YES 7.7090000000000005 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
  ((keysFM_GE :: (Ord c, Ord a) => FiniteMap (a,c) b  ->  (a,c)  ->  [(a,c)]) :: (Ord a, Ord c) => FiniteMap (a,c) b  ->  (a,c)  ->  [(a,c)])

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) 
  instance (Eq a, Eq b) => Eq (FiniteMap 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 (\key elt rest ->(key,elt) : rest) [] fm

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

is transformed to
keysFM_GE0 key elt rest = key : rest

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

mainModule FiniteMap
  ((keysFM_GE :: (Ord c, Ord b) => FiniteMap (b,c) a  ->  (b,c)  ->  [(b,c)]) :: (Ord c, Ord b) => FiniteMap (b,c) a  ->  (b,c)  ->  [(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  ->  a  ->  c  ->  c)  ->  c  ->  FiniteMap b a  ->  c
foldFM k z EmptyFM = z
foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l

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

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

  
keysFM_GE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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



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

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

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

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

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

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

  foldFM_GE :: Ord 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

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

  
keysFM_GE0 key elt rest = key : rest

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM = 0
sizeFM (Branch _ _ 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
  ((keysFM_GE :: (Ord a, Ord b) => FiniteMap (b,a) c  ->  (b,a)  ->  [(b,a)]) :: (Ord b, Ord a) => FiniteMap (b,a) c  ->  (b,a)  ->  [(b,a)])

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

  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 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

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

  
keysFM_GE0 key elt rest = key : rest

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


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

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

  fmToList :: FiniteMap a b  ->  [(a,b)]
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 = z
foldFM_GE k z fr (Branch key elt wv fm_l fm_r) 
 | key >= fr = 
foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
 | otherwise = 
foldFM_GE k z fr fm_r

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

  
keysFM_GE0 key elt rest = key : rest

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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

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

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

is transformed to
compare x y = compare3 x y

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

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

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

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

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

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

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

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

  
keysFM_GE0 key elt rest = key : rest

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


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

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)



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

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

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

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

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

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

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

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

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

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

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

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

  
keysFM_GE0 key elt rest = key : rest

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM = 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
  (keysFM_GE :: (Ord b, Ord c) => FiniteMap (b,c) a  ->  (b,c)  ->  [(b,c)])

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

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

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

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

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

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

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

  
keysFM_GE0 key elt rest = key : rest

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM = 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_primEqNat(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat(vyy30000, vyy4000)

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

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



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

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

new_primPlusNat(Succ(vyy14400), Succ(vyy400000)) → new_primPlusNat(vyy14400, vyy400000)

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

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



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

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

new_primMulNat(Succ(vyy300000), Succ(vyy40000)) → new_primMulNat(vyy300000, Succ(vyy40000))

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

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



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

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

new_primCmpNat(Succ(vyy21300000), Succ(vyy15000)) → new_primCmpNat(vyy21300000, vyy15000)

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

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



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

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

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

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_compare23(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, bfe, app(app(ty_Either, app(app(ty_@2, bae), baf)), hf)) → new_ltEs3(vyy2130010, vyy1510, bae, baf)
new_compare23(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, bfe, app(app(ty_Either, bag), app(app(ty_Either, bbe), bbf))) → new_ltEs2(vyy2130010, vyy1510, bbe, bbf)
new_ltEs2(Right(vyy2130010), Right(vyy1510), bag, app(ty_Maybe, bba)) → new_ltEs(vyy2130010, vyy1510, bba)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), df, app(app(app(ty_@3, fd), ff), fg), fb) → new_lt1(vyy2130011, vyy1511, fd, ff, fg)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(ty_[], gd), dg, fb) → new_lt(vyy2130010, vyy1510, gd)
new_compare2(vyy213000, vyy150, bee, bef, beg) → new_compare21(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, bee, bef, beg), bee, bef, beg)
new_ltEs3(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(app(ty_Either, bea), beb), bdd) → new_lt2(vyy2130010, vyy1510, bea, beb)
new_lt(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), h) → new_primCompAux(vyy2130000, vyy1500, new_compare(vyy2130001, vyy1501, h), h)
new_ltEs3(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(ty_[], bdc), bdd) → new_lt(vyy2130010, vyy1510, bdc)
new_lt(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), h) → new_compare0(vyy2130001, vyy1501, h)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, app(app(app(ty_@3, gf), gg), gh)), dg), fb)) → new_lt1(vyy2130010, vyy1510, gf, gg, gh)
new_compare0(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), h) → new_compare0(vyy2130001, vyy1501, h)
new_ltEs3(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), bca, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs1(vyy2130011, vyy1511, bcd, bce, bcf)
new_ltEs2(Left(vyy2130010), Left(vyy1510), app(app(ty_Either, bac), bad), hf) → new_ltEs2(vyy2130010, vyy1510, bac, bad)
new_ltEs(Just(vyy2130010), Just(vyy1510), app(ty_[], cc)) → new_ltEs0(vyy2130010, vyy1510, cc)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), df, app(ty_Maybe, fc), fb) → new_lt0(vyy2130011, vyy1511, fc)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, df), app(app(ty_Either, fh), ga)), fb)) → new_lt2(vyy2130011, vyy1511, fh, ga)
new_compare23(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, bfe, app(app(ty_Either, app(app(ty_Either, bac), bad)), hf)) → new_ltEs2(vyy2130010, vyy1510, bac, bad)
new_compare23(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, bfe, app(ty_Maybe, app(ty_Maybe, cd))) → new_ltEs(vyy2130010, vyy1510, cd)
new_compare23(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, app(app(app(ty_@3, bee), bef), beg), bfd) → new_compare21(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, bee, bef, beg), bee, bef, beg)
new_compare3(vyy213000, vyy150, beh, bfa) → new_compare22(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, beh, bfa), beh, bfa)
new_compare23(@2(:(vyy2130000, vyy2130001), vyy213001), @2(:(vyy1500, vyy1501), vyy151), False, app(ty_[], h), bfd) → new_compare0(vyy2130001, vyy1501, h)
new_compare23(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, bfe, app(app(ty_@2, app(app(app(ty_@3, bdf), bdg), bdh)), bdd)) → new_lt1(vyy2130010, vyy1510, bdf, bdg, bdh)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, df), app(app(app(ty_@3, fd), ff), fg)), fb)) → new_lt1(vyy2130011, vyy1511, fd, ff, fg)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, app(app(ty_@2, hc), hd)), dg), fb)) → new_lt3(vyy2130010, vyy1510, hc, hd)
new_compare23(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, app(ty_Maybe, cb), bfd) → new_compare20(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, cb), cb)
new_compare23(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, bfe, app(app(ty_@2, bca), app(app(ty_Either, bcg), bch))) → new_ltEs2(vyy2130011, vyy1511, bcg, bch)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(app(ty_@2, hc), hd), dg, fb) → new_lt3(vyy2130010, vyy1510, hc, hd)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, df), app(ty_Maybe, fc)), fb)) → new_lt0(vyy2130011, vyy1511, fc)
new_ltEs3(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), bca, app(app(ty_@2, bda), bdb)) → new_ltEs3(vyy2130011, vyy1511, bda, bdb)
new_ltEs2(Right(vyy2130010), Right(vyy1510), bag, app(app(ty_@2, bbg), bbh)) → new_ltEs3(vyy2130010, vyy1510, bbg, bbh)
new_compare23(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, bfe, app(app(ty_@2, app(app(ty_@2, bec), bed)), bdd)) → new_lt3(vyy2130010, vyy1510, bec, bed)
new_compare23(@2(:(vyy2130000, vyy2130001), vyy213001), @2(:(vyy1500, vyy1501), vyy151), False, app(ty_[], h), bfd) → new_primCompAux(vyy2130000, vyy1500, new_compare(vyy2130001, vyy1501, h), h)
new_ltEs2(Right(vyy2130010), Right(vyy1510), bag, app(ty_[], bah)) → new_ltEs0(vyy2130010, vyy1510, bah)
new_lt1(vyy213000, vyy150, bee, bef, beg) → new_compare21(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, bee, bef, beg), bee, bef, beg)
new_compare23(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, bfe, app(app(ty_@2, app(ty_[], bdc)), bdd)) → new_lt(vyy2130010, vyy1510, bdc)
new_ltEs0(vyy213001, vyy151, de) → new_compare0(vyy213001, vyy151, de)
new_ltEs3(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(app(ty_@2, bec), bed), bdd) → new_lt3(vyy2130010, vyy1510, bec, bed)
new_compare23(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, app(app(ty_Either, beh), bfa), bfd) → new_compare22(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, beh, bfa), beh, bfa)
new_compare23(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, bfe, app(app(ty_@2, bca), app(app(ty_@2, bda), bdb))) → new_ltEs3(vyy2130011, vyy1511, bda, bdb)
new_primCompAux(vyy2130000, vyy1500, vyy192, app(ty_Maybe, bb)) → new_compare1(vyy2130000, vyy1500, bb)
new_primCompAux(vyy2130000, vyy1500, vyy192, app(app(ty_Either, bf), bg)) → new_compare3(vyy2130000, vyy1500, bf, bg)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), df, dg, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs1(vyy2130012, vyy1512, eb, ec, ed)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, df), app(app(ty_@2, gb), gc)), fb)) → new_lt3(vyy2130011, vyy1511, gb, gc)
new_compare23(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, bfe, app(app(ty_@2, app(ty_Maybe, bde)), bdd)) → new_lt0(vyy2130010, vyy1510, bde)
new_ltEs3(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), bca, app(app(ty_Either, bcg), bch)) → new_ltEs2(vyy2130011, vyy1511, bcg, bch)
new_lt0(vyy213000, vyy150, cb) → new_compare20(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, cb), cb)
new_compare23(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, bfe, app(ty_Maybe, app(app(ty_@2, dc), dd))) → new_ltEs3(vyy2130010, vyy1510, dc, dd)
new_compare23(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, bfe, app(ty_[], de)) → new_compare0(vyy213001, vyy151, de)
new_compare23(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, bfe, app(ty_Maybe, app(ty_[], cc))) → new_ltEs0(vyy2130010, vyy1510, cc)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, df), dg), app(app(ty_@2, eg), eh))) → new_ltEs3(vyy2130012, vyy1512, eg, eh)
new_ltEs2(Left(vyy2130010), Left(vyy1510), app(ty_[], he), hf) → new_ltEs0(vyy2130010, vyy1510, he)
new_ltEs3(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(app(app(ty_@3, bdf), bdg), bdh), bdd) → new_lt1(vyy2130010, vyy1510, bdf, bdg, bdh)
new_compare0(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), h) → new_primCompAux(vyy2130000, vyy1500, new_compare(vyy2130001, vyy1501, h), h)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), df, dg, app(app(ty_@2, eg), eh)) → new_ltEs3(vyy2130012, vyy1512, eg, eh)
new_compare23(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, bfe, app(app(ty_Either, bag), app(app(app(ty_@3, bbb), bbc), bbd))) → new_ltEs1(vyy2130010, vyy1510, bbb, bbc, bbd)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, df), dg), app(ty_Maybe, ea))) → new_ltEs(vyy2130012, vyy1512, ea)
new_compare23(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, bfe, app(app(ty_Either, app(app(app(ty_@3, hh), baa), bab)), hf)) → new_ltEs1(vyy2130010, vyy1510, hh, baa, bab)
new_compare21(vyy213000, vyy150, False, bee, bef, beg) → new_ltEs1(vyy213000, vyy150, bee, bef, beg)
new_ltEs2(Left(vyy2130010), Left(vyy1510), app(ty_Maybe, hg), hf) → new_ltEs(vyy2130010, vyy1510, hg)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), df, app(app(ty_@2, gb), gc), fb) → new_lt3(vyy2130011, vyy1511, gb, gc)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, df), dg), app(app(ty_Either, ee), ef))) → new_ltEs2(vyy2130012, vyy1512, ee, ef)
new_compare23(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, bfe, app(app(ty_Either, bag), app(app(ty_@2, bbg), bbh))) → new_ltEs3(vyy2130010, vyy1510, bbg, bbh)
new_ltEs(Just(vyy2130010), Just(vyy1510), app(app(app(ty_@3, ce), cf), cg)) → new_ltEs1(vyy2130010, vyy1510, ce, cf, cg)
new_ltEs(Just(vyy2130010), Just(vyy1510), app(ty_Maybe, cd)) → new_ltEs(vyy2130010, vyy1510, cd)
new_compare23(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, bfe, app(ty_Maybe, app(app(app(ty_@3, ce), cf), cg))) → new_ltEs1(vyy2130010, vyy1510, ce, cf, cg)
new_ltEs2(Left(vyy2130010), Left(vyy1510), app(app(ty_@2, bae), baf), hf) → new_ltEs3(vyy2130010, vyy1510, bae, baf)
new_ltEs2(Left(vyy2130010), Left(vyy1510), app(app(app(ty_@3, hh), baa), bab), hf) → new_ltEs1(vyy2130010, vyy1510, hh, baa, bab)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, app(ty_[], gd)), dg), fb)) → new_lt(vyy2130010, vyy1510, gd)
new_ltEs3(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), bca, app(ty_Maybe, bcc)) → new_ltEs(vyy2130011, vyy1511, bcc)
new_compare23(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, bfe, app(app(ty_Either, bag), app(ty_[], bah))) → new_ltEs0(vyy2130010, vyy1510, bah)
new_lt3(vyy213000, vyy150, bfb, bfc) → new_compare23(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bfb, bfc), bfb, bfc)
new_primCompAux(vyy2130000, vyy1500, vyy192, app(ty_[], ba)) → new_compare0(vyy2130000, vyy1500, ba)
new_compare23(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, bfe, app(app(ty_Either, app(ty_Maybe, hg)), hf)) → new_ltEs(vyy2130010, vyy1510, hg)
new_compare23(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, bfe, app(app(ty_@2, app(app(ty_Either, bea), beb)), bdd)) → new_lt2(vyy2130010, vyy1510, bea, beb)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, df), dg), app(app(app(ty_@3, eb), ec), ed))) → new_ltEs1(vyy2130012, vyy1512, eb, ec, ed)
new_ltEs2(Right(vyy2130010), Right(vyy1510), bag, app(app(app(ty_@3, bbb), bbc), bbd)) → new_ltEs1(vyy2130010, vyy1510, bbb, bbc, bbd)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), df, app(app(ty_Either, fh), ga), fb) → new_lt2(vyy2130011, vyy1511, fh, ga)
new_compare23(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, bfe, app(app(ty_Either, bag), app(ty_Maybe, bba))) → new_ltEs(vyy2130010, vyy1510, bba)
new_ltEs2(Right(vyy2130010), Right(vyy1510), bag, app(app(ty_Either, bbe), bbf)) → new_ltEs2(vyy2130010, vyy1510, bbe, bbf)
new_ltEs(Just(vyy2130010), Just(vyy1510), app(app(ty_Either, da), db)) → new_ltEs2(vyy2130010, vyy1510, da, db)
new_ltEs3(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(ty_Maybe, bde), bdd) → new_lt0(vyy2130010, vyy1510, bde)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(app(ty_Either, ha), hb), dg, fb) → new_lt2(vyy2130010, vyy1510, ha, hb)
new_compare23(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, bfe, app(app(ty_@2, bca), app(app(app(ty_@3, bcd), bce), bcf))) → new_ltEs1(vyy2130011, vyy1511, bcd, bce, bcf)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, df), app(ty_[], fa)), fb)) → new_lt(vyy2130011, vyy1511, fa)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, app(app(ty_Either, ha), hb)), dg), fb)) → new_lt2(vyy2130010, vyy1510, ha, hb)
new_ltEs(Just(vyy2130010), Just(vyy1510), app(app(ty_@2, dc), dd)) → new_ltEs3(vyy2130010, vyy1510, dc, dd)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(ty_Maybe, ge), dg, fb) → new_lt0(vyy2130010, vyy1510, ge)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), df, dg, app(ty_Maybe, ea)) → new_ltEs(vyy2130012, vyy1512, ea)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, app(ty_Maybe, ge)), dg), fb)) → new_lt0(vyy2130010, vyy1510, ge)
new_primCompAux(vyy2130000, vyy1500, vyy192, app(app(ty_@2, bh), ca)) → new_compare4(vyy2130000, vyy1500, bh, ca)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), df, app(ty_[], fa), fb) → new_lt(vyy2130011, vyy1511, fa)
new_compare1(vyy213000, vyy150, cb) → new_compare20(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, cb), cb)
new_compare23(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, bfe, app(app(ty_Either, app(ty_[], he)), hf)) → new_ltEs0(vyy2130010, vyy1510, he)
new_compare23(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, bfe, app(ty_Maybe, app(app(ty_Either, da), db))) → new_ltEs2(vyy2130010, vyy1510, da, db)
new_compare23(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, bfe, app(app(ty_@2, bca), app(ty_[], bcb))) → new_ltEs0(vyy2130011, vyy1511, bcb)
new_primCompAux(vyy2130000, vyy1500, vyy192, app(app(app(ty_@3, bc), bd), be)) → new_compare2(vyy2130000, vyy1500, bc, bd, be)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), df, dg, app(ty_[], dh)) → new_ltEs0(vyy2130012, vyy1512, dh)
new_lt2(vyy213000, vyy150, beh, bfa) → new_compare22(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, beh, bfa), beh, bfa)
new_compare22(vyy213000, vyy150, False, beh, bfa) → new_ltEs2(vyy213000, vyy150, beh, bfa)
new_compare23(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, bfe, app(app(ty_@2, bca), app(ty_Maybe, bcc))) → new_ltEs(vyy2130011, vyy1511, bcc)
new_compare4(vyy213000, vyy150, bfb, bfc) → new_compare23(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bfb, bfc), bfb, bfc)
new_compare23(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, bfe, app(app(app(ty_@3, df), dg), app(ty_[], dh))) → new_ltEs0(vyy2130012, vyy1512, dh)
new_ltEs3(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), bca, app(ty_[], bcb)) → new_ltEs0(vyy2130011, vyy1511, bcb)
new_compare23(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, app(app(ty_@2, bfb), bfc), bfd) → new_compare23(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bfb, bfc), bfb, bfc)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), df, dg, app(app(ty_Either, ee), ef)) → new_ltEs2(vyy2130012, vyy1512, ee, ef)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(app(app(ty_@3, gf), gg), gh), dg, fb) → new_lt1(vyy2130010, vyy1510, gf, gg, gh)
new_compare20(vyy213000, vyy150, False, cb) → new_ltEs(vyy213000, vyy150, cb)

