YES 7.3950000000000005 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
  ((foldFM_GE :: (Ord a, Ord d) => ((a,d)  ->  b  ->  c  ->  c)  ->  c  ->  (a,d)  ->  FiniteMap (a,d) b  ->  c) :: (Ord d, Ord a) => ((a,d)  ->  b  ->  c  ->  c)  ->  c  ->  (a,d)  ->  FiniteMap (a,d) b  ->  c)

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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



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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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

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

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

is transformed to
compare x y = compare3 x y

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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
  ((foldFM_GE :: (Ord d, Ord a) => ((d,a)  ->  b  ->  c  ->  c)  ->  c  ->  (d,a)  ->  FiniteMap (d,a) b  ->  c) :: (Ord a, Ord d) => ((d,a)  ->  b  ->  c  ->  c)  ->  c  ->  (d,a)  ->  FiniteMap (d,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 b a) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

reduce2D vyw vyx = gcd vyw vyx

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

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

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

gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` 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
  ((foldFM_GE :: (Ord c, Ord b) => ((c,b)  ->  a  ->  d  ->  d)  ->  d  ->  (c,b)  ->  FiniteMap (c,b) a  ->  d) :: (Ord c, Ord b) => ((c,b)  ->  a  ->  d  ->  d)  ->  d  ->  (c,b)  ->  FiniteMap (c,b) a  ->  d)

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

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Haskell To QDPs


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

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

new_primCmpNat(Succ(vyy48000), Succ(vyy50000)) → new_primCmpNat(vyy48000, vyy50000)

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(vyy9000), Succ(vyy501000)) → new_primPlusNat(vyy9000, vyy501000)

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(vyy600100), Succ(vyy50100)) → new_primMulNat(vyy600100, Succ(vyy50100))

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(vyy60000), Succ(vyy5000)) → new_primEqNat(vyy60000, vyy5000)

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_esEs1(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(ty_Maybe, ge), gd) → new_esEs0(vyy6000, vyy500, ge)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cc, app(app(ty_@2, da), db), bd) → new_esEs1(vyy6001, vyy501, da, db)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(ty_Either, ca), cb), bc, bd) → new_esEs3(vyy6000, vyy500, ca, cb)
new_esEs0(Just(vyy6000), Just(vyy500), app(app(ty_Either, fg), fh)) → new_esEs3(vyy6000, vyy500, fg, fh)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(ty_Maybe, be), bc, bd) → new_esEs0(vyy6000, vyy500, be)
new_esEs3(Right(vyy6000), Right(vyy500), bda, app(app(ty_Either, bea), beb)) → new_esEs3(vyy6000, vyy500, bea, beb)
new_esEs0(Just(vyy6000), Just(vyy500), app(ty_Maybe, fb)) → new_esEs0(vyy6000, vyy500, fb)
new_esEs1(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(ty_[], gh), gd) → new_esEs2(vyy6000, vyy500, gh)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(app(ty_@3, h), ba), bb), bc, bd) → new_esEs(vyy6000, vyy500, h, ba, bb)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cc, bc, app(app(ty_@2, eb), ec)) → new_esEs1(vyy6002, vyy502, eb, ec)
new_esEs3(Left(vyy6000), Left(vyy500), app(app(ty_Either, bcg), bch), bcb) → new_esEs3(vyy6000, vyy500, bcg, bch)
new_esEs2(:(vyy6000, vyy6001), :(vyy500, vyy501), app(ty_Maybe, bah)) → new_esEs0(vyy6000, vyy500, bah)
new_esEs1(@2(vyy6000, vyy6001), @2(vyy500, vyy501), hc, app(ty_[], bab)) → new_esEs2(vyy6001, vyy501, bab)
new_esEs1(@2(vyy6000, vyy6001), @2(vyy500, vyy501), hc, app(app(ty_Either, bac), bad)) → new_esEs3(vyy6001, vyy501, bac, bad)
new_esEs1(@2(vyy6000, vyy6001), @2(vyy500, vyy501), hc, app(app(ty_@2, hh), baa)) → new_esEs1(vyy6001, vyy501, hh, baa)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cc, app(ty_Maybe, cg), bd) → new_esEs0(vyy6001, vyy501, cg)
new_esEs3(Right(vyy6000), Right(vyy500), bda, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs(vyy6000, vyy500, bdb, bdc, bdd)
new_esEs2(:(vyy6000, vyy6001), :(vyy500, vyy501), app(app(app(ty_@3, bae), baf), bag)) → new_esEs(vyy6000, vyy500, bae, baf, bag)
new_esEs3(Right(vyy6000), Right(vyy500), bda, app(ty_[], bdh)) → new_esEs2(vyy6000, vyy500, bdh)
new_esEs2(:(vyy6000, vyy6001), :(vyy500, vyy501), app(app(ty_@2, bba), bbb)) → new_esEs1(vyy6000, vyy500, bba, bbb)
new_esEs3(Left(vyy6000), Left(vyy500), app(app(ty_@2, bcd), bce), bcb) → new_esEs1(vyy6000, vyy500, bcd, bce)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cc, bc, app(ty_Maybe, ea)) → new_esEs0(vyy6002, vyy502, ea)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cc, app(app(app(ty_@3, cd), ce), cf), bd) → new_esEs(vyy6001, vyy501, cd, ce, cf)
new_esEs2(:(vyy6000, vyy6001), :(vyy500, vyy501), bbf) → new_esEs2(vyy6001, vyy501, bbf)
new_esEs1(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_@2, gf), gg), gd) → new_esEs1(vyy6000, vyy500, gf, gg)
new_esEs0(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, eg), eh), fa)) → new_esEs(vyy6000, vyy500, eg, eh, fa)
new_esEs2(:(vyy6000, vyy6001), :(vyy500, vyy501), app(ty_[], bbc)) → new_esEs2(vyy6000, vyy500, bbc)
new_esEs1(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(ty_Either, ha), hb), gd) → new_esEs3(vyy6000, vyy500, ha, hb)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(ty_[], bh), bc, bd) → new_esEs2(vyy6000, vyy500, bh)
new_esEs2(:(vyy6000, vyy6001), :(vyy500, vyy501), app(app(ty_Either, bbd), bbe)) → new_esEs3(vyy6000, vyy500, bbd, bbe)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cc, app(ty_[], dc), bd) → new_esEs2(vyy6001, vyy501, dc)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cc, bc, app(ty_[], ed)) → new_esEs2(vyy6002, vyy502, ed)
new_esEs1(@2(vyy6000, vyy6001), @2(vyy500, vyy501), hc, app(app(app(ty_@3, hd), he), hf)) → new_esEs(vyy6001, vyy501, hd, he, hf)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), app(app(ty_@2, bf), bg), bc, bd) → new_esEs1(vyy6000, vyy500, bf, bg)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cc, app(app(ty_Either, dd), de), bd) → new_esEs3(vyy6001, vyy501, dd, de)
new_esEs3(Right(vyy6000), Right(vyy500), bda, app(app(ty_@2, bdf), bdg)) → new_esEs1(vyy6000, vyy500, bdf, bdg)
new_esEs1(@2(vyy6000, vyy6001), @2(vyy500, vyy501), hc, app(ty_Maybe, hg)) → new_esEs0(vyy6001, vyy501, hg)
new_esEs3(Left(vyy6000), Left(vyy500), app(ty_Maybe, bcc), bcb) → new_esEs0(vyy6000, vyy500, bcc)
new_esEs3(Right(vyy6000), Right(vyy500), bda, app(ty_Maybe, bde)) → new_esEs0(vyy6000, vyy500, bde)
new_esEs3(Left(vyy6000), Left(vyy500), app(ty_[], bcf), bcb) → new_esEs2(vyy6000, vyy500, bcf)
new_esEs0(Just(vyy6000), Just(vyy500), app(app(ty_@2, fc), fd)) → new_esEs1(vyy6000, vyy500, fc, fd)
new_esEs1(@2(vyy6000, vyy6001), @2(vyy500, vyy501), app(app(app(ty_@3, ga), gb), gc), gd) → new_esEs(vyy6000, vyy500, ga, gb, gc)
new_esEs3(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, bbg), bbh), bca), bcb) → new_esEs(vyy6000, vyy500, bbg, bbh, bca)
new_esEs0(Just(vyy6000), Just(vyy500), app(ty_[], ff)) → new_esEs2(vyy6000, vyy500, ff)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cc, bc, app(app(ty_Either, ee), ef)) → new_esEs3(vyy6002, vyy502, ee, ef)
new_esEs(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cc, bc, app(app(app(ty_@3, df), dg), dh)) → new_esEs(vyy6002, vyy502, df, dg, dh)

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

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



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

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

new_compare22(@2(vyy480, Right(vyy4810)), @2(vyy500, Right(vyy5010)), False, gg, app(app(ty_Either, cb), app(ty_[], cf))) → new_ltEs1(vyy4810, vyy5010, cf)
new_ltEs2(@2(vyy4810, vyy4811), @2(vyy5010, vyy5011), app(app(ty_@2, bag), bah), bad) → new_lt2(vyy4810, vyy5010, bag, bah)
new_ltEs(Right(vyy4810), Right(vyy5010), cb, app(ty_[], cf)) → new_ltEs1(vyy4810, vyy5010, cf)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), bbd, app(ty_Maybe, bdb), bda) → new_lt0(vyy4811, vyy5011, bdb)
new_lt(vyy480, vyy500, gb, gc) → new_compare20(vyy480, vyy500, new_esEs4(vyy480, vyy500, gb, gc), gb, gc)
new_lt0(vyy480, vyy500, gd) → new_compare21(vyy480, vyy500, new_esEs5(vyy480, vyy500, gd), gd)
new_ltEs(Right(vyy4810), Right(vyy5010), cb, app(app(ty_Either, cc), cd)) → new_ltEs(vyy4810, vyy5010, cc, cd)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, bbd), bbe), app(app(ty_Either, bbf), bbg))) → new_ltEs(vyy4812, vyy5012, bbf, bbg)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, bbd), bbe), app(ty_[], bca))) → new_ltEs1(vyy4812, vyy5012, bca)
new_compare22(@2(vyy480, Left(vyy4810)), @2(vyy500, Left(vyy5010)), False, gg, app(app(ty_Either, app(app(ty_Either, h), ba)), bb)) → new_ltEs(vyy4810, vyy5010, h, ba)
new_compare22(@2(vyy480, Just(vyy4810)), @2(vyy500, Just(vyy5010)), False, gg, app(ty_Maybe, app(ty_Maybe, dg))) → new_ltEs0(vyy4810, vyy5010, dg)
new_lt1(:(vyy4800, vyy4801), :(vyy5000, vyy5001), eg) → new_primCompAux(vyy4800, vyy5000, new_compare0(vyy4801, vyy5001, eg), eg)
new_ltEs0(Just(vyy4810), Just(vyy5010), app(ty_Maybe, dg)) → new_ltEs0(vyy4810, vyy5010, dg)
new_compare22(@2(vyy480, @2(vyy4810, vyy4811)), @2(vyy500, @2(vyy5010, vyy5011)), False, gg, app(app(ty_@2, gh), app(app(ty_Either, ha), hb))) → new_ltEs(vyy4811, vyy5011, ha, hb)
new_compare3(vyy480, vyy500, ge, gf) → new_compare22(vyy480, vyy500, new_esEs6(vyy480, vyy500, ge, gf), ge, gf)
new_primCompAux(vyy4800, vyy5000, vyy118, app(ty_[], fc)) → new_compare(vyy4800, vyy5000, fc)
new_compare22(@2(:(vyy4800, vyy4801), vyy481), @2(:(vyy5000, vyy5001), vyy501), False, app(ty_[], eg), bfb) → new_compare(vyy4801, vyy5001, eg)
new_compare22(@2(vyy480, Just(vyy4810)), @2(vyy500, Just(vyy5010)), False, gg, app(ty_Maybe, app(app(app(ty_@3, ec), ed), ee))) → new_ltEs3(vyy4810, vyy5010, ec, ed, ee)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), app(app(ty_@2, bee), bef), bbe, bda) → new_lt2(vyy4810, vyy5010, bee, bef)
new_compare22(@2(vyy480, vyy481), @2(vyy500, vyy501), False, app(ty_Maybe, gd), bfb) → new_compare21(vyy480, vyy500, new_esEs5(vyy480, vyy500, gd), gd)
new_lt1(:(vyy4800, vyy4801), :(vyy5000, vyy5001), eg) → new_compare(vyy4801, vyy5001, eg)
new_primCompAux(vyy4800, vyy5000, vyy118, app(ty_Maybe, fb)) → new_compare2(vyy4800, vyy5000, fb)
new_compare22(@2(vyy480, Just(vyy4810)), @2(vyy500, Just(vyy5010)), False, gg, app(ty_Maybe, app(ty_[], dh))) → new_ltEs1(vyy4810, vyy5010, dh)
new_compare22(@2(vyy480, Right(vyy4810)), @2(vyy500, Right(vyy5010)), False, gg, app(app(ty_Either, cb), app(app(ty_@2, cg), da))) → new_ltEs2(vyy4810, vyy5010, cg, da)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), bbd, bbe, app(app(ty_@2, bcb), bcc)) → new_ltEs2(vyy4812, vyy5012, bcb, bcc)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, app(ty_Maybe, bec)), bbe), bda)) → new_lt0(vyy4810, vyy5010, bec)
new_ltEs2(@2(vyy4810, vyy4811), @2(vyy5010, vyy5011), app(app(app(ty_@3, bba), bbb), bbc), bad) → new_lt3(vyy4810, vyy5010, bba, bbb, bbc)
new_compare22(@2(:(vyy4800, vyy4801), vyy481), @2(:(vyy5000, vyy5001), vyy501), False, app(ty_[], eg), bfb) → new_primCompAux(vyy4800, vyy5000, new_compare0(vyy4801, vyy5001, eg), eg)
new_ltEs(Left(vyy4810), Left(vyy5010), app(ty_Maybe, bc), bb) → new_ltEs0(vyy4810, vyy5010, bc)
new_ltEs(Left(vyy4810), Left(vyy5010), app(app(app(ty_@3, bg), bh), ca), bb) → new_ltEs3(vyy4810, vyy5010, bg, bh, ca)
new_compare22(@2(vyy480, Right(vyy4810)), @2(vyy500, Right(vyy5010)), False, gg, app(app(ty_Either, cb), app(app(app(ty_@3, db), dc), dd))) → new_ltEs3(vyy4810, vyy5010, db, dc, dd)
new_ltEs2(@2(vyy4810, vyy4811), @2(vyy5010, vyy5011), gh, app(ty_[], hd)) → new_ltEs1(vyy4811, vyy5011, hd)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), bbd, app(app(app(ty_@3, bdf), bdg), bdh), bda) → new_lt3(vyy4811, vyy5011, bdf, bdg, bdh)
new_ltEs(Left(vyy4810), Left(vyy5010), app(ty_[], bd), bb) → new_ltEs1(vyy4810, vyy5010, bd)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), bbd, bbe, app(ty_[], bca)) → new_ltEs1(vyy4812, vyy5012, bca)
new_ltEs2(@2(vyy4810, vyy4811), @2(vyy5010, vyy5011), app(ty_Maybe, bae), bad) → new_lt0(vyy4810, vyy5010, bae)
new_compare4(vyy480, vyy500, bfc, bfd, bfe) → new_compare23(vyy480, vyy500, new_esEs7(vyy480, vyy500, bfc, bfd, bfe), bfc, bfd, bfe)
new_compare1(vyy480, vyy500, gb, gc) → new_compare20(vyy480, vyy500, new_esEs4(vyy480, vyy500, gb, gc), gb, gc)
new_ltEs(Right(vyy4810), Right(vyy5010), cb, app(ty_Maybe, ce)) → new_ltEs0(vyy4810, vyy5010, ce)
new_compare22(@2(vyy480, Left(vyy4810)), @2(vyy500, Left(vyy5010)), False, gg, app(app(ty_Either, app(ty_[], bd)), bb)) → new_ltEs1(vyy4810, vyy5010, bd)
new_compare22(@2(vyy480, @2(vyy4810, vyy4811)), @2(vyy500, @2(vyy5010, vyy5011)), False, gg, app(app(ty_@2, app(app(ty_Either, bab), bac)), bad)) → new_lt(vyy4810, vyy5010, bab, bac)
new_compare22(@2(vyy480, Left(vyy4810)), @2(vyy500, Left(vyy5010)), False, gg, app(app(ty_Either, app(app(app(ty_@3, bg), bh), ca)), bb)) → new_ltEs3(vyy4810, vyy5010, bg, bh, ca)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, bbd), app(ty_[], bdc)), bda)) → new_lt1(vyy4811, vyy5011, bdc)
new_ltEs2(@2(vyy4810, vyy4811), @2(vyy5010, vyy5011), app(ty_[], baf), bad) → new_lt1(vyy4810, vyy5010, baf)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, bbd), app(app(ty_Either, bcg), bch)), bda)) → new_lt(vyy4811, vyy5011, bcg, bch)
new_compare22(@2(vyy480, Right(vyy4810)), @2(vyy500, Right(vyy5010)), False, gg, app(app(ty_Either, cb), app(app(ty_Either, cc), cd))) → new_ltEs(vyy4810, vyy5010, cc, cd)
new_compare23(vyy480, vyy500, False, bfc, bfd, bfe) → new_ltEs3(vyy480, vyy500, bfc, bfd, bfe)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), bbd, bbe, app(app(ty_Either, bbf), bbg)) → new_ltEs(vyy4812, vyy5012, bbf, bbg)
new_compare22(@2(vyy480, @2(vyy4810, vyy4811)), @2(vyy500, @2(vyy5010, vyy5011)), False, gg, app(app(ty_@2, gh), app(ty_Maybe, hc))) → new_ltEs0(vyy4811, vyy5011, hc)
new_ltEs2(@2(vyy4810, vyy4811), @2(vyy5010, vyy5011), gh, app(app(ty_Either, ha), hb)) → new_ltEs(vyy4811, vyy5011, ha, hb)
new_ltEs0(Just(vyy4810), Just(vyy5010), app(app(app(ty_@3, ec), ed), ee)) → new_ltEs3(vyy4810, vyy5010, ec, ed, ee)
new_compare22(@2(vyy480, Just(vyy4810)), @2(vyy500, Just(vyy5010)), False, gg, app(ty_Maybe, app(app(ty_@2, ea), eb))) → new_ltEs2(vyy4810, vyy5010, ea, eb)
new_compare22(@2(vyy480, Left(vyy4810)), @2(vyy500, Left(vyy5010)), False, gg, app(app(ty_Either, app(app(ty_@2, be), bf)), bb)) → new_ltEs2(vyy4810, vyy5010, be, bf)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, app(app(ty_Either, bea), beb)), bbe), bda)) → new_lt(vyy4810, vyy5010, bea, beb)
new_lt3(vyy480, vyy500, bfc, bfd, bfe) → new_compare23(vyy480, vyy500, new_esEs7(vyy480, vyy500, bfc, bfd, bfe), bfc, bfd, bfe)
new_ltEs(Left(vyy4810), Left(vyy5010), app(app(ty_Either, h), ba), bb) → new_ltEs(vyy4810, vyy5010, h, ba)
new_ltEs2(@2(vyy4810, vyy4811), @2(vyy5010, vyy5011), gh, app(app(app(ty_@3, hg), hh), baa)) → new_ltEs3(vyy4811, vyy5011, hg, hh, baa)
new_primCompAux(vyy4800, vyy5000, vyy118, app(app(ty_@2, fd), ff)) → new_compare3(vyy4800, vyy5000, fd, ff)
new_ltEs1(vyy481, vyy501, ef) → new_compare(vyy481, vyy501, ef)
new_compare21(vyy480, vyy500, False, gd) → new_ltEs0(vyy480, vyy500, gd)
new_compare22(@2(vyy480, Just(vyy4810)), @2(vyy500, Just(vyy5010)), False, gg, app(ty_Maybe, app(app(ty_Either, de), df))) → new_ltEs(vyy4810, vyy5010, de, df)
new_compare22(@2(vyy480, Right(vyy4810)), @2(vyy500, Right(vyy5010)), False, gg, app(app(ty_Either, cb), app(ty_Maybe, ce))) → new_ltEs0(vyy4810, vyy5010, ce)
new_ltEs(Right(vyy4810), Right(vyy5010), cb, app(app(app(ty_@3, db), dc), dd)) → new_ltEs3(vyy4810, vyy5010, db, dc, dd)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, bbd), app(app(ty_@2, bdd), bde)), bda)) → new_lt2(vyy4811, vyy5011, bdd, bde)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, app(ty_[], bed)), bbe), bda)) → new_lt1(vyy4810, vyy5010, bed)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), bbd, bbe, app(ty_Maybe, bbh)) → new_ltEs0(vyy4812, vyy5012, bbh)
new_compare22(@2(vyy480, @2(vyy4810, vyy4811)), @2(vyy500, @2(vyy5010, vyy5011)), False, gg, app(app(ty_@2, gh), app(app(ty_@2, he), hf))) → new_ltEs2(vyy4811, vyy5011, he, hf)
new_compare22(@2(vyy480, vyy481), @2(vyy500, vyy501), False, gg, app(ty_[], ef)) → new_compare(vyy481, vyy501, ef)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), app(app(ty_Either, bea), beb), bbe, bda) → new_lt(vyy4810, vyy5010, bea, beb)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), bbd, app(app(ty_Either, bcg), bch), bda) → new_lt(vyy4811, vyy5011, bcg, bch)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, bbd), app(app(app(ty_@3, bdf), bdg), bdh)), bda)) → new_lt3(vyy4811, vyy5011, bdf, bdg, bdh)
new_compare22(@2(vyy480, vyy481), @2(vyy500, vyy501), False, app(app(ty_Either, gb), gc), bfb) → new_compare20(vyy480, vyy500, new_esEs4(vyy480, vyy500, gb, gc), gb, gc)
new_compare22(@2(vyy480, @2(vyy4810, vyy4811)), @2(vyy500, @2(vyy5010, vyy5011)), False, gg, app(app(ty_@2, app(app(app(ty_@3, bba), bbb), bbc)), bad)) → new_lt3(vyy4810, vyy5010, bba, bbb, bbc)
new_ltEs2(@2(vyy4810, vyy4811), @2(vyy5010, vyy5011), app(app(ty_Either, bab), bac), bad) → new_lt(vyy4810, vyy5010, bab, bac)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, bbd), app(ty_Maybe, bdb)), bda)) → new_lt0(vyy4811, vyy5011, bdb)
new_primCompAux(vyy4800, vyy5000, vyy118, app(app(ty_Either, eh), fa)) → new_compare1(vyy4800, vyy5000, eh, fa)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), bbd, app(app(ty_@2, bdd), bde), bda) → new_lt2(vyy4811, vyy5011, bdd, bde)
new_compare22(@2(vyy480, @2(vyy4810, vyy4811)), @2(vyy500, @2(vyy5010, vyy5011)), False, gg, app(app(ty_@2, gh), app(app(app(ty_@3, hg), hh), baa))) → new_ltEs3(vyy4811, vyy5011, hg, hh, baa)
new_compare22(@2(vyy480, vyy481), @2(vyy500, vyy501), False, app(app(app(ty_@3, bfc), bfd), bfe), bfb) → new_compare23(vyy480, vyy500, new_esEs7(vyy480, vyy500, bfc, bfd, bfe), bfc, bfd, bfe)
new_compare22(@2(vyy480, Left(vyy4810)), @2(vyy500, Left(vyy5010)), False, gg, app(app(ty_Either, app(ty_Maybe, bc)), bb)) → new_ltEs0(vyy4810, vyy5010, bc)
new_compare20(vyy480, vyy500, False, gb, gc) → new_ltEs(vyy480, vyy500, gb, gc)
new_compare22(@2(vyy480, @2(vyy4810, vyy4811)), @2(vyy500, @2(vyy5010, vyy5011)), False, gg, app(app(ty_@2, app(app(ty_@2, bag), bah)), bad)) → new_lt2(vyy4810, vyy5010, bag, bah)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, bbd), bbe), app(ty_Maybe, bbh))) → new_ltEs0(vyy4812, vyy5012, bbh)
new_compare22(@2(vyy480, @2(vyy4810, vyy4811)), @2(vyy500, @2(vyy5010, vyy5011)), False, gg, app(app(ty_@2, app(ty_Maybe, bae)), bad)) → new_lt0(vyy4810, vyy5010, bae)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, bbd), bbe), app(app(app(ty_@3, bcd), bce), bcf))) → new_ltEs3(vyy4812, vyy5012, bcd, bce, bcf)
new_ltEs2(@2(vyy4810, vyy4811), @2(vyy5010, vyy5011), gh, app(ty_Maybe, hc)) → new_ltEs0(vyy4811, vyy5011, hc)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), bbd, bbe, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs3(vyy4812, vyy5012, bcd, bce, bcf)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), app(ty_[], bed), bbe, bda) → new_lt1(vyy4810, vyy5010, bed)
new_ltEs2(@2(vyy4810, vyy4811), @2(vyy5010, vyy5011), gh, app(app(ty_@2, he), hf)) → new_ltEs2(vyy4811, vyy5011, he, hf)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), app(app(app(ty_@3, beg), beh), bfa), bbe, bda) → new_lt3(vyy4810, vyy5010, beg, beh, bfa)
new_compare(:(vyy4800, vyy4801), :(vyy5000, vyy5001), eg) → new_compare(vyy4801, vyy5001, eg)
new_ltEs0(Just(vyy4810), Just(vyy5010), app(app(ty_@2, ea), eb)) → new_ltEs2(vyy4810, vyy5010, ea, eb)
new_compare(:(vyy4800, vyy4801), :(vyy5000, vyy5001), eg) → new_primCompAux(vyy4800, vyy5000, new_compare0(vyy4801, vyy5001, eg), eg)
new_ltEs0(Just(vyy4810), Just(vyy5010), app(ty_[], dh)) → new_ltEs1(vyy4810, vyy5010, dh)
new_ltEs(Right(vyy4810), Right(vyy5010), cb, app(app(ty_@2, cg), da)) → new_ltEs2(vyy4810, vyy5010, cg, da)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, bbd), bbe), app(app(ty_@2, bcb), bcc))) → new_ltEs2(vyy4812, vyy5012, bcb, bcc)
new_compare2(vyy480, vyy500, gd) → new_compare21(vyy480, vyy500, new_esEs5(vyy480, vyy500, gd), gd)
new_lt2(vyy480, vyy500, ge, gf) → new_compare22(vyy480, vyy500, new_esEs6(vyy480, vyy500, ge, gf), ge, gf)
new_compare22(@2(vyy480, @2(vyy4810, vyy4811)), @2(vyy500, @2(vyy5010, vyy5011)), False, gg, app(app(ty_@2, app(ty_[], baf)), bad)) → new_lt1(vyy4810, vyy5010, baf)
new_ltEs(Left(vyy4810), Left(vyy5010), app(app(ty_@2, be), bf), bb) → new_ltEs2(vyy4810, vyy5010, be, bf)
new_compare22(@2(vyy480, @2(vyy4810, vyy4811)), @2(vyy500, @2(vyy5010, vyy5011)), False, gg, app(app(ty_@2, gh), app(ty_[], hd))) → new_ltEs1(vyy4811, vyy5011, hd)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, app(app(app(ty_@3, beg), beh), bfa)), bbe), bda)) → new_lt3(vyy4810, vyy5010, beg, beh, bfa)
new_primCompAux(vyy4800, vyy5000, vyy118, app(app(app(ty_@3, fg), fh), ga)) → new_compare4(vyy4800, vyy5000, fg, fh, ga)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), bbd, app(ty_[], bdc), bda) → new_lt1(vyy4811, vyy5011, bdc)
new_ltEs0(Just(vyy4810), Just(vyy5010), app(app(ty_Either, de), df)) → new_ltEs(vyy4810, vyy5010, de, df)
new_ltEs3(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), app(ty_Maybe, bec), bbe, bda) → new_lt0(vyy4810, vyy5010, bec)
new_compare22(@2(vyy480, @3(vyy4810, vyy4811, vyy4812)), @2(vyy500, @3(vyy5010, vyy5011, vyy5012)), False, gg, app(app(app(ty_@3, app(app(ty_@2, bee), bef)), bbe), bda)) → new_lt2(vyy4810, vyy5010, bee, bef)
new_compare22(@2(vyy480, vyy481), @2(vyy500, vyy501), False, app(app(ty_@2, ge), gf), bfb) → new_compare22(vyy480, vyy500, new_esEs6(vyy480, vyy500, ge, gf), ge, gf)

