0, x1, x2, x3, x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_asAs(True, x0)
new_compare28(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_compare38(x0, x1, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_compare210(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_sr0(Integer(x0), Integer(x1))
new_primEqNat0(Succ(x0), Zero)
new_ltEs5(Left(x0), Left(x1), ty_Float, x2)
new_lt13(x0, x1, ty_Double)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs15(LT, EQ)
new_esEs15(EQ, LT)
new_compare0(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs9(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Left(x0), Left(x1), ty_Integer, x2)
new_compare26([], :(x0, x1), x2)
new_lt19([], [], x0)
new_primMulInt(Neg(x0), Neg(x1))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Float)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs8(x0, x1, ty_Char)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs28(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Int)
new_compare26([], [], x0)
new_ltEs18(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Float)
new_ltEs5(Right(x0), Right(x1), x2, ty_@0)
new_lt13(x0, x1, ty_@0)
new_compare13(x0, x1)

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

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