The TRS R consists of the following rules:

new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, cdb)) → new_esEs4(vyy3000, vyy400, cdb)
new_esEs16(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs18(new_sr0(vyy3000, vyy400), new_sr0(vyy3001, vyy401))
new_esEs6(Right(vyy3000), Right(vyy400), cag, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_esEs29(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, ty_Ordering) → new_ltEs11(vyy2130010, vyy1510)
new_compare112(vyy213000, vyy150, True, cb) → LT
new_lt21(vyy213000, vyy150, ty_Float) → new_lt13(vyy213000, vyy150)
new_ltEs19(vyy2130012, vyy1512, ty_Integer) → new_ltEs16(vyy2130012, vyy1512)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt19(vyy2130011, vyy1511, ty_Int) → new_lt18(vyy2130011, vyy1511)
new_lt19(vyy2130011, vyy1511, app(app(ty_Either, fh), ga)) → new_lt14(vyy2130011, vyy1511, fh, ga)
new_esEs24(vyy3001, vyy401, app(ty_Ratio, ceg)) → new_esEs15(vyy3001, vyy401, ceg)
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Ordering) → new_ltEs11(vyy2130010, vyy1510)
new_ltEs11(LT, GT) → True
new_esEs21(vyy213000, vyy150, ty_Float) → new_esEs14(vyy213000, vyy150)
new_esEs24(vyy3001, vyy401, app(app(app(ty_@3, cdh), cea), ceb)) → new_esEs5(vyy3001, vyy401, cdh, cea, ceb)
new_esEs13(False, True) → False
new_esEs13(True, False) → False
new_ltEs10(False, True) → True
new_esEs26(vyy3002, vyy402, app(ty_Ratio, chf)) → new_esEs15(vyy3002, vyy402, chf)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, bhd) → new_esEs17(vyy3000, vyy400)
new_esEs19(vyy2130011, vyy1511, app(ty_Ratio, bgg)) → new_esEs15(vyy2130011, vyy1511, bgg)
new_lt6(vyy2130010, vyy1510, ty_Int) → new_lt18(vyy2130010, vyy1510)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs14(vyy3000, vyy400)
new_compare([], :(vyy1500, vyy1501), h) → LT
new_esEs4(Just(vyy3000), Nothing, ccc) → False
new_esEs4(Nothing, Just(vyy400), ccc) → False
new_ltEs20(vyy213001, vyy151, app(ty_[], de)) → new_ltEs6(vyy213001, vyy151, de)
new_esEs24(vyy3001, vyy401, app(ty_Maybe, cef)) → new_esEs4(vyy3001, vyy401, cef)
new_lt19(vyy2130011, vyy1511, ty_Integer) → new_lt5(vyy2130011, vyy1511)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dcb)) → new_esEs15(vyy3000, vyy400, dcb)
new_lt20(vyy2130010, vyy1510, app(app(ty_Either, ha), hb)) → new_lt14(vyy2130010, vyy1510, ha, hb)
new_ltEs4(Left(vyy2130010), Left(vyy1510), app(app(ty_@2, bae), baf), hf) → new_ltEs15(vyy2130010, vyy1510, bae, baf)
new_ltEs6(vyy213001, vyy151, de) → new_fsEs(new_compare(vyy213001, vyy151, de))
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs12(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, cad), bhd) → new_esEs15(vyy3000, vyy400, cad)
new_primMulNat0(Zero, Zero) → Zero
new_compare(:(vyy2130000, vyy2130001), [], h) → GT
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], cab), bhd) → new_esEs11(vyy3000, vyy400, cab)
new_lt20(vyy2130010, vyy1510, app(ty_[], gd)) → new_lt8(vyy2130010, vyy1510, gd)
new_compare13(vyy213000, vyy150, False, bee, bef, beg) → GT
new_esEs6(Right(vyy3000), Right(vyy400), cag, app(app(ty_@2, cbc), cbd)) → new_esEs7(vyy3000, vyy400, cbc, cbd)
new_lt20(vyy2130010, vyy1510, ty_@0) → new_lt7(vyy2130010, vyy1510)
new_lt21(vyy213000, vyy150, ty_@0) → new_lt7(vyy213000, vyy150)
new_ltEs20(vyy213001, vyy151, ty_Float) → new_ltEs12(vyy213001, vyy151)
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, ty_Bool) → new_ltEs10(vyy2130010, vyy1510)
new_sr(Integer(vyy21300000), Integer(vyy15010)) → Integer(new_primMulInt(vyy21300000, vyy15010))
new_esEs11(:(vyy3000, vyy3001), :(vyy400, vyy401), dce) → new_asAs(new_esEs29(vyy3000, vyy400, dce), new_esEs11(vyy3001, vyy401, dce))
new_esEs25(vyy3000, vyy400, app(app(ty_Either, cgb), cgc)) → new_esEs6(vyy3000, vyy400, cgb, cgc)
new_ltEs18(vyy2130011, vyy1511, ty_Integer) → new_ltEs16(vyy2130011, vyy1511)
new_esEs20(vyy2130010, vyy1510, app(ty_Maybe, ge)) → new_esEs4(vyy2130010, vyy1510, ge)
new_lt6(vyy2130010, vyy1510, app(ty_Ratio, bga)) → new_lt15(vyy2130010, vyy1510, bga)
new_ltEs18(vyy2130011, vyy1511, ty_@0) → new_ltEs5(vyy2130011, vyy1511)
new_lt19(vyy2130011, vyy1511, app(ty_Maybe, fc)) → new_lt9(vyy2130011, vyy1511, fc)
new_ltEs18(vyy2130011, vyy1511, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs8(vyy2130011, vyy1511, bcd, bce, bcf)
new_lt20(vyy2130010, vyy1510, app(app(app(ty_@3, gf), gg), gh)) → new_lt4(vyy2130010, vyy1510, gf, gg, gh)
new_lt20(vyy2130010, vyy1510, ty_Int) → new_lt18(vyy2130010, vyy1510)
new_ltEs7(Just(vyy2130010), Just(vyy1510), app(ty_[], cc)) → new_ltEs6(vyy2130010, vyy1510, cc)
new_esEs25(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)
new_lt21(vyy213000, vyy150, ty_Bool) → new_lt11(vyy213000, vyy150)
new_esEs24(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_esEs6(Right(vyy3000), Right(vyy400), cag, app(ty_Ratio, cbg)) → new_esEs15(vyy3000, vyy400, cbg)
new_lt10(vyy213000, vyy150) → new_esEs8(new_compare30(vyy213000, vyy150), LT)
new_compare18(vyy213000, vyy150, cb) → new_compare27(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, cb), cb)
new_lt19(vyy2130011, vyy1511, ty_Float) → new_lt13(vyy2130011, vyy1511)
new_esEs11([], [], dce) → True
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, bhd) → new_esEs14(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_ltEs20(vyy213001, vyy151, ty_Integer) → new_ltEs16(vyy213001, vyy151)
new_esEs21(vyy213000, vyy150, app(app(ty_Either, beh), bfa)) → new_esEs6(vyy213000, vyy150, beh, bfa)
new_ltEs18(vyy2130011, vyy1511, ty_Bool) → new_ltEs10(vyy2130011, vyy1511)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Bool, hf) → new_ltEs10(vyy2130010, vyy1510)
new_compare31(vyy2130000, vyy1500, ty_Bool) → new_compare7(vyy2130000, vyy1500)
new_ltEs10(False, False) → True
new_esEs19(vyy2130011, vyy1511, app(app(app(ty_@3, fd), ff), fg)) → new_esEs5(vyy2130011, vyy1511, fd, ff, fg)
new_esEs26(vyy3002, vyy402, app(ty_Maybe, che)) → new_esEs4(vyy3002, vyy402, che)
new_compare31(vyy2130000, vyy1500, ty_Char) → new_compare30(vyy2130000, vyy1500)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs5(vyy3000, vyy400, dbc, dbd, dbe)
new_esEs25(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs17(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Double, hf) → new_ltEs14(vyy2130010, vyy1510)
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Double) → new_ltEs14(vyy2130010, vyy1510)
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, ty_Double) → new_ltEs14(vyy2130010, vyy1510)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs18(vyy3000, vyy400)
new_compare31(vyy2130000, vyy1500, ty_Integer) → new_compare6(vyy2130000, vyy1500)
new_ltEs19(vyy2130012, vyy1512, app(app(ty_Either, ee), ef)) → new_ltEs4(vyy2130012, vyy1512, ee, ef)
new_pePe(False, vyy197) → vyy197
new_esEs29(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, app(app(ty_@2, cfe), cff)) → new_esEs7(vyy3000, vyy400, cfe, cff)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs18(vyy3001, vyy401)
new_lt20(vyy2130010, vyy1510, ty_Ordering) → new_lt12(vyy2130010, vyy1510)
new_lt20(vyy2130010, vyy1510, ty_Bool) → new_lt11(vyy2130010, vyy1510)
new_esEs20(vyy2130010, vyy1510, ty_Double) → new_esEs16(vyy2130010, vyy1510)
new_lt21(vyy213000, vyy150, app(ty_[], h)) → new_lt8(vyy213000, vyy150, h)
new_esEs29(vyy3000, vyy400, ty_Int) → new_esEs18(vyy3000, vyy400)
new_lt19(vyy2130011, vyy1511, app(ty_[], fa)) → new_lt8(vyy2130011, vyy1511, fa)
new_compare31(vyy2130000, vyy1500, app(ty_Maybe, bb)) → new_compare18(vyy2130000, vyy1500, bb)
new_compare10(vyy177, vyy178, vyy179, vyy180, False, vyy182, bgd, bge) → new_compare11(vyy177, vyy178, vyy179, vyy180, vyy182, bgd, bge)
new_esEs26(vyy3002, vyy402, ty_Char) → new_esEs12(vyy3002, vyy402)
new_esEs24(vyy3001, vyy401, ty_Float) → new_esEs14(vyy3001, vyy401)
new_esEs6(Right(vyy3000), Right(vyy400), cag, ty_Double) → new_esEs16(vyy3000, vyy400)
new_ltEs20(vyy213001, vyy151, app(app(ty_Either, bag), hf)) → new_ltEs4(vyy213001, vyy151, bag, hf)
new_lt20(vyy2130010, vyy1510, app(app(ty_@2, hc), hd)) → new_lt17(vyy2130010, vyy1510, hc, hd)
new_esEs19(vyy2130011, vyy1511, ty_Float) → new_esEs14(vyy2130011, vyy1511)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, bhd) → new_esEs16(vyy3000, vyy400)
new_esEs20(vyy2130010, vyy1510, ty_Char) → new_esEs12(vyy2130010, vyy1510)
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, app(app(ty_Either, bbe), bbf)) → new_ltEs4(vyy2130010, vyy1510, bbe, bbf)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, bhd) → new_esEs10(vyy3000, vyy400)
new_esEs21(vyy213000, vyy150, ty_Int) → new_esEs18(vyy213000, vyy150)
new_lt21(vyy213000, vyy150, ty_Char) → new_lt10(vyy213000, vyy150)
new_esEs18(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_esEs20(vyy2130010, vyy1510, ty_Integer) → new_esEs17(vyy2130010, vyy1510)
new_esEs24(vyy3001, vyy401, app(ty_[], cee)) → new_esEs11(vyy3001, vyy401, cee)
new_compare210(vyy213000, vyy150, False) → new_compare16(vyy213000, vyy150, new_ltEs11(vyy213000, vyy150))
new_ltEs4(Left(vyy2130010), Right(vyy1510), bag, hf) → True
new_esEs29(vyy3000, vyy400, app(ty_[], ddc)) → new_esEs11(vyy3000, vyy400, ddc)
new_ltEs9(vyy213001, vyy151) → new_fsEs(new_compare30(vyy213001, vyy151))
new_primCmpNat0(Zero, Succ(vyy15000)) → LT
new_ltEs20(vyy213001, vyy151, ty_Double) → new_ltEs14(vyy213001, vyy151)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs10(vyy3001, vyy401)
new_esEs6(Right(vyy3000), Left(vyy400), cag, bhd) → False
new_esEs6(Left(vyy3000), Right(vyy400), cag, bhd) → False
new_esEs8(LT, LT) → True
new_esEs19(vyy2130011, vyy1511, app(ty_Maybe, fc)) → new_esEs4(vyy2130011, vyy1511, fc)
new_lt21(vyy213000, vyy150, app(app(ty_@2, bfb), bfc)) → new_lt17(vyy213000, vyy150, bfb, bfc)
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(ty_[], dbh)) → new_esEs11(vyy3000, vyy400, dbh)
new_esEs25(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs29(vyy3000, vyy400, app(app(ty_@2, dda), ddb)) → new_esEs7(vyy3000, vyy400, dda, ddb)
new_esEs29(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_compare15(vyy213000, vyy150, beh, bfa) → new_compare29(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, beh, bfa), beh, bfa)
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs18(vyy3001, vyy401)
new_pePe(True, vyy197) → True
new_primEqNat0(Zero, Zero) → True
new_compare31(vyy2130000, vyy1500, app(app(ty_@2, bh), ca)) → new_compare8(vyy2130000, vyy1500, bh, ca)
new_ltEs13(vyy213001, vyy151, bhb) → new_fsEs(new_compare9(vyy213001, vyy151, bhb))
new_ltEs4(Left(vyy2130010), Left(vyy1510), app(ty_[], he), hf) → new_ltEs6(vyy2130010, vyy1510, he)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_@0, hf) → new_ltEs5(vyy2130010, vyy1510)
new_compare29(vyy213000, vyy150, True, beh, bfa) → EQ
new_ltEs20(vyy213001, vyy151, ty_Bool) → new_ltEs10(vyy213001, vyy151)
new_compare111(vyy213000, vyy150, False, beh, bfa) → GT
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Int, hf) → new_ltEs17(vyy2130010, vyy1510)
new_ltEs5(vyy213001, vyy151) → new_fsEs(new_compare19(vyy213001, vyy151))
new_esEs20(vyy2130010, vyy1510, app(ty_Ratio, bgh)) → new_esEs15(vyy2130010, vyy1510, bgh)
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, ty_Int) → new_ltEs17(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, ty_Char) → new_ltEs9(vyy2130011, vyy1511)
new_ltEs19(vyy2130012, vyy1512, ty_@0) → new_ltEs5(vyy2130012, vyy1512)
new_esEs20(vyy2130010, vyy1510, ty_Bool) → new_esEs13(vyy2130010, vyy1510)
new_esEs6(Right(vyy3000), Right(vyy400), cag, app(app(ty_Either, cbh), cca)) → new_esEs6(vyy3000, vyy400, cbh, cca)
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs12(vyy3001, vyy401)
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Float) → new_ltEs12(vyy2130010, vyy1510)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Char, hf) → new_ltEs9(vyy2130010, vyy1510)
new_lt7(vyy213000, vyy150) → new_esEs8(new_compare19(vyy213000, vyy150), LT)
new_lt6(vyy2130010, vyy1510, ty_Integer) → new_lt5(vyy2130010, vyy1510)
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, ty_@0) → new_ltEs5(vyy2130010, vyy1510)
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, ty_Integer) → new_ltEs16(vyy2130010, vyy1510)
new_lt6(vyy2130010, vyy1510, ty_Char) → new_lt10(vyy2130010, vyy1510)
new_compare29(vyy213000, vyy150, False, beh, bfa) → new_compare111(vyy213000, vyy150, new_ltEs4(vyy213000, vyy150, beh, bfa), beh, bfa)
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dcc), dcd)) → new_esEs6(vyy3000, vyy400, dcc, dcd)
new_compare26(vyy213000, vyy150, False, bee, bef, beg) → new_compare13(vyy213000, vyy150, new_ltEs8(vyy213000, vyy150, bee, bef, beg), bee, bef, beg)
new_esEs24(vyy3001, vyy401, ty_Double) → new_esEs16(vyy3001, vyy401)
new_lt6(vyy2130010, vyy1510, ty_Ordering) → new_lt12(vyy2130010, vyy1510)
new_ltEs8(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), df, dg, fb) → new_pePe(new_lt20(vyy2130010, vyy1510, df), new_asAs(new_esEs20(vyy2130010, vyy1510, df), new_pePe(new_lt19(vyy2130011, vyy1511, dg), new_asAs(new_esEs19(vyy2130011, vyy1511, dg), new_ltEs19(vyy2130012, vyy1512, fb)))))
new_esEs24(vyy3001, vyy401, ty_Char) → new_esEs12(vyy3001, vyy401)
new_esEs24(vyy3001, vyy401, app(app(ty_@2, cec), ced)) → new_esEs7(vyy3001, vyy401, cec, ced)
new_esEs26(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, bhd) → new_esEs12(vyy3000, vyy400)