The TRS R consists of the following rules:

new_esEs7(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cdf, cdg, cdh) → new_asAs(new_esEs24(vyy6000, vyy500, cdf), new_asAs(new_esEs25(vyy6001, vyy501, cdg), new_esEs26(vyy6002, vyy502, cdh)))
new_esEs4(Right(vyy6000), Right(vyy500), cae, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_lt21(vyy4810, vyy5010, ty_Float) → new_lt13(vyy4810, vyy5010)
new_ltEs14(vyy481, vyy501) → new_not(new_esEs8(new_compare13(vyy481, vyy501), GT))
new_esEs21(vyy4810, vyy5010, app(app(ty_@2, bee), bef)) → new_esEs6(vyy4810, vyy5010, bee, bef)
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, ty_Int) → new_ltEs14(vyy4810, vyy5010)
new_lt19(vyy4811, vyy5011, app(app(ty_Either, bcg), bch)) → new_lt10(vyy4811, vyy5011, bcg, bch)
new_lt19(vyy4811, vyy5011, ty_Double) → new_lt7(vyy4811, vyy5011)
new_compare9(Char(vyy4800), Char(vyy5000)) → new_primCmpNat0(vyy4800, vyy5000)
new_ltEs4(EQ, GT) → True
new_compare10(vyy480, vyy500, True, bfc, bfd, bfe) → LT
new_esEs5(Just(vyy6000), Just(vyy500), ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_compare18(vyy480, vyy500, gb, gc) → new_compare27(vyy480, vyy500, new_esEs4(vyy480, vyy500, gb, gc), gb, gc)
new_ltEs7(vyy481, vyy501, ty_@0) → new_ltEs6(vyy481, vyy501)
new_esEs4(Left(vyy6000), Left(vyy500), ty_Bool, bhe) → new_esEs14(vyy6000, vyy500)
new_esEs22(vyy4811, vyy5011, ty_Float) → new_esEs19(vyy4811, vyy5011)
new_lt19(vyy4811, vyy5011, ty_Integer) → new_lt5(vyy4811, vyy5011)
new_ltEs9(Nothing, Just(vyy5010), bgb) → True
new_esEs4(Right(vyy6000), Right(vyy500), cae, ty_Double) → new_esEs16(vyy6000, vyy500)
new_compare29(vyy4800, vyy5000, ty_Double) → new_compare8(vyy4800, vyy5000)
new_esEs23(vyy4810, vyy5010, ty_Bool) → new_esEs14(vyy4810, vyy5010)
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Int) → new_ltEs14(vyy4810, vyy5010)
new_ltEs19(vyy4812, vyy5012, ty_Double) → new_ltEs11(vyy4812, vyy5012)
new_esEs4(Right(vyy6000), Right(vyy500), cae, app(ty_Maybe, cbb)) → new_esEs5(vyy6000, vyy500, cbb)
new_esEs23(vyy4810, vyy5010, ty_Float) → new_esEs19(vyy4810, vyy5010)
new_esEs20(Char(vyy6000), Char(vyy500)) → new_primEqNat0(vyy6000, vyy500)
new_esEs21(vyy4810, vyy5010, ty_@0) → new_esEs17(vyy4810, vyy5010)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs8(Left(vyy4810), Left(vyy5010), app(app(ty_@2, be), bf), bb) → new_ltEs15(vyy4810, vyy5010, be, bf)
new_esEs25(vyy6001, vyy501, ty_Char) → new_esEs20(vyy6001, vyy501)
new_ltEs7(vyy481, vyy501, ty_Int) → new_ltEs14(vyy481, vyy501)
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, ty_Ordering) → new_ltEs4(vyy4810, vyy5010)
new_esEs26(vyy6002, vyy502, app(ty_Ratio, cgh)) → new_esEs10(vyy6002, vyy502, cgh)
new_ltEs7(vyy481, vyy501, app(app(app(ty_@3, bbd), bbe), bda)) → new_ltEs16(vyy481, vyy501, bbd, bbe, bda)
new_esEs28(vyy6001, vyy501, app(ty_Ratio, dbf)) → new_esEs10(vyy6001, vyy501, dbf)
new_sr(Integer(vyy50000), Integer(vyy48010)) → Integer(new_primMulInt(vyy50000, vyy48010))
new_esEs5(Just(vyy6000), Just(vyy500), ty_Double) → new_esEs16(vyy6000, vyy500)
new_esEs22(vyy4811, vyy5011, ty_@0) → new_esEs17(vyy4811, vyy5011)
new_esEs29(vyy6000, vyy500, app(app(ty_Either, ddf), ddg)) → new_esEs4(vyy6000, vyy500, ddf, ddg)
new_ltEs7(vyy481, vyy501, app(app(ty_Either, cb), bb)) → new_ltEs8(vyy481, vyy501, cb, bb)
new_esEs25(vyy6001, vyy501, ty_Double) → new_esEs16(vyy6001, vyy501)
new_ltEs9(Just(vyy4810), Just(vyy5010), app(app(ty_@2, ea), eb)) → new_ltEs15(vyy4810, vyy5010, ea, eb)
new_ltEs19(vyy4812, vyy5012, ty_Bool) → new_ltEs18(vyy4812, vyy5012)
new_lt5(vyy480, vyy500) → new_esEs8(new_compare5(vyy480, vyy500), LT)
new_esEs4(Right(vyy6000), Right(vyy500), cae, app(app(app(ty_@3, caf), cag), cah)) → new_esEs7(vyy6000, vyy500, caf, cag, cah)
new_lt21(vyy4810, vyy5010, app(ty_Maybe, bae)) → new_lt11(vyy4810, vyy5010, bae)
new_esEs4(Left(vyy6000), Left(vyy500), app(app(ty_@2, bhh), caa), bhe) → new_esEs6(vyy6000, vyy500, bhh, caa)
new_esEs19(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_esEs13(new_sr0(vyy6000, vyy500), new_sr0(vyy6001, vyy501))
new_compare29(vyy4800, vyy5000, ty_Bool) → new_compare31(vyy4800, vyy5000)
new_lt19(vyy4811, vyy5011, ty_Float) → new_lt13(vyy4811, vyy5011)
new_compare0(:(vyy4800, vyy4801), :(vyy5000, vyy5001), eg) → new_primCompAux0(vyy4800, vyy5000, new_compare0(vyy4801, vyy5001, eg), eg)
new_lt9(vyy480, vyy500, app(app(app(ty_@3, bfc), bfd), bfe)) → new_lt6(vyy480, vyy500, bfc, bfd, bfe)
new_esEs21(vyy4810, vyy5010, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs7(vyy4810, vyy5010, beg, beh, bfa)
new_esEs5(Just(vyy6000), Just(vyy500), app(ty_Maybe, cch)) → new_esEs5(vyy6000, vyy500, cch)
new_ltEs7(vyy481, vyy501, ty_Double) → new_ltEs11(vyy481, vyy501)
new_esEs4(Left(vyy6000), Left(vyy500), app(ty_Ratio, bhf), bhe) → new_esEs10(vyy6000, vyy500, bhf)
new_esEs22(vyy4811, vyy5011, ty_Integer) → new_esEs9(vyy4811, vyy5011)
new_esEs29(vyy6000, vyy500, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs7(vyy6000, vyy500, dcf, dcg, dch)
new_esEs24(vyy6000, vyy500, ty_@0) → new_esEs17(vyy6000, vyy500)
new_esEs4(Left(vyy6000), Left(vyy500), ty_Ordering, bhe) → new_esEs8(vyy6000, vyy500)
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Char, bb) → new_ltEs5(vyy4810, vyy5010)
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Double) → new_ltEs11(vyy4810, vyy5010)
new_esEs17(@0, @0) → True
new_esEs4(Left(vyy6000), Left(vyy500), ty_Int, bhe) → new_esEs13(vyy6000, vyy500)
new_lt20(vyy4810, vyy5010, ty_Double) → new_lt7(vyy4810, vyy5010)
new_pePe(False, vyy117) → vyy117
new_esEs29(vyy6000, vyy500, ty_Double) → new_esEs16(vyy6000, vyy500)
new_lt9(vyy480, vyy500, app(app(ty_Either, gb), gc)) → new_lt10(vyy480, vyy500, gb, gc)
new_esEs25(vyy6001, vyy501, app(app(ty_Either, cgc), cgd)) → new_esEs4(vyy6001, vyy501, cgc, cgd)
new_lt21(vyy4810, vyy5010, ty_Char) → new_lt8(vyy4810, vyy5010)
new_lt9(vyy480, vyy500, ty_Int) → new_lt14(vyy480, vyy500)
new_esEs18(:(vyy6000, vyy6001), [], dce) → False
new_esEs18([], :(vyy500, vyy501), dce) → False
new_esEs28(vyy6001, vyy501, ty_Char) → new_esEs20(vyy6001, vyy501)
new_esEs22(vyy4811, vyy5011, app(app(ty_Either, bcg), bch)) → new_esEs4(vyy4811, vyy5011, bcg, bch)
new_esEs25(vyy6001, vyy501, ty_Bool) → new_esEs14(vyy6001, vyy501)
new_esEs18(:(vyy6000, vyy6001), :(vyy500, vyy501), dce) → new_asAs(new_esEs29(vyy6000, vyy500, dce), new_esEs18(vyy6001, vyy501, dce))
new_esEs11(vyy6000, vyy500, ty_Int) → new_esEs13(vyy6000, vyy500)
new_esEs29(vyy6000, vyy500, ty_@0) → new_esEs17(vyy6000, vyy500)
new_compare29(vyy4800, vyy5000, ty_Int) → new_compare13(vyy4800, vyy5000)
new_esEs15(vyy480, vyy500, app(app(ty_@2, ge), gf)) → new_esEs6(vyy480, vyy500, ge, gf)
new_ltEs9(Just(vyy4810), Just(vyy5010), app(ty_[], dh)) → new_ltEs12(vyy4810, vyy5010, dh)
new_lt19(vyy4811, vyy5011, app(ty_Ratio, bgh)) → new_lt17(vyy4811, vyy5011, bgh)
new_compare29(vyy4800, vyy5000, ty_@0) → new_compare15(vyy4800, vyy5000)
new_compare17(vyy99, vyy100, vyy101, vyy102, True, vyy104, bfg, bfh) → new_compare11(vyy99, vyy100, vyy101, vyy102, True, bfg, bfh)
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Char) → new_ltEs5(vyy4810, vyy5010)
new_compare29(vyy4800, vyy5000, app(app(ty_@2, fd), ff)) → new_compare19(vyy4800, vyy5000, fd, ff)
new_esEs27(vyy6000, vyy500, ty_Float) → new_esEs19(vyy6000, vyy500)
new_compare15(@0, @0) → EQ
new_esEs22(vyy4811, vyy5011, ty_Ordering) → new_esEs8(vyy4811, vyy5011)
new_ltEs20(vyy4811, vyy5011, app(ty_[], hd)) → new_ltEs12(vyy4811, vyy5011, hd)
new_ltEs6(vyy481, vyy501) → new_not(new_esEs8(new_compare15(vyy481, vyy501), GT))
new_lt9(vyy480, vyy500, ty_Ordering) → new_lt16(vyy480, vyy500)
new_esEs4(Right(vyy6000), Right(vyy500), cae, app(ty_Ratio, cba)) → new_esEs10(vyy6000, vyy500, cba)
new_ltEs10(vyy481, vyy501) → new_not(new_esEs8(new_compare5(vyy481, vyy501), GT))
new_esEs23(vyy4810, vyy5010, app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs7(vyy4810, vyy5010, bba, bbb, bbc)
new_primCmpNat0(Zero, Succ(vyy50000)) → LT
new_esEs21(vyy4810, vyy5010, ty_Bool) → new_esEs14(vyy4810, vyy5010)
new_primCompAux0(vyy4800, vyy5000, vyy118, eg) → new_primCompAux00(vyy118, new_compare29(vyy4800, vyy5000, eg))
new_esEs27(vyy6000, vyy500, app(app(app(ty_@3, daa), dab), dac)) → new_esEs7(vyy6000, vyy500, daa, dab, dac)
new_lt4(vyy480, vyy500, eg) → new_esEs8(new_compare0(vyy480, vyy500, eg), LT)
new_ltEs5(vyy481, vyy501) → new_not(new_esEs8(new_compare9(vyy481, vyy501), GT))
new_ltEs8(Left(vyy4810), Left(vyy5010), app(ty_[], bd), bb) → new_ltEs12(vyy4810, vyy5010, bd)
new_esEs4(Right(vyy6000), Right(vyy500), cae, ty_Integer) → new_esEs9(vyy6000, vyy500)
new_esEs25(vyy6001, vyy501, app(app(ty_@2, cfh), cga)) → new_esEs6(vyy6001, vyy501, cfh, cga)
new_esEs8(LT, LT) → True
new_compare25(vyy480, vyy500, True, bfc, bfd, bfe) → EQ
new_ltEs9(Just(vyy4810), Just(vyy5010), app(ty_Ratio, ccb)) → new_ltEs17(vyy4810, vyy5010, ccb)
new_esEs28(vyy6001, vyy501, ty_Float) → new_esEs19(vyy6001, vyy501)
new_esEs28(vyy6001, vyy501, ty_Double) → new_esEs16(vyy6001, vyy501)
new_ltEs7(vyy481, vyy501, app(app(ty_@2, gh), bad)) → new_ltEs15(vyy481, vyy501, gh, bad)
new_esEs25(vyy6001, vyy501, ty_Ordering) → new_esEs8(vyy6001, vyy501)
new_esEs15(vyy480, vyy500, app(ty_Ratio, bga)) → new_esEs10(vyy480, vyy500, bga)
new_ltEs20(vyy4811, vyy5011, app(ty_Maybe, hc)) → new_ltEs9(vyy4811, vyy5011, hc)
new_pePe(True, vyy117) → True
new_compare0([], [], eg) → EQ
new_esEs24(vyy6000, vyy500, app(app(ty_@2, cef), ceg)) → new_esEs6(vyy6000, vyy500, cef, ceg)
new_primEqNat0(Zero, Zero) → True
new_ltEs20(vyy4811, vyy5011, ty_Ordering) → new_ltEs4(vyy4811, vyy5011)
new_esEs5(Just(vyy6000), Just(vyy500), ty_@0) → new_esEs17(vyy6000, vyy500)
new_esEs25(vyy6001, vyy501, app(ty_[], cgb)) → new_esEs18(vyy6001, vyy501, cgb)
new_primMulNat0(Succ(vyy600100), Succ(vyy50100)) → new_primPlusNat1(new_primMulNat0(vyy600100, Succ(vyy50100)), vyy50100)
new_esEs23(vyy4810, vyy5010, ty_Integer) → new_esEs9(vyy4810, vyy5010)
new_ltEs19(vyy4812, vyy5012, app(app(ty_Either, bbf), bbg)) → new_ltEs8(vyy4812, vyy5012, bbf, bbg)
new_esEs12(vyy6001, vyy501, ty_Int) → new_esEs13(vyy6001, vyy501)
new_esEs24(vyy6000, vyy500, app(ty_[], ceh)) → new_esEs18(vyy6000, vyy500, ceh)
new_esEs29(vyy6000, vyy500, ty_Int) → new_esEs13(vyy6000, vyy500)
new_compare29(vyy4800, vyy5000, app(ty_Ratio, bgd)) → new_compare28(vyy4800, vyy5000, bgd)
new_compare27(vyy480, vyy500, False, gb, gc) → new_compare16(vyy480, vyy500, new_ltEs8(vyy480, vyy500, gb, gc), gb, gc)
new_esEs25(vyy6001, vyy501, ty_Int) → new_esEs13(vyy6001, vyy501)
new_lt9(vyy480, vyy500, app(app(ty_@2, ge), gf)) → new_lt15(vyy480, vyy500, ge, gf)
new_ltEs16(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), bbd, bbe, bda) → new_pePe(new_lt20(vyy4810, vyy5010, bbd), new_asAs(new_esEs21(vyy4810, vyy5010, bbd), new_pePe(new_lt19(vyy4811, vyy5011, bbe), new_asAs(new_esEs22(vyy4811, vyy5011, bbe), new_ltEs19(vyy4812, vyy5012, bda)))))
new_esEs24(vyy6000, vyy500, ty_Double) → new_esEs16(vyy6000, vyy500)
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, ty_@0) → new_ltEs6(vyy4810, vyy5010)
new_esEs26(vyy6002, vyy502, ty_Ordering) → new_esEs8(vyy6002, vyy502)
new_esEs8(GT, GT) → True
new_lt20(vyy4810, vyy5010, app(ty_Maybe, bec)) → new_lt11(vyy4810, vyy5010, bec)
new_esEs21(vyy4810, vyy5010, ty_Double) → new_esEs16(vyy4810, vyy5010)
new_esEs13(vyy600, vyy50) → new_primEqInt(vyy600, vyy50)
new_ltEs20(vyy4811, vyy5011, ty_@0) → new_ltEs6(vyy4811, vyy5011)
new_ltEs20(vyy4811, vyy5011, app(app(ty_@2, he), hf)) → new_ltEs15(vyy4811, vyy5011, he, hf)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs22(vyy4811, vyy5011, app(ty_[], bdc)) → new_esEs18(vyy4811, vyy5011, bdc)
new_ltEs19(vyy4812, vyy5012, app(ty_Maybe, bbh)) → new_ltEs9(vyy4812, vyy5012, bbh)
new_ltEs20(vyy4811, vyy5011, ty_Int) → new_ltEs14(vyy4811, vyy5011)
new_ltEs8(Left(vyy4810), Left(vyy5010), app(ty_Ratio, bge), bb) → new_ltEs17(vyy4810, vyy5010, bge)
new_lt11(vyy480, vyy500, gd) → new_esEs8(new_compare30(vyy480, vyy500, gd), LT)
new_esEs4(Right(vyy6000), Right(vyy500), cae, app(app(ty_Either, cbf), cbg)) → new_esEs4(vyy6000, vyy500, cbf, cbg)
new_compare211(vyy480, vyy500, True, gd) → EQ
new_primEqInt(Neg(Succ(vyy60000)), Neg(Succ(vyy5000))) → new_primEqNat0(vyy60000, vyy5000)
new_ltEs8(Left(vyy4810), Left(vyy5010), app(app(app(ty_@3, bg), bh), ca), bb) → new_ltEs16(vyy4810, vyy5010, bg, bh, ca)
new_esEs23(vyy4810, vyy5010, ty_Ordering) → new_esEs8(vyy4810, vyy5010)
new_esEs4(Left(vyy6000), Left(vyy500), app(app(ty_Either, cac), cad), bhe) → new_esEs4(vyy6000, vyy500, cac, cad)
new_compare7(vyy480, vyy500, bfc, bfd, bfe) → new_compare25(vyy480, vyy500, new_esEs7(vyy480, vyy500, bfc, bfd, bfe), bfc, bfd, bfe)
new_compare10(vyy480, vyy500, False, bfc, bfd, bfe) → GT
new_esEs24(vyy6000, vyy500, ty_Bool) → new_esEs14(vyy6000, vyy500)
new_ltEs19(vyy4812, vyy5012, app(ty_Ratio, bha)) → new_ltEs17(vyy4812, vyy5012, bha)
new_lt9(vyy480, vyy500, ty_Char) → new_lt8(vyy480, vyy500)
new_esEs25(vyy6001, vyy501, app(ty_Ratio, cff)) → new_esEs10(vyy6001, vyy501, cff)
new_esEs28(vyy6001, vyy501, ty_@0) → new_esEs17(vyy6001, vyy501)
new_esEs26(vyy6002, vyy502, app(app(app(ty_@3, cge), cgf), cgg)) → new_esEs7(vyy6002, vyy502, cge, cgf, cgg)
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_@0) → new_ltEs6(vyy4810, vyy5010)
new_ltEs18(True, True) → True
new_lt6(vyy480, vyy500, bfc, bfd, bfe) → new_esEs8(new_compare7(vyy480, vyy500, bfc, bfd, bfe), LT)
new_esEs21(vyy4810, vyy5010, app(ty_[], bed)) → new_esEs18(vyy4810, vyy5010, bed)
new_esEs27(vyy6000, vyy500, ty_Char) → new_esEs20(vyy6000, vyy500)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs13(vyy481, vyy501) → new_not(new_esEs8(new_compare14(vyy481, vyy501), GT))
new_ltEs19(vyy4812, vyy5012, ty_Ordering) → new_ltEs4(vyy4812, vyy5012)
new_lt16(vyy480, vyy500) → new_esEs8(new_compare6(vyy480, vyy500), LT)
new_ltEs20(vyy4811, vyy5011, app(ty_Ratio, cca)) → new_ltEs17(vyy4811, vyy5011, cca)
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, app(ty_Maybe, ce)) → new_ltEs9(vyy4810, vyy5010, ce)
new_primEqInt(Neg(Zero), Neg(Succ(vyy5000))) → False
new_primEqInt(Neg(Succ(vyy60000)), Neg(Zero)) → False
new_ltEs18(False, False) → True
new_esEs8(EQ, EQ) → True
new_compare26(vyy48, vyy50, True, gg, bfb) → EQ
new_primPlusNat1(Zero, vyy50100) → Succ(vyy50100)
new_compare111(vyy480, vyy500, True, gd) → LT
new_compare25(vyy480, vyy500, False, bfc, bfd, bfe) → new_compare10(vyy480, vyy500, new_ltEs16(vyy480, vyy500, bfc, bfd, bfe), bfc, bfd, bfe)
new_lt19(vyy4811, vyy5011, app(app(app(ty_@3, bdf), bdg), bdh)) → new_lt6(vyy4811, vyy5011, bdf, bdg, bdh)
new_ltEs19(vyy4812, vyy5012, ty_Int) → new_ltEs14(vyy4812, vyy5012)
new_esEs24(vyy6000, vyy500, ty_Integer) → new_esEs9(vyy6000, vyy500)
new_esEs21(vyy4810, vyy5010, app(app(ty_Either, bea), beb)) → new_esEs4(vyy4810, vyy5010, bea, beb)
new_esEs26(vyy6002, vyy502, app(ty_[], chd)) → new_esEs18(vyy6002, vyy502, chd)
new_esEs28(vyy6001, vyy501, ty_Int) → new_esEs13(vyy6001, vyy501)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs20(vyy4811, vyy5011, ty_Bool) → new_ltEs18(vyy4811, vyy5011)
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, app(ty_[], cf)) → new_ltEs12(vyy4810, vyy5010, cf)
new_ltEs4(EQ, LT) → False
new_lt19(vyy4811, vyy5011, ty_Ordering) → new_lt16(vyy4811, vyy5011)
new_lt20(vyy4810, vyy5010, ty_Char) → new_lt8(vyy4810, vyy5010)
new_compare28(:%(vyy4800, vyy4801), :%(vyy5000, vyy5001), ty_Int) → new_compare13(new_sr0(vyy4800, vyy5001), new_sr0(vyy5000, vyy4801))
new_esEs25(vyy6001, vyy501, ty_@0) → new_esEs17(vyy6001, vyy501)
new_lt20(vyy4810, vyy5010, app(app(app(ty_@3, beg), beh), bfa)) → new_lt6(vyy4810, vyy5010, beg, beh, bfa)
new_primCmpNat0(Succ(vyy48000), Succ(vyy50000)) → new_primCmpNat0(vyy48000, vyy50000)
new_esEs22(vyy4811, vyy5011, ty_Char) → new_esEs20(vyy4811, vyy5011)
new_esEs4(Left(vyy6000), Left(vyy500), ty_Float, bhe) → new_esEs19(vyy6000, vyy500)
new_esEs9(Integer(vyy6000), Integer(vyy500)) → new_primEqInt(vyy6000, vyy500)
new_primEqInt(Pos(Succ(vyy60000)), Pos(Succ(vyy5000))) → new_primEqNat0(vyy60000, vyy5000)
new_compare17(vyy99, vyy100, vyy101, vyy102, False, vyy104, bfg, bfh) → new_compare11(vyy99, vyy100, vyy101, vyy102, vyy104, bfg, bfh)
new_compare27(vyy480, vyy500, True, gb, gc) → EQ
new_esEs25(vyy6001, vyy501, app(ty_Maybe, cfg)) → new_esEs5(vyy6001, vyy501, cfg)
new_esEs15(vyy480, vyy500, ty_Bool) → new_esEs14(vyy480, vyy500)
new_esEs29(vyy6000, vyy500, app(ty_Maybe, ddb)) → new_esEs5(vyy6000, vyy500, ddb)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_compare26(@2(vyy480, vyy481), @2(vyy500, vyy501), False, gg, bfb) → new_compare17(vyy480, vyy481, vyy500, vyy501, new_lt9(vyy480, vyy500, gg), new_asAs(new_esEs15(vyy480, vyy500, gg), new_ltEs7(vyy481, vyy501, bfb)), gg, bfb)
new_ltEs17(vyy481, vyy501, bgc) → new_not(new_esEs8(new_compare28(vyy481, vyy501, bgc), GT))
new_esEs26(vyy6002, vyy502, ty_Int) → new_esEs13(vyy6002, vyy502)
new_lt14(vyy480, vyy500) → new_esEs8(new_compare13(vyy480, vyy500), LT)
new_primEqNat0(Succ(vyy60000), Succ(vyy5000)) → new_primEqNat0(vyy60000, vyy5000)
new_compare29(vyy4800, vyy5000, app(ty_[], fc)) → new_compare0(vyy4800, vyy5000, fc)
new_esEs27(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_lt20(vyy4810, vyy5010, ty_@0) → new_lt12(vyy4810, vyy5010)
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Float, bb) → new_ltEs13(vyy4810, vyy5010)
new_ltEs20(vyy4811, vyy5011, ty_Char) → new_ltEs5(vyy4811, vyy5011)
new_lt21(vyy4810, vyy5010, ty_@0) → new_lt12(vyy4810, vyy5010)
new_esEs4(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, bhb), bhc), bhd), bhe) → new_esEs7(vyy6000, vyy500, bhb, bhc, bhd)
new_esEs22(vyy4811, vyy5011, ty_Int) → new_esEs13(vyy4811, vyy5011)
new_primCompAux00(vyy124, LT) → LT
new_ltEs4(GT, EQ) → False
new_primCmpInt(Neg(Succ(vyy48000)), Neg(vyy5000)) → new_primCmpNat0(vyy5000, Succ(vyy48000))
new_esEs22(vyy4811, vyy5011, ty_Bool) → new_esEs14(vyy4811, vyy5011)
new_compare16(vyy480, vyy500, True, gb, gc) → LT
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Float) → new_ltEs13(vyy4810, vyy5010)
new_esEs21(vyy4810, vyy5010, ty_Float) → new_esEs19(vyy4810, vyy5010)
new_esEs24(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_compare8(Double(vyy4800, vyy4801), Double(vyy5000, vyy5001)) → new_compare13(new_sr0(vyy4800, vyy5000), new_sr0(vyy4801, vyy5001))
new_esEs28(vyy6001, vyy501, ty_Ordering) → new_esEs8(vyy6001, vyy501)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy5000))) → False
new_primEqInt(Pos(Succ(vyy60000)), Pos(Zero)) → False
new_lt20(vyy4810, vyy5010, app(ty_Ratio, bgg)) → new_lt17(vyy4810, vyy5010, bgg)
new_ltEs4(EQ, EQ) → True
new_primPlusNat0(Succ(vyy9000), Zero) → Succ(vyy9000)
new_primPlusNat0(Zero, Succ(vyy501000)) → Succ(vyy501000)
new_esEs23(vyy4810, vyy5010, ty_@0) → new_esEs17(vyy4810, vyy5010)
new_ltEs9(Just(vyy4810), Just(vyy5010), app(app(ty_Either, de), df)) → new_ltEs8(vyy4810, vyy5010, de, df)
new_primCmpNat0(Zero, Zero) → EQ
new_lt9(vyy480, vyy500, ty_Integer) → new_lt5(vyy480, vyy500)
new_primCmpNat0(Succ(vyy48000), Zero) → GT
new_ltEs9(Just(vyy4810), Just(vyy5010), app(ty_Maybe, dg)) → new_ltEs9(vyy4810, vyy5010, dg)
new_esEs15(vyy480, vyy500, app(ty_Maybe, gd)) → new_esEs5(vyy480, vyy500, gd)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy50000))) → LT
new_ltEs20(vyy4811, vyy5011, ty_Integer) → new_ltEs10(vyy4811, vyy5011)
new_ltEs4(GT, LT) → False
new_esEs27(vyy6000, vyy500, ty_Integer) → new_esEs9(vyy6000, vyy500)
new_primEqInt(Neg(Succ(vyy60000)), Pos(vyy500)) → False
new_primEqInt(Pos(Succ(vyy60000)), Neg(vyy500)) → False
new_esEs4(Left(vyy6000), Left(vyy500), ty_@0, bhe) → new_esEs17(vyy6000, vyy500)
new_esEs27(vyy6000, vyy500, app(ty_Maybe, dae)) → new_esEs5(vyy6000, vyy500, dae)