new_esEs8(GT, GT) → True
new_esEs21(vyy213000, vyy150, ty_Double) → new_esEs16(vyy213000, vyy150)
new_esEs25(vyy3000, vyy400, ty_@0) → new_esEs10(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy1440), vyy40000) → Succ(Succ(new_primPlusNat1(vyy1440, vyy40000)))
new_ltEs20(vyy213001, vyy151, app(app(ty_@2, bca), bdd)) → new_ltEs15(vyy213001, vyy151, bca, bdd)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_lt6(vyy2130010, vyy1510, ty_@0) → new_lt7(vyy2130010, vyy1510)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_lt17(vyy213000, vyy150, bfb, bfc) → new_esEs8(new_compare8(vyy213000, vyy150, bfb, bfc), LT)
new_ltEs12(vyy213001, vyy151) → new_fsEs(new_compare14(vyy213001, vyy151))
new_esEs20(vyy2130010, vyy1510, ty_Ordering) → new_esEs8(vyy2130010, vyy1510)
new_ltEs20(vyy213001, vyy151, ty_Char) → new_ltEs9(vyy213001, vyy151)
new_esEs9(vyy2130010, vyy1510, app(ty_[], bdc)) → new_esEs11(vyy2130010, vyy1510, bdc)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_compare31(vyy2130000, vyy1500, app(app(ty_Either, bf), bg)) → new_compare15(vyy2130000, vyy1500, bf, bg)
new_primPlusNat1(Zero, Succ(vyy400000)) → Succ(vyy400000)
new_primPlusNat1(Succ(vyy14400), Zero) → Succ(vyy14400)
new_compare24(vyy213000, vyy150, False) → new_compare110(vyy213000, vyy150, new_ltEs10(vyy213000, vyy150))
new_esEs21(vyy213000, vyy150, ty_Char) → new_esEs12(vyy213000, vyy150)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Float, hf) → new_ltEs12(vyy2130010, vyy1510)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dca)) → new_esEs4(vyy3000, vyy400, dca)
new_compare16(vyy213000, vyy150, True) → LT
new_ltEs7(Just(vyy2130010), Just(vyy1510), app(app(app(ty_@3, ce), cf), cg)) → new_ltEs8(vyy2130010, vyy1510, ce, cf, cg)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs18(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs9(vyy2130010, vyy1510, ty_Double) → new_esEs16(vyy2130010, vyy1510)
new_esEs21(vyy213000, vyy150, app(app(ty_@2, bfb), bfc)) → new_esEs7(vyy213000, vyy150, bfb, bfc)
new_compare7(vyy213000, vyy150) → new_compare24(vyy213000, vyy150, new_esEs13(vyy213000, vyy150))
new_lt14(vyy213000, vyy150, beh, bfa) → new_esEs8(new_compare15(vyy213000, vyy150, beh, bfa), LT)
new_lt19(vyy2130011, vyy1511, ty_Double) → new_lt16(vyy2130011, vyy1511)
new_esEs25(vyy3000, vyy400, app(ty_Ratio, cga)) → new_esEs15(vyy3000, vyy400, cga)
new_ltEs4(Left(vyy2130010), Left(vyy1510), app(app(ty_Either, bac), bad), hf) → new_ltEs4(vyy2130010, vyy1510, bac, bad)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_esEs8(EQ, EQ) → True
new_esEs20(vyy2130010, vyy1510, ty_@0) → new_esEs10(vyy2130010, vyy1510)
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_compare([], [], h) → EQ
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, app(ty_Maybe, bba)) → new_ltEs7(vyy2130010, vyy1510, bba)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_compare14(Float(vyy2130000, vyy2130001), Float(vyy1500, vyy1501)) → new_compare12(new_sr0(vyy2130000, vyy1500), new_sr0(vyy2130001, vyy1501))
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dbf), dbg)) → new_esEs7(vyy3000, vyy400, dbf, dbg)
new_primCmpNat0(Succ(vyy21300000), Succ(vyy15000)) → new_primCmpNat0(vyy21300000, vyy15000)
new_lt6(vyy2130010, vyy1510, app(ty_[], bdc)) → new_lt8(vyy2130010, vyy1510, bdc)
new_esEs25(vyy3000, vyy400, app(ty_Maybe, cfh)) → new_esEs4(vyy3000, vyy400, cfh)
new_esEs26(vyy3002, vyy402, ty_Integer) → new_esEs17(vyy3002, vyy402)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs18(vyy3000, vyy400)
new_compare31(vyy2130000, vyy1500, ty_Double) → new_compare28(vyy2130000, vyy1500)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs4(Left(vyy2130010), Left(vyy1510), app(app(app(ty_@3, hh), baa), bab), hf) → new_ltEs8(vyy2130010, vyy1510, hh, baa, bab)
new_lt19(vyy2130011, vyy1511, app(app(app(ty_@3, fd), ff), fg)) → new_lt4(vyy2130011, vyy1511, fd, ff, fg)
new_esEs9(vyy2130010, vyy1510, app(app(ty_@2, bec), bed)) → new_esEs7(vyy2130010, vyy1510, bec, bed)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, cdd), cde)) → new_esEs6(vyy3000, vyy400, cdd, cde)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bhe), bhf), bhg), bhd) → new_esEs5(vyy3000, vyy400, bhe, bhf, bhg)
new_ltEs7(Nothing, Just(vyy1510), bgb) → True
new_esEs19(vyy2130011, vyy1511, app(app(ty_Either, fh), ga)) → new_esEs6(vyy2130011, vyy1511, fh, ga)
new_compare31(vyy2130000, vyy1500, app(app(app(ty_@3, bc), bd), be)) → new_compare5(vyy2130000, vyy1500, bc, bd, be)
new_esEs6(Right(vyy3000), Right(vyy400), cag, app(ty_Maybe, cbf)) → new_esEs4(vyy3000, vyy400, cbf)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs18(vyy3001, vyy401)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_lt19(vyy2130011, vyy1511, ty_@0) → new_lt7(vyy2130011, vyy1511)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ccd), cce), ccf)) → new_esEs5(vyy3000, vyy400, ccd, cce, ccf)
new_esEs9(vyy2130010, vyy1510, ty_Int) → new_esEs18(vyy2130010, vyy1510)
new_ltEs19(vyy2130012, vyy1512, ty_Double) → new_ltEs14(vyy2130012, vyy1512)
new_compare8(vyy213000, vyy150, bfb, bfc) → new_compare25(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bfb, bfc), bfb, bfc)
new_lt6(vyy2130010, vyy1510, ty_Double) → new_lt16(vyy2130010, vyy1510)
new_primCompAux00(vyy201, LT) → LT
new_esEs26(vyy3002, vyy402, app(ty_[], chd)) → new_esEs11(vyy3002, vyy402, chd)
new_esEs27(vyy3001, vyy401, app(ty_Ratio, dah)) → new_esEs15(vyy3001, vyy401, dah)
new_compare28(Double(vyy2130000, vyy2130001), Double(vyy1500, vyy1501)) → new_compare12(new_sr0(vyy2130000, vyy1500), new_sr0(vyy2130001, vyy1501))
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, ty_Float) → new_ltEs12(vyy2130010, vyy1510)
new_esEs9(vyy2130010, vyy1510, app(app(ty_Either, bea), beb)) → new_esEs6(vyy2130010, vyy1510, bea, beb)
new_primCmpInt(Neg(Succ(vyy21300000)), Neg(vyy1500)) → new_primCmpNat0(vyy1500, Succ(vyy21300000))
new_esEs24(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs6(Right(vyy3000), Right(vyy400), cag, ty_@0) → new_esEs10(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, daa), dab), dac)) → new_esEs5(vyy3001, vyy401, daa, dab, dac)
new_ltEs19(vyy2130012, vyy1512, ty_Int) → new_ltEs17(vyy2130012, vyy1512)
new_esEs6(Right(vyy3000), Right(vyy400), cag, ty_Char) → new_esEs12(vyy3000, vyy400)
new_lt21(vyy213000, vyy150, app(ty_Maybe, cb)) → new_lt9(vyy213000, vyy150, cb)
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, app(app(app(ty_@3, bbb), bbc), bbd)) → new_ltEs8(vyy2130010, vyy1510, bbb, bbc, bbd)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_lt4(vyy213000, vyy150, bee, bef, beg) → new_esEs8(new_compare5(vyy213000, vyy150, bee, bef, beg), LT)
new_compare19(@0, @0) → EQ
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_@0) → new_ltEs5(vyy2130010, vyy1510)
new_esEs24(vyy3001, vyy401, ty_@0) → new_esEs10(vyy3001, vyy401)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs11(GT, EQ) → False
new_primCmpNat0(Succ(vyy21300000), Zero) → GT
new_ltEs19(vyy2130012, vyy1512, app(ty_Ratio, bgf)) → new_ltEs13(vyy2130012, vyy1512, bgf)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy15000))) → LT
new_compare31(vyy2130000, vyy1500, app(ty_Ratio, ccb)) → new_compare9(vyy2130000, vyy1500, ccb)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Integer, hf) → new_ltEs16(vyy2130010, vyy1510)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs14(vyy3000, vyy400)
new_compare31(vyy2130000, vyy1500, ty_Int) → new_compare12(vyy2130000, vyy1500)
new_primPlusNat1(Succ(vyy14400), Succ(vyy400000)) → Succ(Succ(new_primPlusNat1(vyy14400, vyy400000)))
new_compare6(Integer(vyy2130000), Integer(vyy1500)) → new_primCmpInt(vyy2130000, vyy1500)
new_ltEs18(vyy2130011, vyy1511, app(app(ty_@2, bda), bdb)) → new_ltEs15(vyy2130011, vyy1511, bda, bdb)
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_lt19(vyy2130011, vyy1511, app(ty_Ratio, bgg)) → new_lt15(vyy2130011, vyy1511, bgg)
new_ltEs18(vyy2130011, vyy1511, app(app(ty_Either, bcg), bch)) → new_ltEs4(vyy2130011, vyy1511, bcg, bch)
new_compare(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), h) → new_primCompAux0(vyy2130000, vyy1500, new_compare(vyy2130001, vyy1501, h), h)
new_esEs9(vyy2130010, vyy1510, ty_@0) → new_esEs10(vyy2130010, vyy1510)
new_esEs11(:(vyy3000, vyy3001), [], dce) → False
new_esEs11([], :(vyy400, vyy401), dce) → False
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, cac), bhd) → new_esEs4(vyy3000, vyy400, cac)
new_esEs25(vyy3000, vyy400, ty_Char) → new_esEs12(vyy3000, vyy400)
new_compare12(vyy213000, vyy150) → new_primCmpInt(vyy213000, vyy150)
new_ltEs11(GT, LT) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_compare10(vyy177, vyy178, vyy179, vyy180, True, vyy182, bgd, bge) → new_compare11(vyy177, vyy178, vyy179, vyy180, True, bgd, bge)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy15000))) → new_primCmpNat0(Zero, Succ(vyy15000))
new_primCompAux00(vyy201, EQ) → vyy201
new_ltEs7(Just(vyy2130010), Just(vyy1510), app(app(ty_@2, dc), dd)) → new_ltEs15(vyy2130010, vyy1510, dc, dd)
new_esEs7(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cdf, cdg) → new_asAs(new_esEs25(vyy3000, vyy400, cdf), new_esEs24(vyy3001, vyy401, cdg))
new_compare24(vyy213000, vyy150, True) → EQ
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, app(app(ty_@2, bbg), bbh)) → new_ltEs15(vyy2130010, vyy1510, bbg, bbh)
new_esEs27(vyy3001, vyy401, app(app(ty_@2, dad), dae)) → new_esEs7(vyy3001, vyy401, dad, dae)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs18(vyy3000, vyy400)
new_lt6(vyy2130010, vyy1510, app(app(ty_Either, bea), beb)) → new_lt14(vyy2130010, vyy1510, bea, beb)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_ltEs11(LT, EQ) → True
new_ltEs16(vyy213001, vyy151) → new_fsEs(new_compare6(vyy213001, vyy151))
new_esEs9(vyy2130010, vyy1510, ty_Integer) → new_esEs17(vyy2130010, vyy1510)
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs16(vyy3001, vyy401)
new_ltEs11(LT, LT) → True
new_lt6(vyy2130010, vyy1510, app(app(ty_@2, bec), bed)) → new_lt17(vyy2130010, vyy1510, bec, bed)
new_esEs9(vyy2130010, vyy1510, ty_Ordering) → new_esEs8(vyy2130010, vyy1510)
new_esEs9(vyy2130010, vyy1510, ty_Float) → new_esEs14(vyy2130010, vyy1510)
new_esEs12(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, bhh), caa), bhd) → new_esEs7(vyy3000, vyy400, bhh, caa)
new_ltEs4(Left(vyy2130010), Left(vyy1510), app(ty_Ratio, bff), hf) → new_ltEs13(vyy2130010, vyy1510, bff)
new_not(False) → True
new_ltEs4(Right(vyy2130010), Left(vyy1510), bag, hf) → False
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, cae), caf), bhd) → new_esEs6(vyy3000, vyy400, cae, caf)
new_lt19(vyy2130011, vyy1511, ty_Char) → new_lt10(vyy2130011, vyy1511)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Ordering, hf) → new_ltEs11(vyy2130010, vyy1510)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, cdc)) → new_esEs15(vyy3000, vyy400, cdc)
new_esEs9(vyy2130010, vyy1510, ty_Bool) → new_esEs13(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, app(ty_Ratio, bfh)) → new_ltEs13(vyy2130011, vyy1511, bfh)
new_primCmpInt(Pos(Succ(vyy21300000)), Pos(vyy1500)) → new_primCmpNat0(Succ(vyy21300000), vyy1500)
new_primPlusNat0(Zero, vyy40000) → Succ(vyy40000)
new_esEs19(vyy2130011, vyy1511, app(app(ty_@2, gb), gc)) → new_esEs7(vyy2130011, vyy1511, gb, gc)
new_compare5(vyy213000, vyy150, bee, bef, beg) → new_compare26(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, bee, bef, beg), bee, bef, beg)
new_lt6(vyy2130010, vyy1510, app(app(app(ty_@3, bdf), bdg), bdh)) → new_lt4(vyy2130010, vyy1510, bdf, bdg, bdh)
new_ltEs17(vyy213001, vyy151) → new_fsEs(new_compare12(vyy213001, vyy151))
new_esEs24(vyy3001, vyy401, app(app(ty_Either, ceh), cfa)) → new_esEs6(vyy3001, vyy401, ceh, cfa)
new_lt16(vyy213000, vyy150) → new_esEs8(new_compare28(vyy213000, vyy150), LT)
new_esEs20(vyy2130010, vyy1510, ty_Float) → new_esEs14(vyy2130010, vyy1510)
new_esEs9(vyy2130010, vyy1510, app(ty_Ratio, bga)) → new_esEs15(vyy2130010, vyy1510, bga)
new_lt21(vyy213000, vyy150, ty_Ordering) → new_lt12(vyy213000, vyy150)
new_lt19(vyy2130011, vyy1511, ty_Bool) → new_lt11(vyy2130011, vyy1511)
new_esEs20(vyy2130010, vyy1510, app(ty_[], gd)) → new_esEs11(vyy2130010, vyy1510, gd)
new_ltEs14(vyy213001, vyy151) → new_fsEs(new_compare28(vyy213001, vyy151))
new_esEs26(vyy3002, vyy402, ty_Int) → new_esEs18(vyy3002, vyy402)
new_lt6(vyy2130010, vyy1510, ty_Bool) → new_lt11(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, app(ty_Maybe, bcc)) → new_ltEs7(vyy2130011, vyy1511, bcc)
new_esEs19(vyy2130011, vyy1511, ty_Int) → new_esEs18(vyy2130011, vyy1511)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, bhd) → new_esEs13(vyy3000, vyy400)
new_esEs21(vyy213000, vyy150, app(ty_Ratio, bha)) → new_esEs15(vyy213000, vyy150, bha)
new_ltEs11(GT, GT) → True
new_esEs27(vyy3001, vyy401, app(app(ty_Either, dba), dbb)) → new_esEs6(vyy3001, vyy401, dba, dbb)
new_esEs29(vyy3000, vyy400, app(ty_Ratio, dde)) → new_esEs15(vyy3000, vyy400, dde)
new_esEs6(Right(vyy3000), Right(vyy400), cag, app(ty_[], cbe)) → new_esEs11(vyy3000, vyy400, cbe)
new_esEs20(vyy2130010, vyy1510, ty_Int) → new_esEs18(vyy2130010, vyy1510)
new_ltEs20(vyy213001, vyy151, app(app(app(ty_@3, df), dg), fb)) → new_ltEs8(vyy213001, vyy151, df, dg, fb)