new_ltEs7(vyy481, vyy501, app(ty_Ratio, bgc)) → new_ltEs17(vyy481, vyy501, bgc)
new_ltEs8(Left(vyy4810), Left(vyy5010), app(ty_Maybe, bc), bb) → new_ltEs9(vyy4810, vyy5010, bc)
new_esEs22(vyy4811, vyy5011, app(app(ty_@2, bdd), bde)) → new_esEs6(vyy4811, vyy5011, bdd, bde)
new_esEs4(Right(vyy6000), Right(vyy500), cae, ty_Bool) → new_esEs14(vyy6000, vyy500)
new_primEqInt(Neg(Zero), Pos(Succ(vyy5000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy5000))) → False
new_ltEs9(Just(vyy4810), Nothing, bgb) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy50000))) → new_primCmpNat0(Zero, Succ(vyy50000))
new_primCompAux00(vyy124, EQ) → vyy124
new_compare24(vyy480, vyy500, True) → EQ
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Integer, bb) → new_ltEs10(vyy4810, vyy5010)
new_esEs27(vyy6000, vyy500, ty_Int) → new_esEs13(vyy6000, vyy500)
new_esEs23(vyy4810, vyy5010, app(ty_Ratio, cbh)) → new_esEs10(vyy4810, vyy5010, cbh)
new_compare12(vyy480, vyy500, False) → GT
new_esEs4(Left(vyy6000), Left(vyy500), ty_Double, bhe) → new_esEs16(vyy6000, vyy500)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Bool) → new_ltEs18(vyy4810, vyy5010)
new_esEs27(vyy6000, vyy500, ty_Double) → new_esEs16(vyy6000, vyy500)
new_compare29(vyy4800, vyy5000, ty_Float) → new_compare14(vyy4800, vyy5000)
new_not(False) → True
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, app(app(ty_Either, cc), cd)) → new_ltEs8(vyy4810, vyy5010, cc, cd)
new_esEs24(vyy6000, vyy500, ty_Int) → new_esEs13(vyy6000, vyy500)
new_esEs24(vyy6000, vyy500, ty_Float) → new_esEs19(vyy6000, vyy500)
new_primCmpInt(Pos(Succ(vyy48000)), Pos(vyy5000)) → new_primCmpNat0(Succ(vyy48000), vyy5000)
new_esEs23(vyy4810, vyy5010, app(app(ty_@2, bag), bah)) → new_esEs6(vyy4810, vyy5010, bag, bah)
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Ordering) → new_ltEs4(vyy4810, vyy5010)
new_ltEs9(Nothing, Nothing, bgb) → True
new_esEs4(Right(vyy6000), Right(vyy500), cae, app(ty_[], cbe)) → new_esEs18(vyy6000, vyy500, cbe)
new_ltEs19(vyy4812, vyy5012, app(ty_[], bca)) → new_ltEs12(vyy4812, vyy5012, bca)
new_esEs26(vyy6002, vyy502, ty_Bool) → new_esEs14(vyy6002, vyy502)
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, app(app(app(ty_@3, db), dc), dd)) → new_ltEs16(vyy4810, vyy5010, db, dc, dd)
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, ty_Integer) → new_ltEs10(vyy4810, vyy5010)
new_compare0(:(vyy4800, vyy4801), [], eg) → GT
new_esEs27(vyy6000, vyy500, app(ty_[], dah)) → new_esEs18(vyy6000, vyy500, dah)
new_esEs4(Right(vyy6000), Right(vyy500), cae, app(app(ty_@2, cbc), cbd)) → new_esEs6(vyy6000, vyy500, cbc, cbd)
new_esEs24(vyy6000, vyy500, app(ty_Maybe, cee)) → new_esEs5(vyy6000, vyy500, cee)
new_lt7(vyy480, vyy500) → new_esEs8(new_compare8(vyy480, vyy500), LT)
new_lt19(vyy4811, vyy5011, app(ty_[], bdc)) → new_lt4(vyy4811, vyy5011, bdc)
new_esEs22(vyy4811, vyy5011, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs7(vyy4811, vyy5011, bdf, bdg, bdh)
new_primCmpInt(Pos(Succ(vyy48000)), Neg(vyy5000)) → GT
new_compare210(vyy480, vyy500, False) → new_compare110(vyy480, vyy500, new_ltEs18(vyy480, vyy500))
new_esEs26(vyy6002, vyy502, ty_@0) → new_esEs17(vyy6002, vyy502)
new_ltEs19(vyy4812, vyy5012, ty_Float) → new_ltEs13(vyy4812, vyy5012)
new_esEs29(vyy6000, vyy500, ty_Integer) → new_esEs9(vyy6000, vyy500)
new_primMulInt(Pos(vyy60010), Pos(vyy5010)) → Pos(new_primMulNat0(vyy60010, vyy5010))
new_ltEs7(vyy481, vyy501, app(ty_[], ef)) → new_ltEs12(vyy481, vyy501, ef)
new_esEs28(vyy6001, vyy501, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs7(vyy6001, vyy501, dbc, dbd, dbe)
new_esEs5(Just(vyy6000), Just(vyy500), ty_Int) → new_esEs13(vyy6000, vyy500)
new_esEs23(vyy4810, vyy5010, app(app(ty_Either, bab), bac)) → new_esEs4(vyy4810, vyy5010, bab, bac)
new_lt20(vyy4810, vyy5010, app(app(ty_Either, bea), beb)) → new_lt10(vyy4810, vyy5010, bea, beb)
new_lt19(vyy4811, vyy5011, app(ty_Maybe, bdb)) → new_lt11(vyy4811, vyy5011, bdb)
new_primMulInt(Neg(vyy60010), Neg(vyy5010)) → Pos(new_primMulNat0(vyy60010, vyy5010))
new_esEs27(vyy6000, vyy500, app(app(ty_@2, daf), dag)) → new_esEs6(vyy6000, vyy500, daf, dag)
new_compare110(vyy480, vyy500, True) → LT
new_ltEs19(vyy4812, vyy5012, ty_Integer) → new_ltEs10(vyy4812, vyy5012)
new_esEs29(vyy6000, vyy500, app(app(ty_@2, ddc), ddd)) → new_esEs6(vyy6000, vyy500, ddc, ddd)
new_esEs21(vyy4810, vyy5010, app(ty_Ratio, bgg)) → new_esEs10(vyy4810, vyy5010, bgg)
new_esEs12(vyy6001, vyy501, ty_Integer) → new_esEs9(vyy6001, vyy501)
new_primEqNat0(Succ(vyy60000), Zero) → False
new_primEqNat0(Zero, Succ(vyy5000)) → False
new_ltEs8(Left(vyy4810), Left(vyy5010), app(app(ty_Either, h), ba), bb) → new_ltEs8(vyy4810, vyy5010, h, ba)
new_esEs5(Just(vyy6000), Just(vyy500), ty_Bool) → new_esEs14(vyy6000, vyy500)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs19(vyy4812, vyy5012, ty_@0) → new_ltEs6(vyy4812, vyy5012)
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Integer) → new_ltEs10(vyy4810, vyy5010)
new_ltEs7(vyy481, vyy501, ty_Char) → new_ltEs5(vyy481, vyy501)
new_compare14(Float(vyy4800, vyy4801), Float(vyy5000, vyy5001)) → new_compare13(new_sr0(vyy4800, vyy5000), new_sr0(vyy4801, vyy5001))
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, app(app(ty_@2, cg), da)) → new_ltEs15(vyy4810, vyy5010, cg, da)
new_compare110(vyy480, vyy500, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(vyy6000, vyy500, app(app(ty_Either, cfa), cfb)) → new_esEs4(vyy6000, vyy500, cfa, cfb)
new_esEs5(Just(vyy6000), Just(vyy500), ty_Float) → new_esEs19(vyy6000, vyy500)
new_lt8(vyy480, vyy500) → new_esEs8(new_compare9(vyy480, vyy500), LT)
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, ty_Float) → new_ltEs13(vyy4810, vyy5010)
new_esEs27(vyy6000, vyy500, app(app(ty_Either, dba), dbb)) → new_esEs4(vyy6000, vyy500, dba, dbb)
new_lt9(vyy480, vyy500, ty_Float) → new_lt13(vyy480, vyy500)
new_compare210(vyy480, vyy500, True) → EQ
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_@0, bb) → new_ltEs6(vyy4810, vyy5010)
new_lt18(vyy480, vyy500) → new_esEs8(new_compare31(vyy480, vyy500), LT)
new_lt20(vyy4810, vyy5010, ty_Bool) → new_lt18(vyy4810, vyy5010)
new_lt19(vyy4811, vyy5011, ty_@0) → new_lt12(vyy4811, vyy5011)
new_esEs5(Just(vyy6000), Just(vyy500), ty_Char) → new_esEs20(vyy6000, vyy500)
new_lt21(vyy4810, vyy5010, app(app(app(ty_@3, bba), bbb), bbc)) → new_lt6(vyy4810, vyy5010, bba, bbb, bbc)
new_esEs26(vyy6002, vyy502, app(ty_Maybe, cha)) → new_esEs5(vyy6002, vyy502, cha)
new_ltEs4(LT, GT) → True
new_primPlusNat1(Succ(vyy900), vyy50100) → Succ(Succ(new_primPlusNat0(vyy900, vyy50100)))
new_compare6(vyy480, vyy500) → new_compare24(vyy480, vyy500, new_esEs8(vyy480, vyy500))
new_esEs27(vyy6000, vyy500, app(ty_Ratio, dad)) → new_esEs10(vyy6000, vyy500, dad)
new_lt19(vyy4811, vyy5011, ty_Bool) → new_lt18(vyy4811, vyy5011)
new_ltEs12(vyy481, vyy501, ef) → new_not(new_esEs8(new_compare0(vyy481, vyy501, ef), GT))
new_primCmpInt(Neg(Zero), Neg(Succ(vyy50000))) → new_primCmpNat0(Succ(vyy50000), Zero)
new_lt20(vyy4810, vyy5010, app(app(ty_@2, bee), bef)) → new_lt15(vyy4810, vyy5010, bee, bef)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy50000))) → GT
new_lt21(vyy4810, vyy5010, ty_Integer) → new_lt5(vyy4810, vyy5010)
new_compare5(Integer(vyy4800), Integer(vyy5000)) → new_primCmpInt(vyy4800, vyy5000)
new_ltEs20(vyy4811, vyy5011, ty_Float) → new_ltEs13(vyy4811, vyy5011)
new_esEs15(vyy480, vyy500, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs7(vyy480, vyy500, bfc, bfd, bfe)
new_compare211(vyy480, vyy500, False, gd) → new_compare111(vyy480, vyy500, new_ltEs9(vyy480, vyy500, gd), gd)
new_sr0(vyy6001, vyy501) → new_primMulInt(vyy6001, vyy501)
new_compare11(vyy99, vyy100, vyy101, vyy102, False, bfg, bfh) → GT
new_esEs27(vyy6000, vyy500, ty_@0) → new_esEs17(vyy6000, vyy500)
new_esEs4(Left(vyy6000), Left(vyy500), ty_Integer, bhe) → new_esEs9(vyy6000, vyy500)
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, ty_Bool) → new_ltEs18(vyy4810, vyy5010)
new_esEs28(vyy6001, vyy501, app(app(ty_@2, dbh), dca)) → new_esEs6(vyy6001, vyy501, dbh, dca)
new_esEs23(vyy4810, vyy5010, ty_Int) → new_esEs13(vyy4810, vyy5010)
new_esEs4(Right(vyy6000), Right(vyy500), cae, ty_Int) → new_esEs13(vyy6000, vyy500)
new_compare29(vyy4800, vyy5000, ty_Integer) → new_compare5(vyy4800, vyy5000)
new_compare29(vyy4800, vyy5000, ty_Ordering) → new_compare6(vyy4800, vyy5000)
new_esEs28(vyy6001, vyy501, app(ty_[], dcb)) → new_esEs18(vyy6001, vyy501, dcb)
new_esEs28(vyy6001, vyy501, ty_Integer) → new_esEs9(vyy6001, vyy501)
new_esEs26(vyy6002, vyy502, ty_Char) → new_esEs20(vyy6002, vyy502)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs24(vyy6000, vyy500, app(app(app(ty_@3, cea), ceb), cec)) → new_esEs7(vyy6000, vyy500, cea, ceb, cec)
new_ltEs4(LT, EQ) → True
new_esEs15(vyy480, vyy500, ty_Float) → new_esEs19(vyy480, vyy500)
new_esEs16(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_esEs13(new_sr0(vyy6000, vyy500), new_sr0(vyy6001, vyy501))
new_esEs10(:%(vyy6000, vyy6001), :%(vyy500, vyy501), bff) → new_asAs(new_esEs11(vyy6000, vyy500, bff), new_esEs12(vyy6001, vyy501, bff))
new_asAs(False, vyy71) → False
new_lt15(vyy480, vyy500, ge, gf) → new_esEs8(new_compare19(vyy480, vyy500, ge, gf), LT)
new_primMulInt(Pos(vyy60010), Neg(vyy5010)) → Neg(new_primMulNat0(vyy60010, vyy5010))
new_primMulInt(Neg(vyy60010), Pos(vyy5010)) → Neg(new_primMulNat0(vyy60010, vyy5010))
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Ordering, bb) → new_ltEs4(vyy4810, vyy5010)
new_compare24(vyy480, vyy500, False) → new_compare12(vyy480, vyy500, new_ltEs4(vyy480, vyy500))
new_primMulNat0(Succ(vyy600100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy50100)) → Zero
new_esEs18([], [], dce) → True
new_esEs29(vyy6000, vyy500, ty_Char) → new_esEs20(vyy6000, vyy500)
new_lt19(vyy4811, vyy5011, ty_Char) → new_lt8(vyy4811, vyy5011)
new_esEs21(vyy4810, vyy5010, ty_Ordering) → new_esEs8(vyy4810, vyy5010)
new_ltEs20(vyy4811, vyy5011, ty_Double) → new_ltEs11(vyy4811, vyy5011)
new_esEs5(Just(vyy6000), Just(vyy500), ty_Integer) → new_esEs9(vyy6000, vyy500)
new_lt19(vyy4811, vyy5011, app(app(ty_@2, bdd), bde)) → new_lt15(vyy4811, vyy5011, bdd, bde)
new_compare13(vyy480, vyy500) → new_primCmpInt(vyy480, vyy500)
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Bool, bb) → new_ltEs18(vyy4810, vyy5010)
new_compare12(vyy480, vyy500, True) → LT
new_esEs28(vyy6001, vyy501, ty_Bool) → new_esEs14(vyy6001, vyy501)
new_lt21(vyy4810, vyy5010, app(ty_Ratio, cbh)) → new_lt17(vyy4810, vyy5010, cbh)
new_lt20(vyy4810, vyy5010, app(ty_[], bed)) → new_lt4(vyy4810, vyy5010, bed)
new_esEs5(Just(vyy6000), Just(vyy500), app(app(ty_@2, cda), cdb)) → new_esEs6(vyy6000, vyy500, cda, cdb)
new_lt21(vyy4810, vyy5010, app(app(ty_@2, bag), bah)) → new_lt15(vyy4810, vyy5010, bag, bah)
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Int, bb) → new_ltEs14(vyy4810, vyy5010)
new_ltEs8(Right(vyy4810), Left(vyy5010), cb, bb) → False
new_ltEs9(Just(vyy4810), Just(vyy5010), app(app(app(ty_@3, ec), ed), ee)) → new_ltEs16(vyy4810, vyy5010, ec, ed, ee)
new_lt12(vyy480, vyy500) → new_esEs8(new_compare15(vyy480, vyy500), LT)
new_esEs4(Left(vyy6000), Left(vyy500), app(ty_Maybe, bhg), bhe) → new_esEs5(vyy6000, vyy500, bhg)
new_esEs28(vyy6001, vyy501, app(app(ty_Either, dcc), dcd)) → new_esEs4(vyy6001, vyy501, dcc, dcd)
new_esEs21(vyy4810, vyy5010, ty_Integer) → new_esEs9(vyy4810, vyy5010)
new_esEs15(vyy480, vyy500, app(ty_[], eg)) → new_esEs18(vyy480, vyy500, eg)
new_esEs24(vyy6000, vyy500, ty_Char) → new_esEs20(vyy6000, vyy500)
new_esEs23(vyy4810, vyy5010, app(ty_Maybe, bae)) → new_esEs5(vyy4810, vyy5010, bae)
new_ltEs11(vyy481, vyy501) → new_not(new_esEs8(new_compare8(vyy481, vyy501), GT))
new_lt20(vyy4810, vyy5010, ty_Float) → new_lt13(vyy4810, vyy5010)
new_esEs26(vyy6002, vyy502, ty_Integer) → new_esEs9(vyy6002, vyy502)
new_esEs29(vyy6000, vyy500, app(ty_Ratio, dda)) → new_esEs10(vyy6000, vyy500, dda)
new_esEs21(vyy4810, vyy5010, ty_Int) → new_esEs13(vyy4810, vyy5010)
new_lt17(vyy480, vyy500, bga) → new_esEs8(new_compare28(vyy480, vyy500, bga), LT)
new_compare29(vyy4800, vyy5000, ty_Char) → new_compare9(vyy4800, vyy5000)
new_esEs24(vyy6000, vyy500, app(ty_Ratio, ced)) → new_esEs10(vyy6000, vyy500, ced)
new_lt21(vyy4810, vyy5010, ty_Ordering) → new_lt16(vyy4810, vyy5010)
new_esEs23(vyy4810, vyy5010, ty_Double) → new_esEs16(vyy4810, vyy5010)
new_compare28(:%(vyy4800, vyy4801), :%(vyy5000, vyy5001), ty_Integer) → new_compare5(new_sr(vyy4800, vyy5001), new_sr(vyy5000, vyy4801))
new_lt21(vyy4810, vyy5010, ty_Bool) → new_lt18(vyy4810, vyy5010)
new_compare30(vyy480, vyy500, gd) → new_compare211(vyy480, vyy500, new_esEs5(vyy480, vyy500, gd), gd)
new_lt9(vyy480, vyy500, app(ty_Maybe, gd)) → new_lt11(vyy480, vyy500, gd)
new_ltEs7(vyy481, vyy501, ty_Integer) → new_ltEs10(vyy481, vyy501)
new_compare29(vyy4800, vyy5000, app(ty_Maybe, fb)) → new_compare30(vyy4800, vyy5000, fb)
new_esEs4(Left(vyy6000), Left(vyy500), app(ty_[], cab), bhe) → new_esEs18(vyy6000, vyy500, cab)
new_esEs14(True, True) → True
new_esEs5(Just(vyy6000), Just(vyy500), app(ty_Ratio, ccg)) → new_esEs10(vyy6000, vyy500, ccg)
new_compare111(vyy480, vyy500, False, gd) → GT
new_esEs27(vyy6000, vyy500, ty_Bool) → new_esEs14(vyy6000, vyy500)
new_lt9(vyy480, vyy500, app(ty_Ratio, bga)) → new_lt17(vyy480, vyy500, bga)
new_esEs5(Just(vyy6000), Nothing, ccc) → False
new_esEs5(Nothing, Just(vyy500), ccc) → False
new_esEs22(vyy4811, vyy5011, app(ty_Ratio, bgh)) → new_esEs10(vyy4811, vyy5011, bgh)
new_compare19(vyy480, vyy500, ge, gf) → new_compare26(vyy480, vyy500, new_esEs6(vyy480, vyy500, ge, gf), ge, gf)
new_lt9(vyy480, vyy500, app(ty_[], eg)) → new_lt4(vyy480, vyy500, eg)
new_esEs15(vyy480, vyy500, ty_Integer) → new_esEs9(vyy480, vyy500)
new_esEs29(vyy6000, vyy500, ty_Float) → new_esEs19(vyy6000, vyy500)
new_esEs15(vyy480, vyy500, ty_@0) → new_esEs17(vyy480, vyy500)
new_esEs25(vyy6001, vyy501, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs7(vyy6001, vyy501, cfc, cfd, cfe)
new_esEs25(vyy6001, vyy501, ty_Float) → new_esEs19(vyy6001, vyy501)
new_ltEs18(True, False) → False
new_compare29(vyy4800, vyy5000, app(app(app(ty_@3, fg), fh), ga)) → new_compare7(vyy4800, vyy5000, fg, fh, ga)
new_lt20(vyy4810, vyy5010, ty_Ordering) → new_lt16(vyy4810, vyy5010)
new_esEs21(vyy4810, vyy5010, ty_Char) → new_esEs20(vyy4810, vyy5010)
new_lt20(vyy4810, vyy5010, ty_Integer) → new_lt5(vyy4810, vyy5010)
new_esEs11(vyy6000, vyy500, ty_Integer) → new_esEs9(vyy6000, vyy500)
new_esEs15(vyy480, vyy500, ty_Int) → new_esEs13(vyy480, vyy500)
new_ltEs4(LT, LT) → True
new_lt21(vyy4810, vyy5010, app(app(ty_Either, bab), bac)) → new_lt10(vyy4810, vyy5010, bab, bac)
new_lt10(vyy480, vyy500, gb, gc) → new_esEs8(new_compare18(vyy480, vyy500, gb, gc), LT)
new_compare16(vyy480, vyy500, False, gb, gc) → GT
new_ltEs19(vyy4812, vyy5012, app(app(ty_@2, bcb), bcc)) → new_ltEs15(vyy4812, vyy5012, bcb, bcc)
new_esEs15(vyy480, vyy500, ty_Char) → new_esEs20(vyy480, vyy500)
new_lt9(vyy480, vyy500, ty_@0) → new_lt12(vyy480, vyy500)
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, ty_Char) → new_ltEs5(vyy4810, vyy5010)
new_esEs5(Nothing, Nothing, ccc) → True
new_esEs28(vyy6001, vyy501, app(ty_Maybe, dbg)) → new_esEs5(vyy6001, vyy501, dbg)
new_ltEs20(vyy4811, vyy5011, app(app(app(ty_@3, hg), hh), baa)) → new_ltEs16(vyy4811, vyy5011, hg, hh, baa)
new_ltEs19(vyy4812, vyy5012, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs16(vyy4812, vyy5012, bcd, bce, bcf)
new_esEs26(vyy6002, vyy502, ty_Float) → new_esEs19(vyy6002, vyy502)
new_esEs5(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, ccd), cce), ccf)) → new_esEs7(vyy6000, vyy500, ccd, cce, ccf)
new_esEs14(False, False) → True
new_esEs23(vyy4810, vyy5010, ty_Char) → new_esEs20(vyy4810, vyy5010)
new_esEs22(vyy4811, vyy5011, ty_Double) → new_esEs16(vyy4811, vyy5011)
new_ltEs7(vyy481, vyy501, app(ty_Maybe, bgb)) → new_ltEs9(vyy481, vyy501, bgb)
new_compare11(vyy99, vyy100, vyy101, vyy102, True, bfg, bfh) → LT
new_esEs4(Right(vyy6000), Right(vyy500), cae, ty_Float) → new_esEs19(vyy6000, vyy500)
new_ltEs18(False, True) → True
new_esEs4(Right(vyy6000), Right(vyy500), cae, ty_@0) → new_esEs17(vyy6000, vyy500)
new_primPlusNat0(Succ(vyy9000), Succ(vyy501000)) → Succ(Succ(new_primPlusNat0(vyy9000, vyy501000)))
new_esEs22(vyy4811, vyy5011, app(ty_Maybe, bdb)) → new_esEs5(vyy4811, vyy5011, bdb)
new_lt13(vyy480, vyy500) → new_esEs8(new_compare14(vyy480, vyy500), LT)
new_esEs21(vyy4810, vyy5010, app(ty_Maybe, bec)) → new_esEs5(vyy4810, vyy5010, bec)
new_esEs29(vyy6000, vyy500, app(ty_[], dde)) → new_esEs18(vyy6000, vyy500, dde)
new_compare0([], :(vyy5000, vyy5001), eg) → LT
new_compare29(vyy4800, vyy5000, app(app(ty_Either, eh), fa)) → new_compare18(vyy4800, vyy5000, eh, fa)
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, app(ty_Ratio, bgf)) → new_ltEs17(vyy4810, vyy5010, bgf)
new_esEs26(vyy6002, vyy502, app(app(ty_Either, che), chf)) → new_esEs4(vyy6002, vyy502, che, chf)
new_asAs(True, vyy71) → vyy71
new_lt21(vyy4810, vyy5010, app(ty_[], baf)) → new_lt4(vyy4810, vyy5010, baf)
new_esEs4(Right(vyy6000), Left(vyy500), cae, bhe) → False
new_esEs4(Left(vyy6000), Right(vyy500), cae, bhe) → False
new_ltEs20(vyy4811, vyy5011, app(app(ty_Either, ha), hb)) → new_ltEs8(vyy4811, vyy5011, ha, hb)
new_lt9(vyy480, vyy500, ty_Double) → new_lt7(vyy480, vyy500)
new_compare31(vyy480, vyy500) → new_compare210(vyy480, vyy500, new_esEs14(vyy480, vyy500))
new_ltEs19(vyy4812, vyy5012, ty_Char) → new_ltEs5(vyy4812, vyy5012)
new_esEs4(Left(vyy6000), Left(vyy500), ty_Char, bhe) → new_esEs20(vyy6000, vyy500)
new_ltEs7(vyy481, vyy501, ty_Bool) → new_ltEs18(vyy481, vyy501)
new_lt20(vyy4810, vyy5010, ty_Int) → new_lt14(vyy4810, vyy5010)
new_esEs26(vyy6002, vyy502, app(app(ty_@2, chb), chc)) → new_esEs6(vyy6002, vyy502, chb, chc)
new_esEs26(vyy6002, vyy502, ty_Double) → new_esEs16(vyy6002, vyy502)
new_esEs15(vyy480, vyy500, app(app(ty_Either, gb), gc)) → new_esEs4(vyy480, vyy500, gb, gc)
new_ltEs8(Left(vyy4810), Right(vyy5010), cb, bb) → True
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Double, bb) → new_ltEs11(vyy4810, vyy5010)
new_lt21(vyy4810, vyy5010, ty_Int) → new_lt14(vyy4810, vyy5010)
new_ltEs4(GT, GT) → True
new_ltEs15(@2(vyy4810, vyy4811), @2(vyy5010, vyy5011), gh, bad) → new_pePe(new_lt21(vyy4810, vyy5010, gh), new_asAs(new_esEs23(vyy4810, vyy5010, gh), new_ltEs20(vyy4811, vyy5011, bad)))
new_esEs29(vyy6000, vyy500, ty_Bool) → new_esEs14(vyy6000, vyy500)
new_esEs15(vyy480, vyy500, ty_Ordering) → new_esEs8(vyy480, vyy500)
new_esEs23(vyy4810, vyy5010, app(ty_[], baf)) → new_esEs18(vyy4810, vyy5010, baf)
new_primCompAux00(vyy124, GT) → GT
new_esEs5(Just(vyy6000), Just(vyy500), app(ty_[], cdc)) → new_esEs18(vyy6000, vyy500, cdc)
new_esEs5(Just(vyy6000), Just(vyy500), app(app(ty_Either, cdd), cde)) → new_esEs4(vyy6000, vyy500, cdd, cde)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt19(vyy4811, vyy5011, ty_Int) → new_lt14(vyy4811, vyy5011)
new_ltEs7(vyy481, vyy501, ty_Float) → new_ltEs13(vyy481, vyy501)
new_esEs29(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_ltEs7(vyy481, vyy501, ty_Ordering) → new_ltEs4(vyy481, vyy501)
new_esEs6(@2(vyy6000, vyy6001), @2(vyy500, vyy501), chg, chh) → new_asAs(new_esEs27(vyy6000, vyy500, chg), new_esEs28(vyy6001, vyy501, chh))
new_ltEs8(Right(vyy4810), Right(vyy5010), cb, ty_Double) → new_ltEs11(vyy4810, vyy5010)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vyy48000)), Pos(vyy5000)) → LT
new_lt21(vyy4810, vyy5010, ty_Double) → new_lt7(vyy4810, vyy5010)
new_esEs4(Right(vyy6000), Right(vyy500), cae, ty_Char) → new_esEs20(vyy6000, vyy500)
new_lt9(vyy480, vyy500, ty_Bool) → new_lt18(vyy480, vyy500)
new_not(True) → False
new_esEs15(vyy480, vyy500, ty_Double) → new_esEs16(vyy480, vyy500)
new_esEs25(vyy6001, vyy501, ty_Integer) → new_esEs9(vyy6001, vyy501)