new_esEs20(vyy2130010, vyy1510, app(app(app(ty_@3, gf), gg), gh)) → new_esEs5(vyy2130010, vyy1510, gf, gg, gh)
new_ltEs7(Just(vyy2130010), Just(vyy1510), app(ty_Maybe, cd)) → new_ltEs7(vyy2130010, vyy1510, cd)
new_primCmpInt(Pos(Succ(vyy21300000)), Neg(vyy1500)) → GT
new_esEs21(vyy213000, vyy150, app(app(app(ty_@3, bee), bef), beg)) → new_esEs5(vyy213000, vyy150, bee, bef, beg)
new_esEs9(vyy2130010, vyy1510, ty_Char) → new_esEs12(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, ty_Ordering) → new_ltEs11(vyy2130011, vyy1511)
new_primMulInt(Pos(vyy30000), Pos(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_esEs26(vyy3002, vyy402, ty_@0) → new_esEs10(vyy3002, vyy402)
new_esEs6(Right(vyy3000), Right(vyy400), cag, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs19(vyy2130011, vyy1511, ty_Bool) → new_esEs13(vyy2130011, vyy1511)
new_primMulInt(Neg(vyy30000), Neg(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_compare110(vyy213000, vyy150, True) → LT
new_compare9(:%(vyy2130000, vyy2130001), :%(vyy1500, vyy1501), ty_Integer) → new_compare6(new_sr(vyy2130000, vyy1501), new_sr(vyy1500, vyy2130001))
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_esEs21(vyy213000, vyy150, ty_@0) → new_esEs10(vyy213000, vyy150)
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Integer) → new_ltEs16(vyy2130010, vyy1510)
new_lt20(vyy2130010, vyy1510, app(ty_Ratio, bgh)) → new_lt15(vyy2130010, vyy1510, bgh)
new_esEs26(vyy3002, vyy402, app(app(ty_@2, chb), chc)) → new_esEs7(vyy3002, vyy402, chb, chc)
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Char) → new_ltEs9(vyy2130010, vyy1510)
new_esEs9(vyy2130010, vyy1510, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs5(vyy2130010, vyy1510, bdf, bdg, bdh)
new_compare25(vyy21300, vyy15, True, bfe, bfd) → EQ
new_compare110(vyy213000, vyy150, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, ccc) → True
new_esEs25(vyy3000, vyy400, app(ty_[], cfg)) → new_esEs11(vyy3000, vyy400, cfg)
new_esEs6(Right(vyy3000), Right(vyy400), cag, ty_Float) → new_esEs14(vyy3000, vyy400)
new_lt18(vyy213000, vyy150) → new_esEs8(new_compare12(vyy213000, vyy150), LT)
new_compare210(vyy213000, vyy150, True) → EQ
new_esEs20(vyy2130010, vyy1510, app(app(ty_Either, ha), hb)) → new_esEs6(vyy2130010, vyy1510, ha, hb)
new_ltEs19(vyy2130012, vyy1512, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs8(vyy2130012, vyy1512, eb, ec, ed)
new_ltEs19(vyy2130012, vyy1512, ty_Ordering) → new_ltEs11(vyy2130012, vyy1512)
new_esEs29(vyy3000, vyy400, app(app(ty_Either, ddf), ddg)) → new_esEs6(vyy3000, vyy400, ddf, ddg)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs13(vyy3000, vyy400)
new_ltEs7(Nothing, Nothing, bgb) → True
new_ltEs19(vyy2130012, vyy1512, ty_Bool) → new_ltEs10(vyy2130012, vyy1512)
new_esEs27(vyy3001, vyy401, app(ty_Maybe, dag)) → new_esEs4(vyy3001, vyy401, dag)
new_ltEs20(vyy213001, vyy151, ty_Int) → new_ltEs17(vyy213001, vyy151)
new_ltEs19(vyy2130012, vyy1512, ty_Char) → new_ltEs9(vyy2130012, vyy1512)
new_esEs29(vyy3000, vyy400, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs5(vyy3000, vyy400, dcf, dcg, dch)
new_ltEs20(vyy213001, vyy151, ty_@0) → new_ltEs5(vyy213001, vyy151)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy15000))) → new_primCmpNat0(Succ(vyy15000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy15000))) → GT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, bhd) → new_esEs8(vyy3000, vyy400)
new_lt21(vyy213000, vyy150, ty_Integer) → new_lt5(vyy213000, vyy150)
new_lt20(vyy2130010, vyy1510, app(ty_Maybe, ge)) → new_lt9(vyy2130010, vyy1510, ge)
new_compare31(vyy2130000, vyy1500, app(ty_[], ba)) → new_compare(vyy2130000, vyy1500, ba)
new_sr0(vyy3000, vyy400) → new_primMulInt(vyy3000, vyy400)
new_compare11(vyy177, vyy178, vyy179, vyy180, False, bgd, bge) → GT
new_ltEs18(vyy2130011, vyy1511, ty_Float) → new_ltEs12(vyy2130011, vyy1511)
new_ltEs20(vyy213001, vyy151, ty_Ordering) → new_ltEs11(vyy213001, vyy151)
new_compare25(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, bfe, bfd) → new_compare10(vyy213000, vyy213001, vyy150, vyy151, new_lt21(vyy213000, vyy150, bfe), new_asAs(new_esEs21(vyy213000, vyy150, bfe), new_ltEs20(vyy213001, vyy151, bfd)), bfe, bfd)
new_ltEs7(Just(vyy2130010), Just(vyy1510), app(ty_Ratio, bgc)) → new_ltEs13(vyy2130010, vyy1510, bgc)
new_lt20(vyy2130010, vyy1510, ty_Double) → new_lt16(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, app(ty_[], bcb)) → new_ltEs6(vyy2130011, vyy1511, bcb)
new_esEs21(vyy213000, vyy150, app(ty_Maybe, cb)) → new_esEs4(vyy213000, vyy150, cb)
new_ltEs11(EQ, EQ) → True
new_lt20(vyy2130010, vyy1510, ty_Char) → new_lt10(vyy2130010, vyy1510)
new_esEs21(vyy213000, vyy150, ty_Integer) → new_esEs17(vyy213000, vyy150)
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, app(ty_[], bah)) → new_ltEs6(vyy2130010, vyy1510, bah)
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, app(ty_Ratio, bfg)) → new_ltEs13(vyy2130010, vyy1510, bfg)
new_esEs15(:%(vyy3000, vyy3001), :%(vyy400, vyy401), bhc) → new_asAs(new_esEs23(vyy3000, vyy400, bhc), new_esEs22(vyy3001, vyy401, bhc))
new_esEs10(@0, @0) → True
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Int) → new_ltEs17(vyy2130010, vyy1510)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt6(vyy2130010, vyy1510, app(ty_Maybe, bde)) → new_lt9(vyy2130010, vyy1510, bde)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs10(vyy3000, vyy400)
new_esEs19(vyy2130011, vyy1511, ty_Double) → new_esEs16(vyy2130011, vyy1511)
new_ltEs10(True, False) → False
new_asAs(False, vyy123) → False
new_primMulInt(Neg(vyy30000), Pos(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulInt(Pos(vyy30000), Neg(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40000)) → Zero
new_esEs29(vyy3000, vyy400, ty_Char) → new_esEs12(vyy3000, vyy400)
new_esEs21(vyy213000, vyy150, ty_Ordering) → new_esEs8(vyy213000, vyy150)
new_ltEs11(EQ, LT) → False
new_esEs21(vyy213000, vyy150, ty_Bool) → new_esEs13(vyy213000, vyy150)
new_esEs9(vyy2130010, vyy1510, app(ty_Maybe, bde)) → new_esEs4(vyy2130010, vyy1510, bde)
new_esEs19(vyy2130011, vyy1511, app(ty_[], fa)) → new_esEs11(vyy2130011, vyy1511, fa)
new_lt8(vyy213000, vyy150, h) → new_esEs8(new_compare(vyy213000, vyy150, h), LT)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_esEs13(False, False) → True
new_esEs29(vyy3000, vyy400, ty_Float) → new_esEs14(vyy3000, vyy400)
new_ltEs18(vyy2130011, vyy1511, ty_Int) → new_ltEs17(vyy2130011, vyy1511)
new_lt20(vyy2130010, vyy1510, ty_Float) → new_lt13(vyy2130010, vyy1510)
new_lt21(vyy213000, vyy150, ty_Double) → new_lt16(vyy213000, vyy150)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs16(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, bhd) → new_esEs18(vyy3000, vyy400)
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Bool) → new_ltEs10(vyy2130010, vyy1510)
new_compare17(vyy213000, vyy150) → new_compare210(vyy213000, vyy150, new_esEs8(vyy213000, vyy150))
new_lt5(vyy213000, vyy150) → new_esEs8(new_compare6(vyy213000, vyy150), LT)
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs10(vyy3000, vyy400)
new_ltEs7(Just(vyy2130010), Nothing, bgb) → False
new_lt20(vyy2130010, vyy1510, ty_Integer) → new_lt5(vyy2130010, vyy1510)
new_esEs27(vyy3001, vyy401, app(ty_[], daf)) → new_esEs11(vyy3001, vyy401, daf)
new_compare9(:%(vyy2130000, vyy2130001), :%(vyy1500, vyy1501), ty_Int) → new_compare12(new_sr0(vyy2130000, vyy1501), new_sr0(vyy1500, vyy2130001))
new_ltEs18(vyy2130011, vyy1511, ty_Double) → new_ltEs14(vyy2130011, vyy1511)
new_compare31(vyy2130000, vyy1500, ty_Ordering) → new_compare17(vyy2130000, vyy1500)
new_ltEs19(vyy2130012, vyy1512, app(app(ty_@2, eg), eh)) → new_ltEs15(vyy2130012, vyy1512, eg, eh)
new_lt11(vyy213000, vyy150) → new_esEs8(new_compare7(vyy213000, vyy150), LT)
new_ltEs19(vyy2130012, vyy1512, app(ty_Maybe, ea)) → new_ltEs7(vyy2130012, vyy1512, ea)
new_esEs25(vyy3000, vyy400, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs5(vyy3000, vyy400, cfb, cfc, cfd)
new_ltEs19(vyy2130012, vyy1512, app(ty_[], dh)) → new_ltEs6(vyy2130012, vyy1512, dh)
new_lt12(vyy213000, vyy150) → new_esEs8(new_compare17(vyy213000, vyy150), LT)
new_ltEs4(Right(vyy2130010), Right(vyy1510), bag, ty_Char) → new_ltEs9(vyy2130010, vyy1510)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_ltEs4(Left(vyy2130010), Left(vyy1510), app(ty_Maybe, hg), hf) → new_ltEs7(vyy2130010, vyy1510, hg)
new_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_esEs21(vyy213000, vyy150, app(ty_[], h)) → new_esEs11(vyy213000, vyy150, h)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, ccg), cch)) → new_esEs7(vyy3000, vyy400, ccg, cch)
new_compare112(vyy213000, vyy150, False, cb) → GT
new_esEs19(vyy2130011, vyy1511, ty_Integer) → new_esEs17(vyy2130011, vyy1511)
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cgd, cge, cgf) → new_asAs(new_esEs28(vyy3000, vyy400, cgd), new_asAs(new_esEs27(vyy3001, vyy401, cge), new_esEs26(vyy3002, vyy402, cgf)))
new_compare27(vyy213000, vyy150, True, cb) → EQ
new_lt6(vyy2130010, vyy1510, ty_Float) → new_lt13(vyy2130010, vyy1510)
new_lt19(vyy2130011, vyy1511, ty_Ordering) → new_lt12(vyy2130011, vyy1511)
new_lt9(vyy213000, vyy150, cb) → new_esEs8(new_compare18(vyy213000, vyy150, cb), LT)
new_compare11(vyy177, vyy178, vyy179, vyy180, True, bgd, bge) → LT
new_esEs20(vyy2130010, vyy1510, app(app(ty_@2, hc), hd)) → new_esEs7(vyy2130010, vyy1510, hc, hd)
new_compare26(vyy213000, vyy150, True, bee, bef, beg) → EQ
new_lt13(vyy213000, vyy150) → new_esEs8(new_compare14(vyy213000, vyy150), LT)
new_esEs29(vyy3000, vyy400, ty_@0) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy3002, vyy402, app(app(ty_Either, chg), chh)) → new_esEs6(vyy3002, vyy402, chg, chh)
new_compare111(vyy213000, vyy150, True, beh, bfa) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs10(True, True) → True
new_lt21(vyy213000, vyy150, app(app(ty_Either, beh), bfa)) → new_lt14(vyy213000, vyy150, beh, bfa)
new_asAs(True, vyy123) → vyy123
new_esEs26(vyy3002, vyy402, ty_Float) → new_esEs14(vyy3002, vyy402)
new_primMulNat0(Succ(vyy300000), Succ(vyy40000)) → new_primPlusNat0(new_primMulNat0(vyy300000, Succ(vyy40000)), vyy40000)
new_esEs26(vyy3002, vyy402, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs5(vyy3002, vyy402, cgg, cgh, cha)
new_compare30(Char(vyy2130000), Char(vyy1500)) → new_primCmpNat0(vyy2130000, vyy1500)
new_esEs13(True, True) → True
new_ltEs19(vyy2130012, vyy1512, ty_Float) → new_ltEs12(vyy2130012, vyy1512)
new_esEs14(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs18(new_sr0(vyy3000, vyy400), new_sr0(vyy3001, vyy401))
new_esEs6(Right(vyy3000), Right(vyy400), cag, ty_Int) → new_esEs18(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], cda)) → new_esEs11(vyy3000, vyy400, cda)
new_fsEs(vyy183) → new_not(new_esEs8(vyy183, GT))
new_primCompAux0(vyy2130000, vyy1500, vyy192, h) → new_primCompAux00(vyy192, new_compare31(vyy2130000, vyy1500, h))
new_esEs19(vyy2130011, vyy1511, ty_@0) → new_esEs10(vyy2130011, vyy1511)
new_esEs19(vyy2130011, vyy1511, ty_Ordering) → new_esEs8(vyy2130011, vyy1511)
new_esEs26(vyy3002, vyy402, ty_Double) → new_esEs16(vyy3002, vyy402)
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs14(vyy3001, vyy401)
new_lt21(vyy213000, vyy150, app(ty_Ratio, bha)) → new_lt15(vyy213000, vyy150, bha)
new_esEs29(vyy3000, vyy400, app(ty_Maybe, ddd)) → new_esEs4(vyy3000, vyy400, ddd)
new_ltEs20(vyy213001, vyy151, app(ty_Maybe, bgb)) → new_ltEs7(vyy213001, vyy151, bgb)
new_lt19(vyy2130011, vyy1511, app(app(ty_@2, gb), gc)) → new_lt17(vyy2130011, vyy1511, gb, gc)
new_compare13(vyy213000, vyy150, True, bee, bef, beg) → LT
new_ltEs15(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), bca, bdd) → new_pePe(new_lt6(vyy2130010, vyy1510, bca), new_asAs(new_esEs9(vyy2130010, vyy1510, bca), new_ltEs18(vyy2130011, vyy1511, bdd)))
new_compare31(vyy2130000, vyy1500, ty_Float) → new_compare14(vyy2130000, vyy1500)
new_compare31(vyy2130000, vyy1500, ty_@0) → new_compare19(vyy2130000, vyy1500)
new_lt21(vyy213000, vyy150, ty_Int) → new_lt18(vyy213000, vyy150)
new_primCompAux00(vyy201, GT) → GT
new_lt15(vyy213000, vyy150, bha) → new_esEs8(new_compare9(vyy213000, vyy150, bha), LT)
new_compare27(vyy213000, vyy150, False, cb) → new_compare112(vyy213000, vyy150, new_ltEs7(vyy213000, vyy150, cb), cb)
new_esEs25(vyy3000, vyy400, ty_Float) → new_esEs14(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), cag, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs26(vyy3002, vyy402, ty_Bool) → new_esEs13(vyy3002, vyy402)
new_esEs6(Right(vyy3000), Right(vyy400), cag, app(app(app(ty_@3, cah), cba), cbb)) → new_esEs5(vyy3000, vyy400, cah, cba, cbb)
new_esEs29(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs11(EQ, GT) → True
new_ltEs20(vyy213001, vyy151, app(ty_Ratio, bhb)) → new_ltEs13(vyy213001, vyy151, bhb)
new_lt21(vyy213000, vyy150, app(app(app(ty_@3, bee), bef), beg)) → new_lt4(vyy213000, vyy150, bee, bef, beg)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs12(vyy3000, vyy400)
new_ltEs7(Just(vyy2130010), Just(vyy1510), app(app(ty_Either, da), db)) → new_ltEs4(vyy2130010, vyy1510, da, db)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(vyy21300000)), Pos(vyy1500)) → LT
new_esEs19(vyy2130011, vyy1511, ty_Char) → new_esEs12(vyy2130011, vyy1511)
new_compare16(vyy213000, vyy150, False) → GT
new_not(True) → False

The set Q consists of the following terms:

new_lt21(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Int)
new_esEs11([], [], x0)
new_compare110(x0, x1, True)
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Int)
new_ltEs11(EQ, GT)
new_ltEs11(GT, EQ)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Bool)
new_compare24(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_lt6(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs20(x0, x1, ty_Ordering)
new_lt15(x0, x1, x2)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, app(ty_[], x2))
new_asAs(True, x0)
new_esEs20(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Integer)
new_ltEs11(EQ, EQ)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare30(Char(x0), Char(x1))
new_esEs9(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt16(x0, x1)
new_compare5(x0, x1, x2, x3, x4)
new_esEs25(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCompAux00(x0, GT)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, ty_Float)
new_lt6(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_compare26(x0, x1, True, x2, x3, x4)
new_ltEs20(x0, x1, ty_Char)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, LT)
new_ltEs6(x0, x1, x2)
new_compare111(x0, x1, True, x2, x3)
new_lt20(x0, x1, ty_Int)
new_compare210(x0, x1, True)
new_lt21(x0, x1, ty_Integer)
new_compare31(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Int)
new_esEs8(GT, GT)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Integer)
new_lt21(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_compare11(x0, x1, x2, x3, False, x4, x5)
new_esEs8(LT, LT)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare24(x0, x1, True)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt21(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare111(x0, x1, False, x2, x3)
new_lt6(x0, x1, ty_Float)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs11(LT, GT)
new_ltEs11(GT, LT)
new_ltEs20(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Ordering)
new_sr(Integer(x0), Integer(x1))
new_primEqNat0(Succ(x0), Succ(x1))
new_asAs(False, x0)
new_compare([], :(x0, x1), x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Int)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_@0)
new_lt8(x0, x1, x2)
new_compare17(x0, x1)
new_primEqNat0(Zero, Zero)
new_esEs18(x0, x1)
new_lt18(x0, x1)
new_compare31(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Integer)
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_lt4(x0, x1, x2, x3, x4)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs25(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs7(Just(x0), Nothing, x1)
new_compare31(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_lt6(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs13(False, False)
new_primMulNat0(Zero, Zero)
new_compare16(x0, x1, False)
new_esEs19(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Char)
new_compare13(x0, x1, False, x2, x3, x4)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCompAux0(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Char)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare6(Integer(x0), Integer(x1))
new_ltEs14(x0, x1)
new_esEs24(x0, x1, app(ty_[], x2))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs11(:(x0, x1), [], x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat0(Zero, x0)
new_compare7(x0, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs29(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_compare31(x0, x1, ty_Char)
new_compare29(x0, x1, True, x2, x3)
new_compare31(x0, x1, ty_Ordering)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_lt11(x0, x1)
new_ltEs8(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primCmpNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare([], [], x0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare14(Float(x0, x1), Float(x2, x3))
new_primPlusNat1(Zero, Zero)
new_esEs20(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Integer)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt6(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(False, False)
new_lt20(x0, x1, ty_Char)
new_lt7(x0, x1)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs17(x0, x1)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare25(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_esEs21(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_@0)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_lt6(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_compare11(x0, x1, x2, x3, True, x4, x5)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs10(@0, @0)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs18(x0, x1, ty_Float)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11([], :(x0, x1), x2)
new_esEs4(Nothing, Nothing, x0)
new_lt19(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primPlusNat0(Succ(x0), x1)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs9(x0, x1)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare12(x0, x1)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt21(x0, x1, app(ty_[], x2))
new_lt14(x0, x1, x2, x3)
new_lt9(x0, x1, x2)
new_esEs24(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs18(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_lt21(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs21(x0, x1, ty_Int)
new_ltEs13(x0, x1, x2)
new_esEs28(x0, x1, ty_Integer)
new_esEs9(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Float)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Bool)
new_compare13(x0, x1, True, x2, x3, x4)
new_ltEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, ty_Float)
new_primPlusNat1(Zero, Succ(x0))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare29(x0, x1, False, x2, x3)
new_lt19(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Double)
new_ltEs16(x0, x1)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(Double(x0, x1), Double(x2, x3))
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_compare10(x0, x1, x2, x3, True, x4, x5, x6)
new_compare16(x0, x1, True)
new_ltEs11(LT, LT)
new_ltEs5(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_lt12(x0, x1)
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_compare110(x0, x1, False)
new_ltEs7(Nothing, Nothing, x0)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_ltEs19(x0, x1, ty_Char)
new_ltEs11(EQ, LT)
new_ltEs11(LT, EQ)
new_esEs20(x0, x1, ty_Float)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_lt21(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs17(Integer(x0), Integer(x1))
new_compare26(x0, x1, False, x2, x3, x4)
new_ltEs20(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, False, x2)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs25(x0, x1, ty_@0)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs10(True, True)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_pePe(False, x0)
new_esEs27(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare112(x0, x1, False, x2)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs20(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_@0)
new_compare(:(x0, x1), [], x2)
new_lt19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Int)
new_esEs13(True, False)
new_esEs13(False, True)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare8(x0, x1, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), Zero)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_ltEs7(Nothing, Just(x0), x1)
new_not(True)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, ty_Float)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs13(True, True)
new_compare27(x0, x1, True, x2)
new_esEs29(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs19(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Integer)
new_lt5(x0, x1)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs29(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs19(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt6(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, ty_Bool)
new_ltEs12(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs15(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_compare19(@0, @0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt21(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs10(True, False)
new_ltEs10(False, True)
new_compare18(x0, x1, x2)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_lt20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr0(x0, x1)
new_pePe(True, x0)
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs4(Just(x0), Nothing, x1)
new_lt17(x0, x1, x2, x3)
new_compare10(x0, x1, x2, x3, False, x4, x5, x6)
new_lt6(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_lt10(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare(:(x0, x1), :(x2, x3), x4)
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare15(x0, x1, x2, x3)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Double)
new_esEs9(x0, x1, ty_Ordering)
new_compare25(x0, x1, True, x2, x3)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(x0, x1, ty_Float)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_compare112(x0, x1, True, x2)
new_esEs21(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, ty_Double)
new_esEs12(Char(x0), Char(x1))
new_fsEs(x0)
new_esEs25(x0, x1, ty_Float)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs11(GT, GT)