The set Q consists of the following terms:

new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, x2)
new_lt21(x0, x1, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt21(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_lt9(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, LT)
new_esEs24(x0, x1, ty_Double)
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare111(x0, x1, True, x2)
new_esEs11(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_esEs28(x0, x1, ty_@0)
new_compare29(x0, x1, ty_Int)
new_esEs15(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Char)
new_compare31(x0, x1)
new_compare15(@0, @0)
new_lt21(x0, x1, ty_Char)
new_compare0([], :(x0, x1), x2)
new_lt10(x0, x1, x2, x3)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_compare5(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt19(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Float)
new_asAs(False, x0)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_compare17(x0, x1, x2, x3, False, x4, x5, x6)
new_esEs21(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs15(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_ltEs7(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare29(x0, x1, ty_Integer)
new_lt13(x0, x1)
new_ltEs7(x0, x1, app(ty_[], x2))
new_esEs8(GT, GT)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs12(x0, x1, ty_Int)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_esEs29(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_esEs13(x0, x1)
new_esEs8(LT, LT)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs22(x0, x1, ty_Bool)
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare0(:(x0, x1), [], x2)
new_asAs(True, x0)
new_ltEs17(x0, x1, x2)
new_esEs23(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs18([], [], x0)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCompAux00(x0, GT)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_Double)
new_compare16(x0, x1, False, x2, x3)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_sr0(x0, x1)
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, False, x2)
new_esEs14(True, True)
new_compare24(x0, x1, False)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Char)
new_compare12(x0, x1, True)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs21(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_lt18(x0, x1)
new_primEqNat0(Zero, Zero)
new_primEqNat0(Succ(x0), Zero)
new_compare29(x0, x1, ty_Ordering)
new_esEs15(x0, x1, ty_Int)
new_lt9(x0, x1, ty_@0)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs7(x0, x1, ty_Double)
new_primPlusNat1(Succ(x0), x1)
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs29(x0, x1, ty_Double)
new_compare27(x0, x1, True, x2, x3)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Zero, Zero)
new_esEs24(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Float)
new_lt9(x0, x1, ty_Bool)
new_ltEs4(GT, GT)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare8(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs7(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Double)
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Nothing, Nothing, x0)
new_esEs22(x0, x1, ty_Float)
new_compare29(x0, x1, ty_Bool)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt21(x0, x1, ty_Int)
new_ltEs7(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare18(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, ty_Integer)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, ty_@0)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs21(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, ty_Char)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs18(True, True)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(x0, x1, x2)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primPlusNat0(Zero, Zero)
new_esEs11(x0, x1, ty_Int)
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1)
new_esEs23(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_@0)
new_esEs15(x0, x1, ty_Char)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Zero, Succ(x0))
new_esEs20(Char(x0), Char(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_@0)
new_compare11(x0, x1, x2, x3, False, x4, x5)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Nothing, Just(x0), x1)
new_esEs24(x0, x1, ty_Integer)
new_ltEs4(EQ, EQ)
new_compare26(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_compare29(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs17(@0, @0)
new_compare210(x0, x1, True)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Char)
new_lt17(x0, x1, x2)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_compare17(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs15(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, ty_@0)
new_lt9(x0, x1, ty_Float)
new_sr(Integer(x0), Integer(x1))
new_ltEs4(EQ, LT)
new_ltEs4(LT, EQ)
new_esEs28(x0, x1, ty_Ordering)
new_pePe(True, x0)
new_primPlusNat1(Zero, x0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare27(x0, x1, False, x2, x3)
new_compare9(Char(x0), Char(x1))
new_esEs9(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_ltEs18(False, False)
new_compare110(x0, x1, True)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs29(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Int)
new_ltEs6(x0, x1)
new_ltEs7(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_esEs18(:(x0, x1), [], x2)
new_esEs15(x0, x1, ty_Bool)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_compare28(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare26(x0, x1, True, x2, x3)
new_ltEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare10(x0, x1, False, x2, x3, x4)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Nothing, x1)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs23(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Ordering)
new_lt9(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Integer)
new_compare29(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs7(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_@0)
new_lt7(x0, x1)
new_compare19(x0, x1, x2, x3)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs14(True, False)
new_esEs14(False, True)
new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_lt9(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs4(LT, LT)
new_esEs21(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt9(x0, x1, app(ty_[], x2))
new_primMulNat0(Zero, Succ(x0))
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_compare16(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs7(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Ordering)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare211(x0, x1, True, x2)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs27(x0, x1, ty_Int)
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, x2)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_ltEs20(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare6(x0, x1)
new_esEs15(x0, x1, ty_Ordering)
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs10(x0, x1)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Zero, Zero)
new_compare211(x0, x1, False, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare12(x0, x1, False)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, False)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare210(x0, x1, False)
new_esEs23(x0, x1, ty_@0)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs26(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_esEs15(x0, x1, ty_Double)
new_lt6(x0, x1, x2, x3, x4)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs15(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs22(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Bool)
new_ltEs7(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Just(x0), Nothing, x1)
new_lt9(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_lt5(x0, x1)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_compare7(x0, x1, x2, x3, x4)
new_compare0([], [], x0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Float)
new_lt14(x0, x1)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1)
new_esEs15(x0, x1, ty_Integer)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Double)
new_compare10(x0, x1, True, x2, x3, x4)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs15(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_not(True)
new_esEs12(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs20(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_compare25(x0, x1, True, x2, x3, x4)
new_lt21(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Char)
new_ltEs18(False, True)
new_ltEs18(True, False)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs7(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Bool)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, ty_Char)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs11(x0, x1)
new_compare29(x0, x1, ty_Double)
new_ltEs7(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_ltEs5(x0, x1)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_ltEs7(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Integer)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs24(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_compare11(x0, x1, x2, x3, True, x4, x5)
new_esEs24(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs25(x0, x1, ty_Double)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs23(x0, x1, ty_Double)
new_ltEs13(x0, x1)
new_lt21(x0, x1, app(ty_[], x2))
new_lt16(x0, x1)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_ltEs7(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_primCmpNat0(Zero, Succ(x0))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt19(x0, x1, ty_Char)
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Double)
new_lt8(x0, x1)
new_compare13(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_lt19(x0, x1, ty_@0)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Double)
new_esEs14(False, False)
new_esEs22(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_pePe(False, x0)
new_esEs5(Nothing, Just(x0), x1)
new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_esEs29(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs24(x0, x1, ty_Char)
new_esEs18([], :(x0, x1), x2)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Char)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_@0)
new_ltEs9(Nothing, Nothing, x0)
new_compare25(x0, x1, False, x2, x3, x4)
new_compare24(x0, x1, True)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))

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

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



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

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

new_foldFM_GE1(vyy19, vyy21, vyy22, vyy23, vyy24, vyy25, vyy26, vyy27, vyy28, False, h, ba, bb, bc) → new_foldFM_GE(vyy19, @2(vyy21, vyy22), vyy27, h, ba, bb, bc)
new_foldFM_GE1(vyy19, vyy21, vyy22, vyy23, vyy24, vyy25, vyy26, vyy27, vyy28, False, h, ba, bb, bc) → new_foldFM_GE(vyy19, @2(vyy21, vyy22), vyy28, h, ba, bb, bc)
new_foldFM_GE1(vyy19, vyy21, vyy22, vyy23, vyy24, vyy25, vyy26, vyy27, vyy28, True, h, ba, bb, bc) → new_foldFM_GE(vyy19, @2(vyy21, vyy22), vyy28, h, ba, bb, bc)
new_foldFM_GE(vyy3, @2(vyy50, vyy51), Branch(@2(vyy600, vyy601), vyy61, vyy62, vyy63, vyy64), bd, be, bf, bg) → new_foldFM_GE1(vyy3, vyy50, vyy51, vyy600, vyy601, vyy61, vyy62, vyy63, vyy64, new_esEs30(vyy600, vyy601, vyy50, vyy51, new_esEs31(vyy600, vyy50, be), be, bf), bd, be, bf, bg)

The TRS R consists of the following rules:

new_esEs7(@3(vyy6000, vyy6001, vyy6002), @3(vyy500, vyy501, vyy502), cg, da, db) → new_asAs(new_esEs24(vyy6000, vyy500, cg), new_asAs(new_esEs25(vyy6001, vyy501, da), new_esEs26(vyy6002, vyy502, db)))
new_esEs4(Right(vyy6000), Right(vyy500), dg, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_lt21(vyy4810, vyy5010, ty_Float) → new_lt13(vyy4810, vyy5010)
new_ltEs14(vyy481, vyy501) → new_not(new_esEs8(new_compare13(vyy481, vyy501), GT))
new_esEs21(vyy4810, vyy5010, app(app(ty_@2, bcf), bcg)) → new_esEs6(vyy4810, vyy5010, bcf, bcg)
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, ty_Int) → new_ltEs14(vyy4810, vyy5010)
new_lt19(vyy4811, vyy5011, app(app(ty_Either, bdd), bde)) → new_lt10(vyy4811, vyy5011, bdd, bde)
new_lt19(vyy4811, vyy5011, ty_Double) → new_lt7(vyy4811, vyy5011)
new_compare9(Char(vyy4800), Char(vyy5000)) → new_primCmpNat0(vyy4800, vyy5000)
new_ltEs4(EQ, GT) → True
new_compare10(vyy480, vyy500, True, ca, cb, cc) → LT
new_esEs5(Just(vyy6000), Just(vyy500), ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_compare18(vyy480, vyy500, ea, eb) → new_compare27(vyy480, vyy500, new_esEs4(vyy480, vyy500, ea, eb), ea, eb)
new_ltEs7(vyy481, vyy501, ty_@0) → new_ltEs6(vyy481, vyy501)
new_esEs31(vyy600, vyy50, ty_Ordering) → new_esEs8(vyy600, vyy50)
new_esEs4(Left(vyy6000), Left(vyy500), ty_Bool, dh) → new_esEs14(vyy6000, vyy500)
new_esEs22(vyy4811, vyy5011, ty_Float) → new_esEs19(vyy4811, vyy5011)
new_lt19(vyy4811, vyy5011, ty_Integer) → new_lt5(vyy4811, vyy5011)
new_esEs4(Right(vyy6000), Right(vyy500), dg, ty_Double) → new_esEs16(vyy6000, vyy500)
new_ltEs9(Nothing, Just(vyy5010), fc) → True
new_compare29(vyy4800, vyy5000, ty_Double) → new_compare8(vyy4800, vyy5000)
new_esEs23(vyy4810, vyy5010, ty_Bool) → new_esEs14(vyy4810, vyy5010)
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Int) → new_ltEs14(vyy4810, vyy5010)
new_ltEs19(vyy4812, vyy5012, ty_Double) → new_ltEs11(vyy4812, vyy5012)
new_esEs4(Right(vyy6000), Right(vyy500), dg, app(ty_Maybe, cbb)) → new_esEs5(vyy6000, vyy500, cbb)
new_esEs31(vyy600, vyy50, ty_@0) → new_esEs17(vyy600, vyy50)
new_esEs23(vyy4810, vyy5010, ty_Float) → new_esEs19(vyy4810, vyy5010)
new_esEs20(Char(vyy6000), Char(vyy500)) → new_primEqNat0(vyy6000, vyy500)
new_esEs21(vyy4810, vyy5010, ty_@0) → new_esEs17(vyy4810, vyy5010)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs8(Left(vyy4810), Left(vyy5010), app(app(ty_@2, bab), bac), fb) → new_ltEs15(vyy4810, vyy5010, bab, bac)
new_esEs25(vyy6001, vyy501, ty_Char) → new_esEs20(vyy6001, vyy501)
new_ltEs7(vyy481, vyy501, ty_Int) → new_ltEs14(vyy481, vyy501)
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, ty_Ordering) → new_ltEs4(vyy4810, vyy5010)
new_esEs26(vyy6002, vyy502, app(ty_Ratio, dbg)) → new_esEs10(vyy6002, vyy502, dbg)
new_ltEs7(vyy481, vyy501, app(app(app(ty_@3, fh), ga), gb)) → new_ltEs16(vyy481, vyy501, fh, ga, gb)
new_esEs28(vyy6001, vyy501, app(ty_Ratio, dec)) → new_esEs10(vyy6001, vyy501, dec)
new_sr(Integer(vyy50000), Integer(vyy48010)) → Integer(new_primMulInt(vyy50000, vyy48010))
new_esEs5(Just(vyy6000), Just(vyy500), ty_Double) → new_esEs16(vyy6000, vyy500)
new_esEs22(vyy4811, vyy5011, ty_@0) → new_esEs17(vyy4811, vyy5011)
new_esEs29(vyy6000, vyy500, app(app(ty_Either, dgb), dgc)) → new_esEs4(vyy6000, vyy500, dgb, dgc)
new_ltEs7(vyy481, vyy501, app(app(ty_Either, fa), fb)) → new_ltEs8(vyy481, vyy501, fa, fb)
new_esEs25(vyy6001, vyy501, ty_Double) → new_esEs16(vyy6001, vyy501)
new_ltEs19(vyy4812, vyy5012, ty_Bool) → new_ltEs18(vyy4812, vyy5012)
new_ltEs9(Just(vyy4810), Just(vyy5010), app(app(ty_@2, ceh), cfa)) → new_ltEs15(vyy4810, vyy5010, ceh, cfa)
new_lt5(vyy480, vyy500) → new_esEs8(new_compare5(vyy480, vyy500), LT)
new_esEs4(Right(vyy6000), Right(vyy500), dg, app(app(app(ty_@3, caf), cag), cah)) → new_esEs7(vyy6000, vyy500, caf, cag, cah)
new_lt21(vyy4810, vyy5010, app(ty_Maybe, ccb)) → new_lt11(vyy4810, vyy5010, ccb)
new_esEs4(Left(vyy6000), Left(vyy500), app(app(ty_@2, caa), cab), dh) → new_esEs6(vyy6000, vyy500, caa, cab)
new_esEs32(vyy38, vyy40, ty_Char) → new_esEs20(vyy38, vyy40)
new_esEs19(Float(vyy6000, vyy6001), Float(vyy500, vyy501)) → new_esEs13(new_sr0(vyy6000, vyy500), new_sr0(vyy6001, vyy501))
new_compare29(vyy4800, vyy5000, ty_Bool) → new_compare31(vyy4800, vyy5000)
new_lt19(vyy4811, vyy5011, ty_Float) → new_lt13(vyy4811, vyy5011)
new_esEs32(vyy38, vyy40, app(ty_[], bha)) → new_esEs18(vyy38, vyy40, bha)
new_compare0(:(vyy4800, vyy4801), :(vyy5000, vyy5001), bh) → new_primCompAux0(vyy4800, vyy5000, new_compare0(vyy4801, vyy5001, bh), bh)
new_esEs21(vyy4810, vyy5010, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs7(vyy4810, vyy5010, bch, bda, bdb)
new_lt9(vyy480, vyy500, app(app(app(ty_@3, ca), cb), cc)) → new_lt6(vyy480, vyy500, ca, cb, cc)
new_esEs5(Just(vyy6000), Just(vyy500), app(ty_Maybe, cgb)) → new_esEs5(vyy6000, vyy500, cgb)
new_ltEs7(vyy481, vyy501, ty_Double) → new_ltEs11(vyy481, vyy501)
new_esEs4(Left(vyy6000), Left(vyy500), app(ty_Ratio, bhg), dh) → new_esEs10(vyy6000, vyy500, bhg)
new_esEs22(vyy4811, vyy5011, ty_Integer) → new_esEs9(vyy4811, vyy5011)
new_esEs29(vyy6000, vyy500, app(app(app(ty_@3, dfb), dfc), dfd)) → new_esEs7(vyy6000, vyy500, dfb, dfc, dfd)
new_esEs24(vyy6000, vyy500, ty_@0) → new_esEs17(vyy6000, vyy500)
new_esEs4(Left(vyy6000), Left(vyy500), ty_Ordering, dh) → new_esEs8(vyy6000, vyy500)
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Char, fb) → new_ltEs5(vyy4810, vyy5010)
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Double) → new_ltEs11(vyy4810, vyy5010)
new_esEs17(@0, @0) → True
new_esEs4(Left(vyy6000), Left(vyy500), ty_Int, dh) → new_esEs13(vyy6000, vyy500)
new_esEs32(vyy38, vyy40, app(app(ty_@2, bgg), bgh)) → new_esEs6(vyy38, vyy40, bgg, bgh)
new_lt20(vyy4810, vyy5010, ty_Double) → new_lt7(vyy4810, vyy5010)
new_pePe(False, vyy117) → vyy117
new_esEs29(vyy6000, vyy500, ty_Double) → new_esEs16(vyy6000, vyy500)
new_lt9(vyy480, vyy500, app(app(ty_Either, ea), eb)) → new_lt10(vyy480, vyy500, ea, eb)
new_esEs25(vyy6001, vyy501, app(app(ty_Either, dbb), dbc)) → new_esEs4(vyy6001, vyy501, dbb, dbc)
new_lt21(vyy4810, vyy5010, ty_Char) → new_lt8(vyy4810, vyy5010)
new_lt9(vyy480, vyy500, ty_Int) → new_lt14(vyy480, vyy500)
new_esEs18(:(vyy6000, vyy6001), [], df) → False
new_esEs18([], :(vyy500, vyy501), df) → False
new_esEs28(vyy6001, vyy501, ty_Char) → new_esEs20(vyy6001, vyy501)
new_esEs32(vyy38, vyy40, ty_Float) → new_esEs19(vyy38, vyy40)
new_esEs22(vyy4811, vyy5011, app(app(ty_Either, bdd), bde)) → new_esEs4(vyy4811, vyy5011, bdd, bde)
new_esEs25(vyy6001, vyy501, ty_Bool) → new_esEs14(vyy6001, vyy501)
new_esEs18(:(vyy6000, vyy6001), :(vyy500, vyy501), df) → new_asAs(new_esEs29(vyy6000, vyy500, df), new_esEs18(vyy6001, vyy501, df))
new_esEs11(vyy6000, vyy500, ty_Int) → new_esEs13(vyy6000, vyy500)
new_esEs29(vyy6000, vyy500, ty_@0) → new_esEs17(vyy6000, vyy500)
new_compare29(vyy4800, vyy5000, ty_Int) → new_compare13(vyy4800, vyy5000)
new_esEs15(vyy480, vyy500, app(app(ty_@2, ef), eg)) → new_esEs6(vyy480, vyy500, ef, eg)
new_lt19(vyy4811, vyy5011, app(ty_Ratio, bee)) → new_lt17(vyy4811, vyy5011, bee)
new_ltEs9(Just(vyy4810), Just(vyy5010), app(ty_[], ceg)) → new_ltEs12(vyy4810, vyy5010, ceg)
new_compare29(vyy4800, vyy5000, ty_@0) → new_compare15(vyy4800, vyy5000)
new_compare17(vyy99, vyy100, vyy101, vyy102, True, vyy104, ce, cf) → new_compare11(vyy99, vyy100, vyy101, vyy102, True, ce, cf)
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Char) → new_ltEs5(vyy4810, vyy5010)
new_compare29(vyy4800, vyy5000, app(app(ty_@2, gh), ha)) → new_compare19(vyy4800, vyy5000, gh, ha)
new_esEs27(vyy6000, vyy500, ty_Float) → new_esEs19(vyy6000, vyy500)
new_compare15(@0, @0) → EQ
new_esEs22(vyy4811, vyy5011, ty_Ordering) → new_esEs8(vyy4811, vyy5011)
new_ltEs20(vyy4811, vyy5011, app(ty_[], cde)) → new_ltEs12(vyy4811, vyy5011, cde)
new_ltEs6(vyy481, vyy501) → new_not(new_esEs8(new_compare15(vyy481, vyy501), GT))
new_lt9(vyy480, vyy500, ty_Ordering) → new_lt16(vyy480, vyy500)
new_esEs4(Right(vyy6000), Right(vyy500), dg, app(ty_Ratio, cba)) → new_esEs10(vyy6000, vyy500, cba)
new_ltEs10(vyy481, vyy501) → new_not(new_esEs8(new_compare5(vyy481, vyy501), GT))
new_esEs23(vyy4810, vyy5010, app(app(app(ty_@3, ccf), ccg), cch)) → new_esEs7(vyy4810, vyy5010, ccf, ccg, cch)
new_esEs21(vyy4810, vyy5010, ty_Bool) → new_esEs14(vyy4810, vyy5010)
new_primCmpNat0(Zero, Succ(vyy50000)) → LT
new_esEs32(vyy38, vyy40, ty_Bool) → new_esEs14(vyy38, vyy40)
new_primCompAux0(vyy4800, vyy5000, vyy118, bh) → new_primCompAux00(vyy118, new_compare29(vyy4800, vyy5000, bh))
new_esEs27(vyy6000, vyy500, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs7(vyy6000, vyy500, dcf, dcg, dch)
new_lt4(vyy480, vyy500, bh) → new_esEs8(new_compare0(vyy480, vyy500, bh), LT)
new_ltEs5(vyy481, vyy501) → new_not(new_esEs8(new_compare9(vyy481, vyy501), GT))
new_ltEs8(Left(vyy4810), Left(vyy5010), app(ty_[], baa), fb) → new_ltEs12(vyy4810, vyy5010, baa)
new_esEs4(Right(vyy6000), Right(vyy500), dg, ty_Integer) → new_esEs9(vyy6000, vyy500)
new_esEs25(vyy6001, vyy501, app(app(ty_@2, dag), dah)) → new_esEs6(vyy6001, vyy501, dag, dah)
new_esEs8(LT, LT) → True
new_compare25(vyy480, vyy500, True, ca, cb, cc) → EQ
new_esEs31(vyy600, vyy50, app(ty_Maybe, dc)) → new_esEs5(vyy600, vyy50, dc)
new_ltEs9(Just(vyy4810), Just(vyy5010), app(ty_Ratio, cfe)) → new_ltEs17(vyy4810, vyy5010, cfe)
new_esEs28(vyy6001, vyy501, ty_Float) → new_esEs19(vyy6001, vyy501)
new_esEs28(vyy6001, vyy501, ty_Double) → new_esEs16(vyy6001, vyy501)
new_ltEs7(vyy481, vyy501, app(app(ty_@2, ff), fg)) → new_ltEs15(vyy481, vyy501, ff, fg)
new_esEs25(vyy6001, vyy501, ty_Ordering) → new_esEs8(vyy6001, vyy501)
new_esEs15(vyy480, vyy500, app(ty_Ratio, eh)) → new_esEs10(vyy480, vyy500, eh)
new_ltEs20(vyy4811, vyy5011, app(ty_Maybe, cdd)) → new_ltEs9(vyy4811, vyy5011, cdd)
new_compare0([], [], bh) → EQ
new_pePe(True, vyy117) → True
new_esEs24(vyy6000, vyy500, app(app(ty_@2, che), chf)) → new_esEs6(vyy6000, vyy500, che, chf)
new_primEqNat0(Zero, Zero) → True
new_ltEs20(vyy4811, vyy5011, ty_Ordering) → new_ltEs4(vyy4811, vyy5011)
new_esEs5(Just(vyy6000), Just(vyy500), ty_@0) → new_esEs17(vyy6000, vyy500)
new_esEs25(vyy6001, vyy501, app(ty_[], dba)) → new_esEs18(vyy6001, vyy501, dba)
new_primMulNat0(Succ(vyy600100), Succ(vyy50100)) → new_primPlusNat1(new_primMulNat0(vyy600100, Succ(vyy50100)), vyy50100)
new_esEs23(vyy4810, vyy5010, ty_Integer) → new_esEs9(vyy4810, vyy5010)
new_ltEs19(vyy4812, vyy5012, app(app(ty_Either, bef), beg)) → new_ltEs8(vyy4812, vyy5012, bef, beg)
new_esEs12(vyy6001, vyy501, ty_Int) → new_esEs13(vyy6001, vyy501)
new_esEs24(vyy6000, vyy500, app(ty_[], chg)) → new_esEs18(vyy6000, vyy500, chg)
new_esEs29(vyy6000, vyy500, ty_Int) → new_esEs13(vyy6000, vyy500)
new_compare29(vyy4800, vyy5000, app(ty_Ratio, he)) → new_compare28(vyy4800, vyy5000, he)
new_compare27(vyy480, vyy500, False, ea, eb) → new_compare16(vyy480, vyy500, new_ltEs8(vyy480, vyy500, ea, eb), ea, eb)
new_esEs25(vyy6001, vyy501, ty_Int) → new_esEs13(vyy6001, vyy501)
new_lt9(vyy480, vyy500, app(app(ty_@2, ef), eg)) → new_lt15(vyy480, vyy500, ef, eg)
new_ltEs16(@3(vyy4810, vyy4811, vyy4812), @3(vyy5010, vyy5011, vyy5012), fh, ga, gb) → new_pePe(new_lt20(vyy4810, vyy5010, fh), new_asAs(new_esEs21(vyy4810, vyy5010, fh), new_pePe(new_lt19(vyy4811, vyy5011, ga), new_asAs(new_esEs22(vyy4811, vyy5011, ga), new_ltEs19(vyy4812, vyy5012, gb)))))
new_esEs24(vyy6000, vyy500, ty_Double) → new_esEs16(vyy6000, vyy500)
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, ty_@0) → new_ltEs6(vyy4810, vyy5010)
new_esEs26(vyy6002, vyy502, ty_Ordering) → new_esEs8(vyy6002, vyy502)
new_esEs31(vyy600, vyy50, app(app(app(ty_@3, cg), da), db)) → new_esEs7(vyy600, vyy50, cg, da, db)
new_esEs8(GT, GT) → True
new_lt20(vyy4810, vyy5010, app(ty_Maybe, bcd)) → new_lt11(vyy4810, vyy5010, bcd)
new_esEs21(vyy4810, vyy5010, ty_Double) → new_esEs16(vyy4810, vyy5010)
new_esEs13(vyy600, vyy50) → new_primEqInt(vyy600, vyy50)
new_ltEs20(vyy4811, vyy5011, ty_@0) → new_ltEs6(vyy4811, vyy5011)
new_ltEs20(vyy4811, vyy5011, app(app(ty_@2, cdf), cdg)) → new_ltEs15(vyy4811, vyy5011, cdf, cdg)
new_esEs8(LT, GT) → False
new_esEs22(vyy4811, vyy5011, app(ty_[], bdg)) → new_esEs18(vyy4811, vyy5011, bdg)
new_esEs8(GT, LT) → False
new_ltEs19(vyy4812, vyy5012, app(ty_Maybe, beh)) → new_ltEs9(vyy4812, vyy5012, beh)
new_ltEs20(vyy4811, vyy5011, ty_Int) → new_ltEs14(vyy4811, vyy5011)
new_ltEs8(Left(vyy4810), Left(vyy5010), app(ty_Ratio, bag), fb) → new_ltEs17(vyy4810, vyy5010, bag)
new_lt11(vyy480, vyy500, ee) → new_esEs8(new_compare30(vyy480, vyy500, ee), LT)
new_esEs4(Right(vyy6000), Right(vyy500), dg, app(app(ty_Either, cbf), cbg)) → new_esEs4(vyy6000, vyy500, cbf, cbg)
new_compare211(vyy480, vyy500, True, ee) → EQ
new_primEqInt(Neg(Succ(vyy60000)), Neg(Succ(vyy5000))) → new_primEqNat0(vyy60000, vyy5000)
new_ltEs8(Left(vyy4810), Left(vyy5010), app(app(app(ty_@3, bad), bae), baf), fb) → new_ltEs16(vyy4810, vyy5010, bad, bae, baf)
new_esEs23(vyy4810, vyy5010, ty_Ordering) → new_esEs8(vyy4810, vyy5010)
new_esEs31(vyy600, vyy50, app(app(ty_Either, dg), dh)) → new_esEs4(vyy600, vyy50, dg, dh)
new_esEs4(Left(vyy6000), Left(vyy500), app(app(ty_Either, cad), cae), dh) → new_esEs4(vyy6000, vyy500, cad, cae)
new_compare7(vyy480, vyy500, ca, cb, cc) → new_compare25(vyy480, vyy500, new_esEs7(vyy480, vyy500, ca, cb, cc), ca, cb, cc)
new_compare10(vyy480, vyy500, False, ca, cb, cc) → GT
new_esEs24(vyy6000, vyy500, ty_Bool) → new_esEs14(vyy6000, vyy500)
new_ltEs19(vyy4812, vyy5012, app(ty_Ratio, bfg)) → new_ltEs17(vyy4812, vyy5012, bfg)
new_lt9(vyy480, vyy500, ty_Char) → new_lt8(vyy480, vyy500)
new_esEs25(vyy6001, vyy501, app(ty_Ratio, dae)) → new_esEs10(vyy6001, vyy501, dae)
new_esEs28(vyy6001, vyy501, ty_@0) → new_esEs17(vyy6001, vyy501)
new_esEs26(vyy6002, vyy502, app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs7(vyy6002, vyy502, dbd, dbe, dbf)
new_ltEs18(True, True) → True