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_GE10(vyy67, vyy15, vyy16, vyy210, vyy211, vyy212, EmptyFM, vyy214, False, h, ba, bb) → new_foldFM_GE(vyy67, vyy15, vyy16, vyy214, h, ba, bb)
new_foldFM_GE10(vyy67, vyy15, vyy16, vyy210, vyy211, vyy212, Branch(vyy2130, vyy2131, vyy2132, vyy2133, vyy2134), vyy214, False, h, ba, bb) → new_foldFM_GE1(new_keysFM_GE0(vyy210, vyy211, new_foldFM_GE0(vyy67, vyy15, vyy16, vyy214, h, ba, bb), h, ba, bb), vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, h, ba, bb)
new_foldFM_GE10(vyy67, vyy15, vyy16, vyy210, vyy211, vyy212, Branch(vyy2130, vyy2131, vyy2132, vyy2133, vyy2134), vyy214, False, h, ba, bb) → new_foldFM_GE(vyy67, vyy15, vyy16, vyy214, h, ba, bb)
new_foldFM_GE10(vyy67, vyy15, vyy16, vyy210, vyy211, vyy212, vyy213, Branch(vyy2140, vyy2141, vyy2142, vyy2143, vyy2144), True, h, ba, bb) → new_foldFM_GE1(vyy67, vyy15, vyy16, vyy2140, vyy2141, vyy2142, vyy2143, vyy2144, h, ba, bb)
new_foldFM_GE(vyy67, vyy15, vyy16, Branch(vyy2140, vyy2141, vyy2142, vyy2143, vyy2144), h, ba, bb) → new_foldFM_GE1(vyy67, vyy15, vyy16, vyy2140, vyy2141, vyy2142, vyy2143, vyy2144, h, ba, bb)
new_foldFM_GE1(vyy125, vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, h, ba, bb) → new_foldFM_GE10(vyy125, vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, new_esEs8(new_compare25(vyy2130, @2(vyy15, vyy16), new_esEs7(vyy2130, @2(vyy15, vyy16), h, ba), h, ba), LT), h, ba, bb)

The TRS R consists of the following rules:

new_esEs16(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs18(new_sr0(vyy3000, vyy400), new_sr0(vyy3001, vyy401))
new_esEs6(Right(vyy3000), Right(vyy400), caa, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, cde)) → new_esEs4(vyy3000, vyy400, cde)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_esEs29(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, ty_Ordering) → new_ltEs11(vyy2130010, vyy1510)
new_compare112(vyy213000, vyy150, True, bfh) → LT
new_lt21(vyy213000, vyy150, ty_Float) → new_lt13(vyy213000, vyy150)
new_ltEs19(vyy2130012, vyy1512, ty_Integer) → new_ltEs16(vyy2130012, vyy1512)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt19(vyy2130011, vyy1511, ty_Int) → new_lt18(vyy2130011, vyy1511)
new_lt19(vyy2130011, vyy1511, app(app(ty_Either, bea), beb)) → new_lt14(vyy2130011, vyy1511, bea, beb)
new_esEs24(vyy3001, vyy401, app(ty_Ratio, cfb)) → new_esEs15(vyy3001, vyy401, cfb)
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Ordering) → new_ltEs11(vyy2130010, vyy1510)
new_ltEs11(LT, GT) → True
new_esEs21(vyy213000, vyy150, ty_Float) → new_esEs14(vyy213000, vyy150)
new_esEs24(vyy3001, vyy401, app(app(app(ty_@3, cec), ced), cee)) → new_esEs5(vyy3001, vyy401, cec, ced, cee)
new_esEs13(False, True) → False
new_esEs13(True, False) → False
new_ltEs10(False, True) → True
new_esEs26(vyy3002, vyy402, app(ty_Ratio, daa)) → new_esEs15(vyy3002, vyy402, daa)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, bgf) → new_esEs17(vyy3000, vyy400)
new_esEs19(vyy2130011, vyy1511, app(ty_Ratio, bec)) → new_esEs15(vyy2130011, vyy1511, bec)
new_lt6(vyy2130010, vyy1510, ty_Int) → new_lt18(vyy2130010, vyy1510)
new_foldFM_GE11(vyy67, vyy15, vyy16, vyy210, vyy211, vyy212, vyy213, vyy214, True, h, ba, bb) → new_foldFM_GE0(vyy67, vyy15, vyy16, vyy214, h, ba, bb)
new_esEs28(vyy3000, vyy400, ty_Float) → new_esEs14(vyy3000, vyy400)
new_compare([], :(vyy1500, vyy1501), ee) → LT
new_esEs4(Just(vyy3000), Nothing, ccf) → False
new_esEs4(Nothing, Just(vyy400), ccf) → False
new_ltEs20(vyy213001, vyy151, app(ty_[], bbd)) → new_ltEs6(vyy213001, vyy151, bbd)
new_esEs24(vyy3001, vyy401, app(ty_Maybe, cfa)) → new_esEs4(vyy3001, vyy401, cfa)
new_lt19(vyy2130011, vyy1511, ty_Integer) → new_lt5(vyy2130011, vyy1511)
new_esEs28(vyy3000, vyy400, app(ty_Ratio, dce)) → new_esEs15(vyy3000, vyy400, dce)
new_lt20(vyy2130010, vyy1510, app(app(ty_Either, bfc), bfd)) → new_lt14(vyy2130010, vyy1510, bfc, bfd)
new_ltEs4(Left(vyy2130010), Left(vyy1510), app(app(ty_@2, cg), da), bf) → new_ltEs15(vyy2130010, vyy1510, cg, da)
new_ltEs6(vyy213001, vyy151, bbd) → new_fsEs(new_compare(vyy213001, vyy151, bbd))
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs12(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, bhf), bgf) → new_esEs15(vyy3000, vyy400, bhf)
new_primMulNat0(Zero, Zero) → Zero
new_compare(:(vyy2130000, vyy2130001), [], ee) → GT
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], bhd), bgf) → new_esEs11(vyy3000, vyy400, bhd)
new_lt20(vyy2130010, vyy1510, app(ty_[], bef)) → new_lt8(vyy2130010, vyy1510, bef)
new_compare13(vyy213000, vyy150, False, bc, bd, be) → GT
new_esEs6(Right(vyy3000), Right(vyy400), caa, app(app(ty_@2, cae), caf)) → new_esEs7(vyy3000, vyy400, cae, caf)
new_lt20(vyy2130010, vyy1510, ty_@0) → new_lt7(vyy2130010, vyy1510)
new_lt21(vyy213000, vyy150, ty_@0) → new_lt7(vyy213000, vyy150)
new_ltEs20(vyy213001, vyy151, ty_Float) → new_ltEs12(vyy213001, vyy151)
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, ty_Bool) → new_ltEs10(vyy2130010, vyy1510)
new_sr(Integer(vyy21300000), Integer(vyy15010)) → Integer(new_primMulInt(vyy21300000, vyy15010))
new_esEs11(:(vyy3000, vyy3001), :(vyy400, vyy401), dch) → new_asAs(new_esEs29(vyy3000, vyy400, dch), new_esEs11(vyy3001, vyy401, dch))
new_esEs25(vyy3000, vyy400, app(app(ty_Either, cge), cgf)) → new_esEs6(vyy3000, vyy400, cge, cgf)
new_ltEs18(vyy2130011, vyy1511, ty_Integer) → new_ltEs16(vyy2130011, vyy1511)
new_esEs20(vyy2130010, vyy1510, app(ty_Maybe, beg)) → new_esEs4(vyy2130010, vyy1510, beg)
new_lt6(vyy2130010, vyy1510, app(ty_Ratio, hb)) → new_lt15(vyy2130010, vyy1510, hb)
new_ltEs18(vyy2130011, vyy1511, ty_@0) → new_ltEs5(vyy2130011, vyy1511)
new_lt19(vyy2130011, vyy1511, app(ty_Maybe, bde)) → new_lt9(vyy2130011, vyy1511, bde)
new_ltEs18(vyy2130011, vyy1511, app(app(app(ty_@3, fb), fc), fd)) → new_ltEs8(vyy2130011, vyy1511, fb, fc, fd)
new_lt20(vyy2130010, vyy1510, app(app(app(ty_@3, beh), bfa), bfb)) → new_lt4(vyy2130010, vyy1510, beh, bfa, bfb)
new_lt20(vyy2130010, vyy1510, ty_Int) → new_lt18(vyy2130010, vyy1510)
new_ltEs7(Just(vyy2130010), Just(vyy1510), app(ty_[], hf)) → new_ltEs6(vyy2130010, vyy1510, hf)
new_esEs25(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)
new_lt21(vyy213000, vyy150, ty_Bool) → new_lt11(vyy213000, vyy150)
new_esEs24(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_esEs6(Right(vyy3000), Right(vyy400), caa, app(ty_Ratio, cba)) → new_esEs15(vyy3000, vyy400, cba)
new_lt10(vyy213000, vyy150) → new_esEs8(new_compare30(vyy213000, vyy150), LT)
new_compare18(vyy213000, vyy150, bfh) → new_compare27(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, bfh), bfh)
new_lt19(vyy2130011, vyy1511, ty_Float) → new_lt13(vyy2130011, vyy1511)
new_esEs11([], [], dch) → True
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, bgf) → new_esEs14(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_ltEs20(vyy213001, vyy151, ty_Integer) → new_ltEs16(vyy213001, vyy151)
new_esEs21(vyy213000, vyy150, app(app(ty_Either, bbe), bbf)) → new_esEs6(vyy213000, vyy150, bbe, bbf)
new_ltEs18(vyy2130011, vyy1511, ty_Bool) → new_ltEs10(vyy2130011, vyy1511)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Bool, bf) → new_ltEs10(vyy2130010, vyy1510)
new_compare31(vyy2130000, vyy1500, ty_Bool) → new_compare7(vyy2130000, vyy1500)
new_ltEs10(False, False) → True
new_esEs19(vyy2130011, vyy1511, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs5(vyy2130011, vyy1511, bdf, bdg, bdh)
new_esEs26(vyy3002, vyy402, app(ty_Maybe, chh)) → new_esEs4(vyy3002, vyy402, chh)
new_compare31(vyy2130000, vyy1500, ty_Char) → new_compare30(vyy2130000, vyy1500)
new_esEs28(vyy3000, vyy400, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs5(vyy3000, vyy400, dbf, dbg, dbh)
new_esEs25(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs17(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Double, bf) → new_ltEs14(vyy2130010, vyy1510)
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Double) → new_ltEs14(vyy2130010, vyy1510)
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, ty_Double) → new_ltEs14(vyy2130010, vyy1510)
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs18(vyy3000, vyy400)
new_compare31(vyy2130000, vyy1500, ty_Integer) → new_compare6(vyy2130000, vyy1500)
new_ltEs19(vyy2130012, vyy1512, app(app(ty_Either, bcg), bch)) → new_ltEs4(vyy2130012, vyy1512, bcg, bch)
new_pePe(False, vyy197) → vyy197
new_esEs29(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, app(app(ty_@2, cfh), cga)) → new_esEs7(vyy3000, vyy400, cfh, cga)
new_esEs27(vyy3001, vyy401, ty_Int) → new_esEs18(vyy3001, vyy401)
new_lt20(vyy2130010, vyy1510, ty_Ordering) → new_lt12(vyy2130010, vyy1510)
new_lt20(vyy2130010, vyy1510, ty_Bool) → new_lt11(vyy2130010, vyy1510)
new_esEs20(vyy2130010, vyy1510, ty_Double) → new_esEs16(vyy2130010, vyy1510)
new_lt21(vyy213000, vyy150, app(ty_[], ee)) → new_lt8(vyy213000, vyy150, ee)
new_esEs29(vyy3000, vyy400, ty_Int) → new_esEs18(vyy3000, vyy400)
new_lt19(vyy2130011, vyy1511, app(ty_[], bdd)) → new_lt8(vyy2130011, vyy1511, bdd)
new_compare31(vyy2130000, vyy1500, app(ty_Maybe, cbe)) → new_compare18(vyy2130000, vyy1500, cbe)
new_compare10(vyy177, vyy178, vyy179, vyy180, False, vyy182, bbb, bbc) → new_compare11(vyy177, vyy178, vyy179, vyy180, vyy182, bbb, bbc)
new_esEs26(vyy3002, vyy402, ty_Char) → new_esEs12(vyy3002, vyy402)
new_esEs24(vyy3001, vyy401, ty_Float) → new_esEs14(vyy3001, vyy401)
new_esEs6(Right(vyy3000), Right(vyy400), caa, ty_Double) → new_esEs16(vyy3000, vyy400)
new_ltEs20(vyy213001, vyy151, app(app(ty_Either, db), bf)) → new_ltEs4(vyy213001, vyy151, db, bf)
new_lt20(vyy2130010, vyy1510, app(app(ty_@2, bff), bfg)) → new_lt17(vyy2130010, vyy1510, bff, bfg)
new_esEs19(vyy2130011, vyy1511, ty_Float) → new_esEs14(vyy2130011, vyy1511)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, bgf) → new_esEs16(vyy3000, vyy400)
new_esEs20(vyy2130010, vyy1510, ty_Char) → new_esEs12(vyy2130010, vyy1510)
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, app(app(ty_Either, dh), ea)) → new_ltEs4(vyy2130010, vyy1510, dh, ea)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, bgf) → new_esEs10(vyy3000, vyy400)
new_esEs21(vyy213000, vyy150, ty_Int) → new_esEs18(vyy213000, vyy150)
new_lt21(vyy213000, vyy150, ty_Char) → new_lt10(vyy213000, vyy150)
new_esEs18(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_keysFM_GE0(vyy210, vyy211, vyy124, h, ba, bb) → :(vyy210, vyy124)
new_esEs20(vyy2130010, vyy1510, ty_Integer) → new_esEs17(vyy2130010, vyy1510)
new_esEs24(vyy3001, vyy401, app(ty_[], ceh)) → new_esEs11(vyy3001, vyy401, ceh)
new_compare210(vyy213000, vyy150, False) → new_compare16(vyy213000, vyy150, new_ltEs11(vyy213000, vyy150))
new_ltEs4(Left(vyy2130010), Right(vyy1510), db, bf) → True
new_esEs29(vyy3000, vyy400, app(ty_[], ddf)) → new_esEs11(vyy3000, vyy400, ddf)
new_ltEs9(vyy213001, vyy151) → new_fsEs(new_compare30(vyy213001, vyy151))
new_primCmpNat0(Zero, Succ(vyy15000)) → LT
new_ltEs20(vyy213001, vyy151, ty_Double) → new_ltEs14(vyy213001, vyy151)
new_esEs27(vyy3001, vyy401, ty_@0) → new_esEs10(vyy3001, vyy401)
new_esEs6(Right(vyy3000), Left(vyy400), caa, bgf) → False
new_esEs6(Left(vyy3000), Right(vyy400), caa, bgf) → False
new_esEs8(LT, LT) → True
new_esEs19(vyy2130011, vyy1511, app(ty_Maybe, bde)) → new_esEs4(vyy2130011, vyy1511, bde)
new_lt21(vyy213000, vyy150, app(app(ty_@2, bah), bba)) → new_lt17(vyy213000, vyy150, bah, bba)
new_foldFM_GE0(vyy67, vyy15, vyy16, EmptyFM, h, ba, bb) → vyy67
new_esEs28(vyy3000, vyy400, ty_Double) → new_esEs16(vyy3000, vyy400)
new_esEs28(vyy3000, vyy400, app(ty_[], dcc)) → new_esEs11(vyy3000, vyy400, dcc)
new_esEs25(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs29(vyy3000, vyy400, app(app(ty_@2, ddd), dde)) → new_esEs7(vyy3000, vyy400, ddd, dde)
new_esEs29(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_compare15(vyy213000, vyy150, bbe, bbf) → new_compare29(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, bbe, bbf), bbe, bbf)
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs18(vyy3001, vyy401)
new_pePe(True, vyy197) → True
new_primEqNat0(Zero, Zero) → True
new_compare31(vyy2130000, vyy1500, app(app(ty_@2, ccd), cce)) → new_compare8(vyy2130000, vyy1500, ccd, cce)
new_ltEs13(vyy213001, vyy151, bgd) → new_fsEs(new_compare9(vyy213001, vyy151, bgd))
new_ltEs4(Left(vyy2130010), Left(vyy1510), app(ty_[], bg), bf) → new_ltEs6(vyy2130010, vyy1510, bg)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_@0, bf) → new_ltEs5(vyy2130010, vyy1510)
new_compare29(vyy213000, vyy150, True, bbe, bbf) → EQ
new_ltEs20(vyy213001, vyy151, ty_Bool) → new_ltEs10(vyy213001, vyy151)
new_compare111(vyy213000, vyy150, False, bbe, bbf) → GT
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Int, bf) → new_ltEs17(vyy2130010, vyy1510)
new_ltEs5(vyy213001, vyy151) → new_fsEs(new_compare19(vyy213001, vyy151))
new_esEs20(vyy2130010, vyy1510, app(ty_Ratio, bfe)) → new_esEs15(vyy2130010, vyy1510, bfe)
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, ty_Int) → new_ltEs17(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, ty_Char) → new_ltEs9(vyy2130011, vyy1511)
new_ltEs19(vyy2130012, vyy1512, ty_@0) → new_ltEs5(vyy2130012, vyy1512)
new_esEs20(vyy2130010, vyy1510, ty_Bool) → new_esEs13(vyy2130010, vyy1510)
new_esEs6(Right(vyy3000), Right(vyy400), caa, app(app(ty_Either, cbb), cbc)) → new_esEs6(vyy3000, vyy400, cbb, cbc)
new_esEs27(vyy3001, vyy401, ty_Char) → new_esEs12(vyy3001, vyy401)
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Float) → new_ltEs12(vyy2130010, vyy1510)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Char, bf) → new_ltEs9(vyy2130010, vyy1510)
new_lt7(vyy213000, vyy150) → new_esEs8(new_compare19(vyy213000, vyy150), LT)
new_lt6(vyy2130010, vyy1510, ty_Integer) → new_lt5(vyy2130010, vyy1510)
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, ty_@0) → new_ltEs5(vyy2130010, vyy1510)
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, ty_Integer) → new_ltEs16(vyy2130010, vyy1510)
new_lt6(vyy2130010, vyy1510, ty_Char) → new_lt10(vyy2130010, vyy1510)