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_@0) → new_ltEs6(vyy4810, vyy5010)
new_lt6(vyy480, vyy500, ca, cb, cc) → new_esEs8(new_compare7(vyy480, vyy500, ca, cb, cc), LT)
new_esEs21(vyy4810, vyy5010, app(ty_[], bce)) → new_esEs18(vyy4810, vyy5010, bce)
new_esEs27(vyy6000, vyy500, ty_Char) → new_esEs20(vyy6000, vyy500)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs13(vyy481, vyy501) → new_not(new_esEs8(new_compare14(vyy481, vyy501), GT))
new_ltEs19(vyy4812, vyy5012, ty_Ordering) → new_ltEs4(vyy4812, vyy5012)
new_lt16(vyy480, vyy500) → new_esEs8(new_compare6(vyy480, vyy500), LT)
new_ltEs20(vyy4811, vyy5011, app(ty_Ratio, cec)) → new_ltEs17(vyy4811, vyy5011, cec)
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, app(ty_Maybe, bbb)) → new_ltEs9(vyy4810, vyy5010, bbb)
new_primEqInt(Neg(Zero), Neg(Succ(vyy5000))) → False
new_primEqInt(Neg(Succ(vyy60000)), Neg(Zero)) → False
new_ltEs18(False, False) → True
new_esEs8(EQ, EQ) → True
new_compare26(vyy48, vyy50, True, ec, ed) → EQ
new_primPlusNat1(Zero, vyy50100) → Succ(vyy50100)
new_compare111(vyy480, vyy500, True, ee) → LT
new_esEs32(vyy38, vyy40, app(ty_Ratio, bge)) → new_esEs10(vyy38, vyy40, bge)
new_compare25(vyy480, vyy500, False, ca, cb, cc) → new_compare10(vyy480, vyy500, new_ltEs16(vyy480, vyy500, ca, cb, cc), ca, cb, cc)
new_lt19(vyy4811, vyy5011, app(app(app(ty_@3, beb), bec), bed)) → new_lt6(vyy4811, vyy5011, beb, bec, bed)
new_ltEs19(vyy4812, vyy5012, ty_Int) → new_ltEs14(vyy4812, vyy5012)
new_esEs24(vyy6000, vyy500, ty_Integer) → new_esEs9(vyy6000, vyy500)
new_esEs21(vyy4810, vyy5010, app(app(ty_Either, bcb), bcc)) → new_esEs4(vyy4810, vyy5010, bcb, bcc)
new_esEs26(vyy6002, vyy502, app(ty_[], dcc)) → new_esEs18(vyy6002, vyy502, dcc)
new_esEs28(vyy6001, vyy501, ty_Int) → new_esEs13(vyy6001, vyy501)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs20(vyy4811, vyy5011, ty_Bool) → new_ltEs18(vyy4811, vyy5011)
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, app(ty_[], bbc)) → new_ltEs12(vyy4810, vyy5010, bbc)
new_ltEs4(EQ, LT) → False
new_lt19(vyy4811, vyy5011, ty_Ordering) → new_lt16(vyy4811, vyy5011)
new_lt20(vyy4810, vyy5010, ty_Char) → new_lt8(vyy4810, vyy5010)
new_compare28(:%(vyy4800, vyy4801), :%(vyy5000, vyy5001), ty_Int) → new_compare13(new_sr0(vyy4800, vyy5001), new_sr0(vyy5000, vyy4801))
new_esEs25(vyy6001, vyy501, ty_@0) → new_esEs17(vyy6001, vyy501)
new_lt20(vyy4810, vyy5010, app(app(app(ty_@3, bch), bda), bdb)) → new_lt6(vyy4810, vyy5010, bch, bda, bdb)
new_primCmpNat0(Succ(vyy48000), Succ(vyy50000)) → new_primCmpNat0(vyy48000, vyy50000)
new_esEs22(vyy4811, vyy5011, ty_Char) → new_esEs20(vyy4811, vyy5011)
new_esEs4(Left(vyy6000), Left(vyy500), ty_Float, dh) → new_esEs19(vyy6000, vyy500)
new_esEs9(Integer(vyy6000), Integer(vyy500)) → new_primEqInt(vyy6000, vyy500)
new_primEqInt(Pos(Succ(vyy60000)), Pos(Succ(vyy5000))) → new_primEqNat0(vyy60000, vyy5000)
new_compare17(vyy99, vyy100, vyy101, vyy102, False, vyy104, ce, cf) → new_compare11(vyy99, vyy100, vyy101, vyy102, vyy104, ce, cf)
new_compare27(vyy480, vyy500, True, ea, eb) → EQ
new_esEs25(vyy6001, vyy501, app(ty_Maybe, daf)) → new_esEs5(vyy6001, vyy501, daf)
new_esEs15(vyy480, vyy500, ty_Bool) → new_esEs14(vyy480, vyy500)
new_esEs29(vyy6000, vyy500, app(ty_Maybe, dff)) → new_esEs5(vyy6000, vyy500, dff)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_compare26(@2(vyy480, vyy481), @2(vyy500, vyy501), False, ec, ed) → new_compare17(vyy480, vyy481, vyy500, vyy501, new_lt9(vyy480, vyy500, ec), new_asAs(new_esEs15(vyy480, vyy500, ec), new_ltEs7(vyy481, vyy501, ed)), ec, ed)
new_ltEs17(vyy481, vyy501, gc) → new_not(new_esEs8(new_compare28(vyy481, vyy501, gc), GT))
new_esEs26(vyy6002, vyy502, ty_Int) → new_esEs13(vyy6002, vyy502)
new_lt14(vyy480, vyy500) → new_esEs8(new_compare13(vyy480, vyy500), LT)
new_primEqNat0(Succ(vyy60000), Succ(vyy5000)) → new_primEqNat0(vyy60000, vyy5000)
new_compare29(vyy4800, vyy5000, app(ty_[], gg)) → new_compare0(vyy4800, vyy5000, gg)
new_esEs27(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_lt20(vyy4810, vyy5010, ty_@0) → new_lt12(vyy4810, vyy5010)
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Float, fb) → new_ltEs13(vyy4810, vyy5010)
new_ltEs20(vyy4811, vyy5011, ty_Char) → new_ltEs5(vyy4811, vyy5011)
new_lt21(vyy4810, vyy5010, ty_@0) → new_lt12(vyy4810, vyy5010)
new_esEs4(Left(vyy6000), Left(vyy500), app(app(app(ty_@3, bhd), bhe), bhf), dh) → new_esEs7(vyy6000, vyy500, bhd, bhe, bhf)
new_esEs22(vyy4811, vyy5011, ty_Int) → new_esEs13(vyy4811, vyy5011)
new_primCompAux00(vyy124, LT) → LT
new_ltEs4(GT, EQ) → False
new_primCmpInt(Neg(Succ(vyy48000)), Neg(vyy5000)) → new_primCmpNat0(vyy5000, Succ(vyy48000))
new_esEs22(vyy4811, vyy5011, ty_Bool) → new_esEs14(vyy4811, vyy5011)
new_compare16(vyy480, vyy500, True, ea, eb) → LT
new_esEs21(vyy4810, vyy5010, ty_Float) → new_esEs19(vyy4810, vyy5010)
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Float) → new_ltEs13(vyy4810, vyy5010)
new_esEs24(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_compare8(Double(vyy4800, vyy4801), Double(vyy5000, vyy5001)) → new_compare13(new_sr0(vyy4800, vyy5000), new_sr0(vyy4801, vyy5001))
new_esEs28(vyy6001, vyy501, ty_Ordering) → new_esEs8(vyy6001, vyy501)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy5000))) → False
new_primEqInt(Pos(Succ(vyy60000)), Pos(Zero)) → False
new_lt20(vyy4810, vyy5010, app(ty_Ratio, bdc)) → new_lt17(vyy4810, vyy5010, bdc)
new_ltEs4(EQ, EQ) → True
new_primPlusNat0(Succ(vyy9000), Zero) → Succ(vyy9000)
new_primPlusNat0(Zero, Succ(vyy501000)) → Succ(vyy501000)
new_esEs23(vyy4810, vyy5010, ty_@0) → new_esEs17(vyy4810, vyy5010)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs9(Just(vyy4810), Just(vyy5010), app(app(ty_Either, ced), cee)) → new_ltEs8(vyy4810, vyy5010, ced, cee)
new_lt9(vyy480, vyy500, ty_Integer) → new_lt5(vyy480, vyy500)
new_primCmpNat0(Succ(vyy48000), Zero) → GT
new_ltEs9(Just(vyy4810), Just(vyy5010), app(ty_Maybe, cef)) → new_ltEs9(vyy4810, vyy5010, cef)
new_esEs15(vyy480, vyy500, app(ty_Maybe, ee)) → new_esEs5(vyy480, vyy500, ee)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy50000))) → LT
new_ltEs20(vyy4811, vyy5011, ty_Integer) → new_ltEs10(vyy4811, vyy5011)
new_ltEs4(GT, LT) → False
new_esEs27(vyy6000, vyy500, ty_Integer) → new_esEs9(vyy6000, vyy500)
new_esEs32(vyy38, vyy40, ty_@0) → new_esEs17(vyy38, vyy40)
new_esEs31(vyy600, vyy50, app(ty_Ratio, cd)) → new_esEs10(vyy600, vyy50, cd)
new_primEqInt(Neg(Succ(vyy60000)), Pos(vyy500)) → False
new_primEqInt(Pos(Succ(vyy60000)), Neg(vyy500)) → False
new_esEs32(vyy38, vyy40, app(ty_Maybe, bgf)) → new_esEs5(vyy38, vyy40, bgf)
new_esEs4(Left(vyy6000), Left(vyy500), ty_@0, dh) → new_esEs17(vyy6000, vyy500)
new_esEs30(vyy37, vyy38, vyy39, vyy40, False, bfh, bga) → new_esEs8(new_compare26(@2(vyy37, vyy38), @2(vyy39, vyy40), False, bfh, bga), LT)
new_esEs27(vyy6000, vyy500, app(ty_Maybe, ddb)) → new_esEs5(vyy6000, vyy500, ddb)
new_ltEs7(vyy481, vyy501, app(ty_Ratio, gc)) → new_ltEs17(vyy481, vyy501, gc)
new_ltEs8(Left(vyy4810), Left(vyy5010), app(ty_Maybe, hh), fb) → new_ltEs9(vyy4810, vyy5010, hh)
new_esEs22(vyy4811, vyy5011, app(app(ty_@2, bdh), bea)) → new_esEs6(vyy4811, vyy5011, bdh, bea)
new_esEs4(Right(vyy6000), Right(vyy500), dg, ty_Bool) → new_esEs14(vyy6000, vyy500)
new_primEqInt(Neg(Zero), Pos(Succ(vyy5000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy5000))) → False
new_ltEs9(Just(vyy4810), Nothing, fc) → False
new_primCompAux00(vyy124, EQ) → vyy124
new_primCmpInt(Pos(Zero), Pos(Succ(vyy50000))) → new_primCmpNat0(Zero, Succ(vyy50000))
new_compare24(vyy480, vyy500, True) → EQ
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Integer, fb) → new_ltEs10(vyy4810, vyy5010)
new_esEs27(vyy6000, vyy500, ty_Int) → new_esEs13(vyy6000, vyy500)
new_esEs23(vyy4810, vyy5010, app(ty_Ratio, cda)) → new_esEs10(vyy4810, vyy5010, cda)
new_compare12(vyy480, vyy500, False) → GT
new_esEs4(Left(vyy6000), Left(vyy500), ty_Double, dh) → new_esEs16(vyy6000, vyy500)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Bool) → new_ltEs18(vyy4810, vyy5010)
new_esEs27(vyy6000, vyy500, ty_Double) → new_esEs16(vyy6000, vyy500)
new_esEs31(vyy600, vyy50, ty_Int) → new_esEs13(vyy600, vyy50)
new_compare29(vyy4800, vyy5000, ty_Float) → new_compare14(vyy4800, vyy5000)
new_not(False) → True
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, app(app(ty_Either, bah), bba)) → new_ltEs8(vyy4810, vyy5010, bah, bba)
new_esEs24(vyy6000, vyy500, ty_Int) → new_esEs13(vyy6000, vyy500)
new_esEs24(vyy6000, vyy500, ty_Float) → new_esEs19(vyy6000, vyy500)
new_primCmpInt(Pos(Succ(vyy48000)), Pos(vyy5000)) → new_primCmpNat0(Succ(vyy48000), vyy5000)
new_esEs23(vyy4810, vyy5010, app(app(ty_@2, ccd), cce)) → new_esEs6(vyy4810, vyy5010, ccd, cce)
new_esEs4(Right(vyy6000), Right(vyy500), dg, app(ty_[], cbe)) → new_esEs18(vyy6000, vyy500, cbe)
new_ltEs9(Nothing, Nothing, fc) → True
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Ordering) → new_ltEs4(vyy4810, vyy5010)
new_esEs32(vyy38, vyy40, ty_Ordering) → new_esEs8(vyy38, vyy40)
new_ltEs19(vyy4812, vyy5012, app(ty_[], bfa)) → new_ltEs12(vyy4812, vyy5012, bfa)
new_esEs26(vyy6002, vyy502, ty_Bool) → new_esEs14(vyy6002, vyy502)
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, app(app(app(ty_@3, bbf), bbg), bbh)) → new_ltEs16(vyy4810, vyy5010, bbf, bbg, bbh)
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, ty_Integer) → new_ltEs10(vyy4810, vyy5010)
new_compare0(:(vyy4800, vyy4801), [], bh) → GT
new_esEs31(vyy600, vyy50, ty_Integer) → new_esEs9(vyy600, vyy50)
new_esEs27(vyy6000, vyy500, app(ty_[], dde)) → new_esEs18(vyy6000, vyy500, dde)
new_esEs4(Right(vyy6000), Right(vyy500), dg, app(app(ty_@2, cbc), cbd)) → new_esEs6(vyy6000, vyy500, cbc, cbd)
new_esEs24(vyy6000, vyy500, app(ty_Maybe, chd)) → new_esEs5(vyy6000, vyy500, chd)
new_lt7(vyy480, vyy500) → new_esEs8(new_compare8(vyy480, vyy500), LT)
new_lt19(vyy4811, vyy5011, app(ty_[], bdg)) → new_lt4(vyy4811, vyy5011, bdg)
new_esEs22(vyy4811, vyy5011, app(app(app(ty_@3, beb), bec), bed)) → new_esEs7(vyy4811, vyy5011, beb, bec, bed)
new_primCmpInt(Pos(Succ(vyy48000)), Neg(vyy5000)) → GT
new_compare210(vyy480, vyy500, False) → new_compare110(vyy480, vyy500, new_ltEs18(vyy480, vyy500))
new_esEs26(vyy6002, vyy502, ty_@0) → new_esEs17(vyy6002, vyy502)
new_ltEs19(vyy4812, vyy5012, ty_Float) → new_ltEs13(vyy4812, vyy5012)
new_esEs29(vyy6000, vyy500, ty_Integer) → new_esEs9(vyy6000, vyy500)
new_esEs31(vyy600, vyy50, app(ty_[], df)) → new_esEs18(vyy600, vyy50, df)
new_primMulInt(Pos(vyy60010), Pos(vyy5010)) → Pos(new_primMulNat0(vyy60010, vyy5010))
new_ltEs7(vyy481, vyy501, app(ty_[], fd)) → new_ltEs12(vyy481, vyy501, fd)
new_esEs28(vyy6001, vyy501, app(app(app(ty_@3, ddh), dea), deb)) → new_esEs7(vyy6001, vyy501, ddh, dea, deb)
new_esEs5(Just(vyy6000), Just(vyy500), ty_Int) → new_esEs13(vyy6000, vyy500)
new_esEs23(vyy4810, vyy5010, app(app(ty_Either, cbh), cca)) → new_esEs4(vyy4810, vyy5010, cbh, cca)
new_lt20(vyy4810, vyy5010, app(app(ty_Either, bcb), bcc)) → new_lt10(vyy4810, vyy5010, bcb, bcc)
new_lt19(vyy4811, vyy5011, app(ty_Maybe, bdf)) → new_lt11(vyy4811, vyy5011, bdf)
new_primMulInt(Neg(vyy60010), Neg(vyy5010)) → Pos(new_primMulNat0(vyy60010, vyy5010))
new_esEs27(vyy6000, vyy500, app(app(ty_@2, ddc), ddd)) → new_esEs6(vyy6000, vyy500, ddc, ddd)
new_compare110(vyy480, vyy500, True) → LT
new_ltEs19(vyy4812, vyy5012, ty_Integer) → new_ltEs10(vyy4812, vyy5012)
new_esEs29(vyy6000, vyy500, app(app(ty_@2, dfg), dfh)) → new_esEs6(vyy6000, vyy500, dfg, dfh)
new_esEs21(vyy4810, vyy5010, app(ty_Ratio, bdc)) → new_esEs10(vyy4810, vyy5010, bdc)
new_esEs12(vyy6001, vyy501, ty_Integer) → new_esEs9(vyy6001, vyy501)
new_primEqNat0(Succ(vyy60000), Zero) → False
new_primEqNat0(Zero, Succ(vyy5000)) → False
new_ltEs8(Left(vyy4810), Left(vyy5010), app(app(ty_Either, hf), hg), fb) → new_ltEs8(vyy4810, vyy5010, hf, hg)
new_esEs5(Just(vyy6000), Just(vyy500), ty_Bool) → new_esEs14(vyy6000, vyy500)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs19(vyy4812, vyy5012, ty_@0) → new_ltEs6(vyy4812, vyy5012)
new_ltEs9(Just(vyy4810), Just(vyy5010), ty_Integer) → new_ltEs10(vyy4810, vyy5010)
new_ltEs7(vyy481, vyy501, ty_Char) → new_ltEs5(vyy481, vyy501)
new_compare14(Float(vyy4800, vyy4801), Float(vyy5000, vyy5001)) → new_compare13(new_sr0(vyy4800, vyy5000), new_sr0(vyy4801, vyy5001))
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, app(app(ty_@2, bbd), bbe)) → new_ltEs15(vyy4810, vyy5010, bbd, bbe)
new_compare110(vyy480, vyy500, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(vyy6000, vyy500, app(app(ty_Either, chh), daa)) → new_esEs4(vyy6000, vyy500, chh, daa)
new_lt8(vyy480, vyy500) → new_esEs8(new_compare9(vyy480, vyy500), LT)
new_esEs5(Just(vyy6000), Just(vyy500), ty_Float) → new_esEs19(vyy6000, vyy500)
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, ty_Float) → new_ltEs13(vyy4810, vyy5010)
new_esEs27(vyy6000, vyy500, app(app(ty_Either, ddf), ddg)) → new_esEs4(vyy6000, vyy500, ddf, ddg)
new_esEs32(vyy38, vyy40, ty_Integer) → new_esEs9(vyy38, vyy40)
new_lt9(vyy480, vyy500, ty_Float) → new_lt13(vyy480, vyy500)
new_compare210(vyy480, vyy500, True) → EQ
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_@0, fb) → new_ltEs6(vyy4810, vyy5010)
new_lt18(vyy480, vyy500) → new_esEs8(new_compare31(vyy480, vyy500), LT)
new_lt20(vyy4810, vyy5010, ty_Bool) → new_lt18(vyy4810, vyy5010)
new_lt19(vyy4811, vyy5011, ty_@0) → new_lt12(vyy4811, vyy5011)
new_esEs5(Just(vyy6000), Just(vyy500), ty_Char) → new_esEs20(vyy6000, vyy500)
new_lt21(vyy4810, vyy5010, app(app(app(ty_@3, ccf), ccg), cch)) → new_lt6(vyy4810, vyy5010, ccf, ccg, cch)
new_esEs26(vyy6002, vyy502, app(ty_Maybe, dbh)) → new_esEs5(vyy6002, vyy502, dbh)
new_ltEs4(LT, GT) → True
new_primPlusNat1(Succ(vyy900), vyy50100) → Succ(Succ(new_primPlusNat0(vyy900, vyy50100)))
new_compare6(vyy480, vyy500) → new_compare24(vyy480, vyy500, new_esEs8(vyy480, vyy500))
new_esEs27(vyy6000, vyy500, app(ty_Ratio, dda)) → new_esEs10(vyy6000, vyy500, dda)
new_lt19(vyy4811, vyy5011, ty_Bool) → new_lt18(vyy4811, vyy5011)
new_ltEs12(vyy481, vyy501, fd) → new_not(new_esEs8(new_compare0(vyy481, vyy501, fd), GT))
new_primCmpInt(Neg(Zero), Neg(Succ(vyy50000))) → new_primCmpNat0(Succ(vyy50000), Zero)
new_lt20(vyy4810, vyy5010, app(app(ty_@2, bcf), bcg)) → new_lt15(vyy4810, vyy5010, bcf, bcg)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy50000))) → GT
new_lt21(vyy4810, vyy5010, ty_Integer) → new_lt5(vyy4810, vyy5010)
new_compare5(Integer(vyy4800), Integer(vyy5000)) → new_primCmpInt(vyy4800, vyy5000)
new_ltEs20(vyy4811, vyy5011, ty_Float) → new_ltEs13(vyy4811, vyy5011)
new_esEs15(vyy480, vyy500, app(app(app(ty_@3, ca), cb), cc)) → new_esEs7(vyy480, vyy500, ca, cb, cc)
new_compare211(vyy480, vyy500, False, ee) → new_compare111(vyy480, vyy500, new_ltEs9(vyy480, vyy500, ee), ee)
new_sr0(vyy6001, vyy501) → new_primMulInt(vyy6001, vyy501)
new_compare11(vyy99, vyy100, vyy101, vyy102, False, ce, cf) → GT
new_esEs27(vyy6000, vyy500, ty_@0) → new_esEs17(vyy6000, vyy500)
new_esEs4(Left(vyy6000), Left(vyy500), ty_Integer, dh) → new_esEs9(vyy6000, vyy500)
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, ty_Bool) → new_ltEs18(vyy4810, vyy5010)
new_esEs28(vyy6001, vyy501, app(app(ty_@2, dee), def)) → new_esEs6(vyy6001, vyy501, dee, def)
new_esEs23(vyy4810, vyy5010, ty_Int) → new_esEs13(vyy4810, vyy5010)
new_esEs4(Right(vyy6000), Right(vyy500), dg, ty_Int) → new_esEs13(vyy6000, vyy500)
new_compare29(vyy4800, vyy5000, ty_Integer) → new_compare5(vyy4800, vyy5000)
new_compare29(vyy4800, vyy5000, ty_Ordering) → new_compare6(vyy4800, vyy5000)
new_esEs28(vyy6001, vyy501, app(ty_[], deg)) → new_esEs18(vyy6001, vyy501, deg)
new_esEs28(vyy6001, vyy501, ty_Integer) → new_esEs9(vyy6001, vyy501)
new_esEs26(vyy6002, vyy502, ty_Char) → new_esEs20(vyy6002, vyy502)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs24(vyy6000, vyy500, app(app(app(ty_@3, cgh), cha), chb)) → new_esEs7(vyy6000, vyy500, cgh, cha, chb)
new_ltEs4(LT, EQ) → True
new_esEs31(vyy600, vyy50, ty_Float) → new_esEs19(vyy600, vyy50)
new_esEs15(vyy480, vyy500, ty_Float) → new_esEs19(vyy480, vyy500)
new_esEs16(Double(vyy6000, vyy6001), Double(vyy500, vyy501)) → new_esEs13(new_sr0(vyy6000, vyy500), new_sr0(vyy6001, vyy501))
new_esEs10(:%(vyy6000, vyy6001), :%(vyy500, vyy501), cd) → new_asAs(new_esEs11(vyy6000, vyy500, cd), new_esEs12(vyy6001, vyy501, cd))
new_asAs(False, vyy71) → False
new_lt15(vyy480, vyy500, ef, eg) → new_esEs8(new_compare19(vyy480, vyy500, ef, eg), LT)
new_primMulInt(Pos(vyy60010), Neg(vyy5010)) → Neg(new_primMulNat0(vyy60010, vyy5010))
new_primMulInt(Neg(vyy60010), Pos(vyy5010)) → Neg(new_primMulNat0(vyy60010, vyy5010))
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Ordering, fb) → new_ltEs4(vyy4810, vyy5010)
new_compare24(vyy480, vyy500, False) → new_compare12(vyy480, vyy500, new_ltEs4(vyy480, vyy500))
new_primMulNat0(Succ(vyy600100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy50100)) → Zero
new_esEs18([], [], df) → True
new_esEs29(vyy6000, vyy500, ty_Char) → new_esEs20(vyy6000, vyy500)
new_esEs32(vyy38, vyy40, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs7(vyy38, vyy40, bgb, bgc, bgd)
new_lt19(vyy4811, vyy5011, ty_Char) → new_lt8(vyy4811, vyy5011)
new_esEs21(vyy4810, vyy5010, ty_Ordering) → new_esEs8(vyy4810, vyy5010)
new_ltEs20(vyy4811, vyy5011, ty_Double) → new_ltEs11(vyy4811, vyy5011)
new_esEs31(vyy600, vyy50, ty_Double) → new_esEs16(vyy600, vyy50)
new_esEs5(Just(vyy6000), Just(vyy500), ty_Integer) → new_esEs9(vyy6000, vyy500)
new_lt19(vyy4811, vyy5011, app(app(ty_@2, bdh), bea)) → new_lt15(vyy4811, vyy5011, bdh, bea)
new_compare13(vyy480, vyy500) → new_primCmpInt(vyy480, vyy500)
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Bool, fb) → new_ltEs18(vyy4810, vyy5010)
new_compare12(vyy480, vyy500, True) → LT
new_esEs28(vyy6001, vyy501, ty_Bool) → new_esEs14(vyy6001, vyy501)
new_lt21(vyy4810, vyy5010, app(ty_Ratio, cda)) → new_lt17(vyy4810, vyy5010, cda)
new_lt20(vyy4810, vyy5010, app(ty_[], bce)) → new_lt4(vyy4810, vyy5010, bce)
new_esEs5(Just(vyy6000), Just(vyy500), app(app(ty_@2, cgc), cgd)) → new_esEs6(vyy6000, vyy500, cgc, cgd)
new_lt21(vyy4810, vyy5010, app(app(ty_@2, ccd), cce)) → new_lt15(vyy4810, vyy5010, ccd, cce)
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Int, fb) → new_ltEs14(vyy4810, vyy5010)
new_ltEs8(Right(vyy4810), Left(vyy5010), fa, fb) → False
new_lt12(vyy480, vyy500) → new_esEs8(new_compare15(vyy480, vyy500), LT)
new_ltEs9(Just(vyy4810), Just(vyy5010), app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs16(vyy4810, vyy5010, cfb, cfc, cfd)
new_esEs4(Left(vyy6000), Left(vyy500), app(ty_Maybe, bhh), dh) → new_esEs5(vyy6000, vyy500, bhh)
new_esEs28(vyy6001, vyy501, app(app(ty_Either, deh), dfa)) → new_esEs4(vyy6001, vyy501, deh, dfa)
new_esEs21(vyy4810, vyy5010, ty_Integer) → new_esEs9(vyy4810, vyy5010)
new_esEs15(vyy480, vyy500, app(ty_[], bh)) → new_esEs18(vyy480, vyy500, bh)
new_esEs24(vyy6000, vyy500, ty_Char) → new_esEs20(vyy6000, vyy500)
new_esEs23(vyy4810, vyy5010, app(ty_Maybe, ccb)) → new_esEs5(vyy4810, vyy5010, ccb)
new_ltEs11(vyy481, vyy501) → new_not(new_esEs8(new_compare8(vyy481, vyy501), GT))
new_lt20(vyy4810, vyy5010, ty_Float) → new_lt13(vyy4810, vyy5010)
new_esEs26(vyy6002, vyy502, ty_Integer) → new_esEs9(vyy6002, vyy502)
new_esEs29(vyy6000, vyy500, app(ty_Ratio, dfe)) → new_esEs10(vyy6000, vyy500, dfe)
new_esEs21(vyy4810, vyy5010, ty_Int) → new_esEs13(vyy4810, vyy5010)
new_lt17(vyy480, vyy500, eh) → new_esEs8(new_compare28(vyy480, vyy500, eh), LT)
new_compare29(vyy4800, vyy5000, ty_Char) → new_compare9(vyy4800, vyy5000)
new_esEs24(vyy6000, vyy500, app(ty_Ratio, chc)) → new_esEs10(vyy6000, vyy500, chc)
new_lt21(vyy4810, vyy5010, ty_Ordering) → new_lt16(vyy4810, vyy5010)
new_esEs23(vyy4810, vyy5010, ty_Double) → new_esEs16(vyy4810, vyy5010)
new_compare28(:%(vyy4800, vyy4801), :%(vyy5000, vyy5001), ty_Integer) → new_compare5(new_sr(vyy4800, vyy5001), new_sr(vyy5000, vyy4801))
new_lt21(vyy4810, vyy5010, ty_Bool) → new_lt18(vyy4810, vyy5010)
new_compare30(vyy480, vyy500, ee) → new_compare211(vyy480, vyy500, new_esEs5(vyy480, vyy500, ee), ee)
new_lt9(vyy480, vyy500, app(ty_Maybe, ee)) → new_lt11(vyy480, vyy500, ee)
new_ltEs7(vyy481, vyy501, ty_Integer) → new_ltEs10(vyy481, vyy501)
new_compare29(vyy4800, vyy5000, app(ty_Maybe, gf)) → new_compare30(vyy4800, vyy5000, gf)
new_esEs4(Left(vyy6000), Left(vyy500), app(ty_[], cac), dh) → new_esEs18(vyy6000, vyy500, cac)
new_esEs14(True, True) → True
new_compare111(vyy480, vyy500, False, ee) → GT
new_esEs5(Just(vyy6000), Just(vyy500), app(ty_Ratio, cga)) → new_esEs10(vyy6000, vyy500, cga)
new_esEs27(vyy6000, vyy500, ty_Bool) → new_esEs14(vyy6000, vyy500)
new_lt9(vyy480, vyy500, app(ty_Ratio, eh)) → new_lt17(vyy480, vyy500, eh)
new_esEs22(vyy4811, vyy5011, app(ty_Ratio, bee)) → new_esEs10(vyy4811, vyy5011, bee)
new_esEs5(Nothing, Just(vyy500), dc) → False
new_esEs5(Just(vyy6000), Nothing, dc) → False
new_compare19(vyy480, vyy500, ef, eg) → new_compare26(vyy480, vyy500, new_esEs6(vyy480, vyy500, ef, eg), ef, eg)
new_lt9(vyy480, vyy500, app(ty_[], bh)) → new_lt4(vyy480, vyy500, bh)
new_esEs15(vyy480, vyy500, ty_Integer) → new_esEs9(vyy480, vyy500)
new_esEs29(vyy6000, vyy500, ty_Float) → new_esEs19(vyy6000, vyy500)
new_esEs15(vyy480, vyy500, ty_@0) → new_esEs17(vyy480, vyy500)
new_esEs25(vyy6001, vyy501, app(app(app(ty_@3, dab), dac), dad)) → new_esEs7(vyy6001, vyy501, dab, dac, dad)
new_esEs25(vyy6001, vyy501, ty_Float) → new_esEs19(vyy6001, vyy501)
new_ltEs18(True, False) → False
new_compare29(vyy4800, vyy5000, app(app(app(ty_@3, hb), hc), hd)) → new_compare7(vyy4800, vyy5000, hb, hc, hd)
new_lt20(vyy4810, vyy5010, ty_Ordering) → new_lt16(vyy4810, vyy5010)
new_esEs21(vyy4810, vyy5010, ty_Char) → new_esEs20(vyy4810, vyy5010)
new_lt20(vyy4810, vyy5010, ty_Integer) → new_lt5(vyy4810, vyy5010)
new_esEs11(vyy6000, vyy500, ty_Integer) → new_esEs9(vyy6000, vyy500)
new_esEs32(vyy38, vyy40, app(app(ty_Either, bhb), bhc)) → new_esEs4(vyy38, vyy40, bhb, bhc)
new_esEs15(vyy480, vyy500, ty_Int) → new_esEs13(vyy480, vyy500)
new_ltEs4(LT, LT) → True
new_lt21(vyy4810, vyy5010, app(app(ty_Either, cbh), cca)) → new_lt10(vyy4810, vyy5010, cbh, cca)
new_lt10(vyy480, vyy500, ea, eb) → new_esEs8(new_compare18(vyy480, vyy500, ea, eb), LT)
new_compare16(vyy480, vyy500, False, ea, eb) → GT
new_ltEs19(vyy4812, vyy5012, app(app(ty_@2, bfb), bfc)) → new_ltEs15(vyy4812, vyy5012, bfb, bfc)
new_esEs15(vyy480, vyy500, ty_Char) → new_esEs20(vyy480, vyy500)
new_lt9(vyy480, vyy500, ty_@0) → new_lt12(vyy480, vyy500)
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, ty_Char) → new_ltEs5(vyy4810, vyy5010)
new_esEs5(Nothing, Nothing, dc) → True
new_esEs28(vyy6001, vyy501, app(ty_Maybe, ded)) → new_esEs5(vyy6001, vyy501, ded)
new_ltEs20(vyy4811, vyy5011, app(app(app(ty_@3, cdh), cea), ceb)) → new_ltEs16(vyy4811, vyy5011, cdh, cea, ceb)
new_ltEs19(vyy4812, vyy5012, app(app(app(ty_@3, bfd), bfe), bff)) → new_ltEs16(vyy4812, vyy5012, bfd, bfe, bff)
new_esEs26(vyy6002, vyy502, ty_Float) → new_esEs19(vyy6002, vyy502)
new_esEs5(Just(vyy6000), Just(vyy500), app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs7(vyy6000, vyy500, cff, cfg, cfh)
new_esEs14(False, False) → True
new_esEs23(vyy4810, vyy5010, ty_Char) → new_esEs20(vyy4810, vyy5010)
new_esEs31(vyy600, vyy50, ty_Char) → new_esEs20(vyy600, vyy50)
new_esEs22(vyy4811, vyy5011, ty_Double) → new_esEs16(vyy4811, vyy5011)
new_ltEs7(vyy481, vyy501, app(ty_Maybe, fc)) → new_ltEs9(vyy481, vyy501, fc)
new_compare11(vyy99, vyy100, vyy101, vyy102, True, ce, cf) → LT
new_esEs4(Right(vyy6000), Right(vyy500), dg, ty_Float) → new_esEs19(vyy6000, vyy500)
new_ltEs18(False, True) → True
new_esEs4(Right(vyy6000), Right(vyy500), dg, ty_@0) → new_esEs17(vyy6000, vyy500)
new_esEs22(vyy4811, vyy5011, app(ty_Maybe, bdf)) → new_esEs5(vyy4811, vyy5011, bdf)
new_primPlusNat0(Succ(vyy9000), Succ(vyy501000)) → Succ(Succ(new_primPlusNat0(vyy9000, vyy501000)))
new_lt13(vyy480, vyy500) → new_esEs8(new_compare14(vyy480, vyy500), LT)
new_esEs21(vyy4810, vyy5010, app(ty_Maybe, bcd)) → new_esEs5(vyy4810, vyy5010, bcd)
new_esEs29(vyy6000, vyy500, app(ty_[], dga)) → new_esEs18(vyy6000, vyy500, dga)
new_compare0([], :(vyy5000, vyy5001), bh) → LT
new_compare29(vyy4800, vyy5000, app(app(ty_Either, gd), ge)) → new_compare18(vyy4800, vyy5000, gd, ge)
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, app(ty_Ratio, bca)) → new_ltEs17(vyy4810, vyy5010, bca)
new_esEs26(vyy6002, vyy502, app(app(ty_Either, dcd), dce)) → new_esEs4(vyy6002, vyy502, dcd, dce)
new_asAs(True, vyy71) → vyy71
new_lt21(vyy4810, vyy5010, app(ty_[], ccc)) → new_lt4(vyy4810, vyy5010, ccc)
new_esEs4(Right(vyy6000), Left(vyy500), dg, dh) → False
new_esEs4(Left(vyy6000), Right(vyy500), dg, dh) → False
new_ltEs20(vyy4811, vyy5011, app(app(ty_Either, cdb), cdc)) → new_ltEs8(vyy4811, vyy5011, cdb, cdc)
new_esEs30(vyy37, vyy38, vyy39, vyy40, True, bfh, bga) → new_esEs8(new_compare26(@2(vyy37, vyy38), @2(vyy39, vyy40), new_esEs32(vyy38, vyy40, bga), bfh, bga), LT)
new_esEs32(vyy38, vyy40, ty_Double) → new_esEs16(vyy38, vyy40)
new_lt9(vyy480, vyy500, ty_Double) → new_lt7(vyy480, vyy500)
new_compare31(vyy480, vyy500) → new_compare210(vyy480, vyy500, new_esEs14(vyy480, vyy500))
new_ltEs19(vyy4812, vyy5012, ty_Char) → new_ltEs5(vyy4812, vyy5012)
new_esEs4(Left(vyy6000), Left(vyy500), ty_Char, dh) → new_esEs20(vyy6000, vyy500)
new_ltEs7(vyy481, vyy501, ty_Bool) → new_ltEs18(vyy481, vyy501)
new_lt20(vyy4810, vyy5010, ty_Int) → new_lt14(vyy4810, vyy5010)
new_esEs26(vyy6002, vyy502, app(app(ty_@2, dca), dcb)) → new_esEs6(vyy6002, vyy502, dca, dcb)
new_esEs26(vyy6002, vyy502, ty_Double) → new_esEs16(vyy6002, vyy502)
new_esEs15(vyy480, vyy500, app(app(ty_Either, ea), eb)) → new_esEs4(vyy480, vyy500, ea, eb)
new_ltEs8(Left(vyy4810), Right(vyy5010), fa, fb) → True
new_ltEs8(Left(vyy4810), Left(vyy5010), ty_Double, fb) → new_ltEs11(vyy4810, vyy5010)
new_esEs31(vyy600, vyy50, ty_Bool) → new_esEs14(vyy600, vyy50)
new_lt21(vyy4810, vyy5010, ty_Int) → new_lt14(vyy4810, vyy5010)
new_ltEs4(GT, GT) → True
new_ltEs15(@2(vyy4810, vyy4811), @2(vyy5010, vyy5011), ff, fg) → new_pePe(new_lt21(vyy4810, vyy5010, ff), new_asAs(new_esEs23(vyy4810, vyy5010, ff), new_ltEs20(vyy4811, vyy5011, fg)))
new_esEs29(vyy6000, vyy500, ty_Bool) → new_esEs14(vyy6000, vyy500)
new_esEs15(vyy480, vyy500, ty_Ordering) → new_esEs8(vyy480, vyy500)
new_esEs23(vyy4810, vyy5010, app(ty_[], ccc)) → new_esEs18(vyy4810, vyy5010, ccc)
new_primCompAux00(vyy124, GT) → GT
new_esEs32(vyy38, vyy40, ty_Int) → new_esEs13(vyy38, vyy40)
new_esEs31(vyy600, vyy50, app(app(ty_@2, dd), de)) → new_esEs6(vyy600, vyy50, dd, de)
new_esEs5(Just(vyy6000), Just(vyy500), app(ty_[], cge)) → new_esEs18(vyy6000, vyy500, cge)
new_esEs5(Just(vyy6000), Just(vyy500), app(app(ty_Either, cgf), cgg)) → new_esEs4(vyy6000, vyy500, cgf, cgg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt19(vyy4811, vyy5011, ty_Int) → new_lt14(vyy4811, vyy5011)
new_ltEs7(vyy481, vyy501, ty_Float) → new_ltEs13(vyy481, vyy501)
new_esEs29(vyy6000, vyy500, ty_Ordering) → new_esEs8(vyy6000, vyy500)
new_ltEs7(vyy481, vyy501, ty_Ordering) → new_ltEs4(vyy481, vyy501)
new_esEs6(@2(vyy6000, vyy6001), @2(vyy500, vyy501), dd, de) → new_asAs(new_esEs27(vyy6000, vyy500, dd), new_esEs28(vyy6001, vyy501, de))
new_ltEs8(Right(vyy4810), Right(vyy5010), fa, ty_Double) → new_ltEs11(vyy4810, vyy5010)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpInt(Neg(Succ(vyy48000)), Pos(vyy5000)) → LT
new_lt21(vyy4810, vyy5010, ty_Double) → new_lt7(vyy4810, vyy5010)
new_esEs4(Right(vyy6000), Right(vyy500), dg, ty_Char) → new_esEs20(vyy6000, vyy500)
new_lt9(vyy480, vyy500, ty_Bool) → new_lt18(vyy480, vyy500)
new_not(True) → False
new_esEs15(vyy480, vyy500, ty_Double) → new_esEs16(vyy480, vyy500)
new_esEs25(vyy6001, vyy501, ty_Integer) → new_esEs9(vyy6001, vyy501)

The set Q consists of the following terms:

new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Ordering)
new_lt21(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Char)
new_compare26(x0, x1, True, x2, x3)
new_compare29(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, LT)
new_esEs24(x0, x1, ty_Double)
new_esEs11(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Nothing, Nothing, x0)
new_primEqNat0(Zero, Succ(x0))
new_esEs28(x0, x1, ty_@0)
new_compare29(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs7(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_compare28(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Int)
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare30(x0, x1, x2)
new_esEs28(x0, x1, ty_Char)
new_compare31(x0, x1)
new_compare15(@0, @0)
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, x2, x3, x4)
new_lt21(x0, x1, ty_Char)
new_esEs15(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), ty_Float)
new_compare5(Integer(x0), Integer(x1))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt21(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_lt9(x0, x1, app(ty_Ratio, x2))
new_asAs(False, x0)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_Integer)
new_lt13(x0, x1)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1, app(ty_[], x2))
new_esEs8(GT, GT)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Int)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_esEs31(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare16(x0, x1, False, x2, x3)
new_esEs13(x0, x1)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(LT, LT)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_Bool)
new_compare14(Float(x0, x1), Float(x2, x3))
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_compare211(x0, x1, False, x2)
new_asAs(True, x0)
new_primCompAux0(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Float)
new_compare10(x0, x1, True, x2, x3, x4)
new_primCompAux00(x0, GT)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_sr0(x0, x1)
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Char)
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs14(True, True)
new_compare24(x0, x1, False)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Char)
new_compare12(x0, x1, True)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs21(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_lt18(x0, x1)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Zero)
new_esEs5(Nothing, Just(x0), x1)
new_primEqNat0(Succ(x0), Zero)
new_compare29(x0, x1, ty_Ordering)
new_esEs15(x0, x1, ty_Int)
new_esEs32(x0, x1, ty_Bool)
new_lt9(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs7(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_compare0(:(x0, x1), [], x2)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), x1)
new_esEs29(x0, x1, ty_Double)
new_ltEs9(Nothing, Just(x0), x1)
new_primMulNat0(Zero, Zero)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs17(x0, x1, x2)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, ty_Double)
new_lt10(x0, x1, x2, x3)
new_esEs31(x0, x1, ty_Float)
new_lt9(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_ltEs4(GT, GT)
new_compare8(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_ltEs7(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_@0)
new_compare27(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Double)
new_ltEs7(x0, x1, app(ty_Maybe, x2))
new_esEs5(Nothing, Nothing, x0)
new_ltEs7(x0, x1, app(ty_[], x2))
new_lt4(x0, x1, x2)
new_esEs22(x0, x1, ty_Float)
new_esEs18([], [], x0)
new_compare29(x0, x1, ty_Bool)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, ty_Int)
new_ltEs7(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare17(x0, x1, x2, x3, True, x4, x5, x6)
new_compare26(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_esEs25(x0, x1, ty_Integer)
new_lt21(x0, x1, ty_@0)
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_compare111(x0, x1, False, x2)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs28(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Int)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs21(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs27(x0, x1, ty_Integer)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt9(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Zero)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(True, True)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_primPlusNat0(Zero, Zero)
new_esEs32(x0, x1, ty_Double)
new_esEs11(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(x0, x1)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Char)
new_lt20(x0, x1, ty_@0)
new_esEs15(x0, x1, ty_Char)
new_primPlusNat0(Zero, Succ(x0))
new_esEs20(Char(x0), Char(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs18([], :(x0, x1), x2)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_ltEs4(EQ, EQ)
new_compare29(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs17(@0, @0)
new_compare210(x0, x1, True)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs15(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_lt9(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_sr(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs28(x0, x1, ty_Ordering)
new_pePe(True, x0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, x0)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_compare9(Char(x0), Char(x1))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt17(x0, x1, x2)
new_esEs9(Integer(x0), Integer(x1))
new_esEs32(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs28(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, ty_Double)
new_ltEs18(False, False)
new_compare110(x0, x1, True)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs29(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Int)
new_ltEs6(x0, x1)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_esEs15(x0, x1, ty_Bool)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs5(Just(x0), Nothing, x1)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs23(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_compare19(x0, x1, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs7(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_@0)
new_compare17(x0, x1, x2, x3, False, x4, x5, x6)
new_lt7(x0, x1)
new_esEs22(x0, x1, ty_Double)
new_compare18(x0, x1, x2, x3)
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_esEs14(True, False)
new_esEs14(False, True)
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt9(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Float)
new_ltEs4(LT, LT)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, x2, x3, False, x4, x5)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_compare0([], [], x0)
new_esEs27(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare7(x0, x1, x2, x3, x4)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_ltEs20(x0, x1, ty_Float)
new_esEs15(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primPlusNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(x0, x1)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs15(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_Integer)
new_ltEs10(x0, x1)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCmpNat0(Zero, Zero)
new_compare10(x0, x1, False, x2, x3, x4)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare12(x0, x1, False)
new_ltEs19(x0, x1, ty_Integer)
new_compare110(x0, x1, False)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False)
new_esEs23(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_esEs15(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs7(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt9(x0, x1, ty_Int)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, True, x2, x3, x4)
new_lt9(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, ty_Bool)
new_primMulNat0(Succ(x0), Zero)
new_lt5(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Float)
new_esEs18(:(x0, x1), [], x2)
new_lt14(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt12(x0, x1)
new_esEs15(x0, x1, ty_Integer)
new_ltEs12(x0, x1, x2)
new_esEs28(x0, x1, ty_Double)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs15(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Char)
new_not(True)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs12(x0, x1, ty_Integer)
new_ltEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare16(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_compare211(x0, x1, True, x2)
new_not(False)
new_lt21(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Char)
new_ltEs18(False, True)
new_ltEs18(True, False)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, ty_Bool)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs31(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Ordering)
new_lt11(x0, x1, x2)
new_ltEs7(x0, x1, ty_Ordering)
new_lt15(x0, x1, x2, x3)
new_esEs32(x0, x1, ty_@0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, ty_Char)
new_compare11(x0, x1, x2, x3, True, x4, x5)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, ty_Char)
new_ltEs11(x0, x1)
new_compare29(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs5(x0, x1)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_esEs30(x0, x1, x2, x3, True, x4, x5)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Just(x0), Nothing, x1)
new_ltEs7(x0, x1, ty_@0)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_compare111(x0, x1, True, x2)
new_esEs26(x0, x1, ty_Integer)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs24(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs25(x0, x1, ty_Double)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs23(x0, x1, ty_Double)
new_ltEs13(x0, x1)
new_lt16(x0, x1)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs7(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_primCmpNat0(Zero, Succ(x0))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, ty_Char)
new_esEs30(x0, x1, x2, x3, False, x4, x5)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Double)
new_lt8(x0, x1)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Double)
new_esEs14(False, False)
new_esEs22(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs32(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_esEs31(x0, x1, ty_@0)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_pePe(False, x0)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs26(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_esEs29(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Char)
new_compare0([], :(x0, x1), x2)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_@0)
new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Ordering)
new_compare24(x0, x1, True)
new_esEs21(x0, x1, app(ty_Ratio, x2))

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

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