new_compare29(vyy213000, vyy150, False, bbe, bbf) → new_compare111(vyy213000, vyy150, new_ltEs4(vyy213000, vyy150, bbe, bbf), bbe, bbf)
new_esEs28(vyy3000, vyy400, app(app(ty_Either, dcf), dcg)) → new_esEs6(vyy3000, vyy400, dcf, dcg)
new_compare26(vyy213000, vyy150, False, bc, bd, be) → new_compare13(vyy213000, vyy150, new_ltEs8(vyy213000, vyy150, bc, bd, be), bc, bd, be)
new_esEs24(vyy3001, vyy401, ty_Double) → new_esEs16(vyy3001, vyy401)
new_lt6(vyy2130010, vyy1510, ty_Ordering) → new_lt12(vyy2130010, vyy1510)
new_ltEs8(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), bbg, bbh, bca) → new_pePe(new_lt20(vyy2130010, vyy1510, bbg), new_asAs(new_esEs20(vyy2130010, vyy1510, bbg), new_pePe(new_lt19(vyy2130011, vyy1511, bbh), new_asAs(new_esEs19(vyy2130011, vyy1511, bbh), new_ltEs19(vyy2130012, vyy1512, bca)))))
new_esEs24(vyy3001, vyy401, ty_Char) → new_esEs12(vyy3001, vyy401)
new_esEs24(vyy3001, vyy401, app(app(ty_@2, cef), ceg)) → new_esEs7(vyy3001, vyy401, cef, ceg)
new_esEs26(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, bgf) → new_esEs12(vyy3000, vyy400)
new_esEs8(GT, GT) → True
new_esEs21(vyy213000, vyy150, ty_Double) → new_esEs16(vyy213000, vyy150)
new_esEs25(vyy3000, vyy400, ty_@0) → new_esEs10(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy1440), vyy40000) → Succ(Succ(new_primPlusNat1(vyy1440, vyy40000)))
new_ltEs20(vyy213001, vyy151, app(app(ty_@2, ef), eg)) → new_ltEs15(vyy213001, vyy151, ef, eg)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_lt6(vyy2130010, vyy1510, ty_@0) → new_lt7(vyy2130010, vyy1510)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_lt17(vyy213000, vyy150, bah, bba) → new_esEs8(new_compare8(vyy213000, vyy150, bah, bba), LT)
new_ltEs12(vyy213001, vyy151) → new_fsEs(new_compare14(vyy213001, vyy151))
new_esEs20(vyy2130010, vyy1510, ty_Ordering) → new_esEs8(vyy2130010, vyy1510)
new_ltEs20(vyy213001, vyy151, ty_Char) → new_ltEs9(vyy213001, vyy151)
new_esEs9(vyy2130010, vyy1510, app(ty_[], gc)) → new_esEs11(vyy2130010, vyy1510, gc)
new_esEs27(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_compare31(vyy2130000, vyy1500, app(app(ty_Either, cca), ccb)) → new_compare15(vyy2130000, vyy1500, cca, ccb)
new_primPlusNat1(Zero, Succ(vyy400000)) → Succ(vyy400000)
new_primPlusNat1(Succ(vyy14400), Zero) → Succ(vyy14400)
new_compare24(vyy213000, vyy150, False) → new_compare110(vyy213000, vyy150, new_ltEs10(vyy213000, vyy150))
new_esEs21(vyy213000, vyy150, ty_Char) → new_esEs12(vyy213000, vyy150)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Float, bf) → new_ltEs12(vyy2130010, vyy1510)
new_esEs28(vyy3000, vyy400, app(ty_Maybe, dcd)) → new_esEs4(vyy3000, vyy400, dcd)
new_compare16(vyy213000, vyy150, True) → LT
new_ltEs7(Just(vyy2130010), Just(vyy1510), app(app(app(ty_@3, hh), baa), bab)) → new_ltEs8(vyy2130010, vyy1510, hh, baa, bab)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs18(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs9(vyy2130010, vyy1510, ty_Double) → new_esEs16(vyy2130010, vyy1510)
new_esEs21(vyy213000, vyy150, app(app(ty_@2, bah), bba)) → new_esEs7(vyy213000, vyy150, bah, bba)
new_compare7(vyy213000, vyy150) → new_compare24(vyy213000, vyy150, new_esEs13(vyy213000, vyy150))
new_lt14(vyy213000, vyy150, bbe, bbf) → new_esEs8(new_compare15(vyy213000, vyy150, bbe, bbf), LT)
new_lt19(vyy2130011, vyy1511, ty_Double) → new_lt16(vyy2130011, vyy1511)
new_esEs25(vyy3000, vyy400, app(ty_Ratio, cgd)) → new_esEs15(vyy3000, vyy400, cgd)
new_ltEs4(Left(vyy2130010), Left(vyy1510), app(app(ty_Either, cd), ce), bf) → new_ltEs4(vyy2130010, vyy1510, cd, ce)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_esEs8(EQ, EQ) → True
new_esEs20(vyy2130010, vyy1510, ty_@0) → new_esEs10(vyy2130010, vyy1510)
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_compare([], [], ee) → EQ
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, app(ty_Maybe, dd)) → new_ltEs7(vyy2130010, vyy1510, dd)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_compare14(Float(vyy2130000, vyy2130001), Float(vyy1500, vyy1501)) → new_compare12(new_sr0(vyy2130000, vyy1500), new_sr0(vyy2130001, vyy1501))
new_esEs28(vyy3000, vyy400, app(app(ty_@2, dca), dcb)) → new_esEs7(vyy3000, vyy400, dca, dcb)
new_primCmpNat0(Succ(vyy21300000), Succ(vyy15000)) → new_primCmpNat0(vyy21300000, vyy15000)
new_lt6(vyy2130010, vyy1510, app(ty_[], gc)) → new_lt8(vyy2130010, vyy1510, gc)
new_esEs25(vyy3000, vyy400, app(ty_Maybe, cgc)) → new_esEs4(vyy3000, vyy400, cgc)
new_esEs26(vyy3002, vyy402, ty_Integer) → new_esEs17(vyy3002, vyy402)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs18(vyy3000, vyy400)
new_compare31(vyy2130000, vyy1500, ty_Double) → new_compare28(vyy2130000, vyy1500)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_ltEs4(Left(vyy2130010), Left(vyy1510), app(app(app(ty_@3, ca), cb), cc), bf) → new_ltEs8(vyy2130010, vyy1510, ca, cb, cc)
new_lt19(vyy2130011, vyy1511, app(app(app(ty_@3, bdf), bdg), bdh)) → new_lt4(vyy2130011, vyy1511, bdf, bdg, bdh)
new_esEs9(vyy2130010, vyy1510, app(app(ty_@2, hc), hd)) → new_esEs7(vyy2130010, vyy1510, hc, hd)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, cdg), cdh)) → new_esEs6(vyy3000, vyy400, cdg, cdh)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bgg), bgh), bha), bgf) → new_esEs5(vyy3000, vyy400, bgg, bgh, bha)
new_ltEs7(Nothing, Just(vyy1510), he) → True
new_esEs19(vyy2130011, vyy1511, app(app(ty_Either, bea), beb)) → new_esEs6(vyy2130011, vyy1511, bea, beb)
new_compare31(vyy2130000, vyy1500, app(app(app(ty_@3, cbf), cbg), cbh)) → new_compare5(vyy2130000, vyy1500, cbf, cbg, cbh)
new_esEs6(Right(vyy3000), Right(vyy400), caa, app(ty_Maybe, cah)) → new_esEs4(vyy3000, vyy400, cah)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs18(vyy3001, vyy401)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_esEs27(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs27(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_lt19(vyy2130011, vyy1511, ty_@0) → new_lt7(vyy2130011, vyy1511)
new_foldFM_GE11(vyy67, vyy15, vyy16, vyy210, vyy211, vyy212, Branch(vyy2130, vyy2131, vyy2132, vyy2133, vyy2134), vyy214, False, h, ba, bb) → new_foldFM_GE12(new_keysFM_GE0(vyy210, vyy211, new_foldFM_GE0(vyy67, vyy15, vyy16, vyy214, h, ba, bb), h, ba, bb), vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, h, ba, bb)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ccg), cch), cda)) → new_esEs5(vyy3000, vyy400, ccg, cch, cda)
new_esEs9(vyy2130010, vyy1510, ty_Int) → new_esEs18(vyy2130010, vyy1510)
new_ltEs19(vyy2130012, vyy1512, ty_Double) → new_ltEs14(vyy2130012, vyy1512)
new_compare8(vyy213000, vyy150, bah, bba) → new_compare25(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bah, bba), bah, bba)
new_lt6(vyy2130010, vyy1510, ty_Double) → new_lt16(vyy2130010, vyy1510)
new_primCompAux00(vyy201, LT) → LT
new_esEs26(vyy3002, vyy402, app(ty_[], chg)) → new_esEs11(vyy3002, vyy402, chg)
new_esEs27(vyy3001, vyy401, app(ty_Ratio, dbc)) → new_esEs15(vyy3001, vyy401, dbc)
new_compare28(Double(vyy2130000, vyy2130001), Double(vyy1500, vyy1501)) → new_compare12(new_sr0(vyy2130000, vyy1500), new_sr0(vyy2130001, vyy1501))
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, ty_Float) → new_ltEs12(vyy2130010, vyy1510)
new_esEs9(vyy2130010, vyy1510, app(app(ty_Either, gh), ha)) → new_esEs6(vyy2130010, vyy1510, gh, ha)
new_primCmpInt(Neg(Succ(vyy21300000)), Neg(vyy1500)) → new_primCmpNat0(vyy1500, Succ(vyy21300000))
new_esEs24(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs6(Right(vyy3000), Right(vyy400), caa, ty_@0) → new_esEs10(vyy3000, vyy400)
new_esEs27(vyy3001, vyy401, app(app(app(ty_@3, dad), dae), daf)) → new_esEs5(vyy3001, vyy401, dad, dae, daf)
new_ltEs19(vyy2130012, vyy1512, ty_Int) → new_ltEs17(vyy2130012, vyy1512)
new_esEs6(Right(vyy3000), Right(vyy400), caa, ty_Char) → new_esEs12(vyy3000, vyy400)
new_lt21(vyy213000, vyy150, app(ty_Maybe, bfh)) → new_lt9(vyy213000, vyy150, bfh)
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, app(app(app(ty_@3, de), df), dg)) → new_ltEs8(vyy2130010, vyy1510, de, df, dg)
new_esEs28(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_lt4(vyy213000, vyy150, bc, bd, be) → new_esEs8(new_compare5(vyy213000, vyy150, bc, bd, be), LT)
new_compare19(@0, @0) → EQ
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_@0) → new_ltEs5(vyy2130010, vyy1510)
new_foldFM_GE0(vyy67, vyy15, vyy16, Branch(vyy2140, vyy2141, vyy2142, vyy2143, vyy2144), h, ba, bb) → new_foldFM_GE12(vyy67, vyy15, vyy16, vyy2140, vyy2141, vyy2142, vyy2143, vyy2144, h, ba, bb)
new_esEs24(vyy3001, vyy401, ty_@0) → new_esEs10(vyy3001, vyy401)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs11(GT, EQ) → False
new_primCmpNat0(Succ(vyy21300000), Zero) → GT
new_ltEs19(vyy2130012, vyy1512, app(ty_Ratio, bda)) → new_ltEs13(vyy2130012, vyy1512, bda)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy15000))) → LT
new_compare31(vyy2130000, vyy1500, app(ty_Ratio, ccc)) → new_compare9(vyy2130000, vyy1500, ccc)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Integer, bf) → new_ltEs16(vyy2130010, vyy1510)
new_compare31(vyy2130000, vyy1500, ty_Int) → new_compare12(vyy2130000, vyy1500)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs14(vyy3000, vyy400)
new_primPlusNat1(Succ(vyy14400), Succ(vyy400000)) → Succ(Succ(new_primPlusNat1(vyy14400, vyy400000)))
new_compare6(Integer(vyy2130000), Integer(vyy1500)) → new_primCmpInt(vyy2130000, vyy1500)
new_ltEs18(vyy2130011, vyy1511, app(app(ty_@2, ga), gb)) → new_ltEs15(vyy2130011, vyy1511, ga, gb)
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_lt19(vyy2130011, vyy1511, app(ty_Ratio, bec)) → new_lt15(vyy2130011, vyy1511, bec)
new_ltEs18(vyy2130011, vyy1511, app(app(ty_Either, ff), fg)) → new_ltEs4(vyy2130011, vyy1511, ff, fg)
new_compare(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), ee) → new_primCompAux0(vyy2130000, vyy1500, new_compare(vyy2130001, vyy1501, ee), ee)
new_esEs9(vyy2130010, vyy1510, ty_@0) → new_esEs10(vyy2130010, vyy1510)
new_esEs11(:(vyy3000, vyy3001), [], dch) → False
new_esEs11([], :(vyy400, vyy401), dch) → False
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, bhe), bgf) → new_esEs4(vyy3000, vyy400, bhe)
new_esEs25(vyy3000, vyy400, ty_Char) → new_esEs12(vyy3000, vyy400)
new_compare12(vyy213000, vyy150) → new_primCmpInt(vyy213000, vyy150)
new_ltEs11(GT, LT) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_compare10(vyy177, vyy178, vyy179, vyy180, True, vyy182, bbb, bbc) → new_compare11(vyy177, vyy178, vyy179, vyy180, True, bbb, bbc)
new_primCmpInt(Pos(Zero), Pos(Succ(vyy15000))) → new_primCmpNat0(Zero, Succ(vyy15000))
new_primCompAux00(vyy201, EQ) → vyy201
new_ltEs7(Just(vyy2130010), Just(vyy1510), app(app(ty_@2, baf), bag)) → new_ltEs15(vyy2130010, vyy1510, baf, bag)
new_esEs7(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cea, ceb) → new_asAs(new_esEs25(vyy3000, vyy400, cea), new_esEs24(vyy3001, vyy401, ceb))
new_compare24(vyy213000, vyy150, True) → EQ
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, app(app(ty_@2, ec), ed)) → new_ltEs15(vyy2130010, vyy1510, ec, ed)
new_esEs27(vyy3001, vyy401, app(app(ty_@2, dag), dah)) → new_esEs7(vyy3001, vyy401, dag, dah)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs18(vyy3000, vyy400)
new_lt6(vyy2130010, vyy1510, app(app(ty_Either, gh), ha)) → new_lt14(vyy2130010, vyy1510, gh, ha)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_ltEs11(LT, EQ) → True
new_ltEs16(vyy213001, vyy151) → new_fsEs(new_compare6(vyy213001, vyy151))
new_esEs9(vyy2130010, vyy1510, ty_Integer) → new_esEs17(vyy2130010, vyy1510)
new_esEs27(vyy3001, vyy401, ty_Double) → new_esEs16(vyy3001, vyy401)
new_ltEs11(LT, LT) → True
new_lt6(vyy2130010, vyy1510, app(app(ty_@2, hc), hd)) → new_lt17(vyy2130010, vyy1510, hc, hd)
new_esEs9(vyy2130010, vyy1510, ty_Ordering) → new_esEs8(vyy2130010, vyy1510)
new_esEs9(vyy2130010, vyy1510, ty_Float) → new_esEs14(vyy2130010, vyy1510)
new_esEs12(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, bhb), bhc), bgf) → new_esEs7(vyy3000, vyy400, bhb, bhc)
new_ltEs4(Left(vyy2130010), Left(vyy1510), app(ty_Ratio, cf), bf) → new_ltEs13(vyy2130010, vyy1510, cf)
new_not(False) → True
new_ltEs4(Right(vyy2130010), Left(vyy1510), db, bf) → False
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, bhg), bhh), bgf) → new_esEs6(vyy3000, vyy400, bhg, bhh)
new_lt19(vyy2130011, vyy1511, ty_Char) → new_lt10(vyy2130011, vyy1511)
new_ltEs4(Left(vyy2130010), Left(vyy1510), ty_Ordering, bf) → new_ltEs11(vyy2130010, vyy1510)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, cdf)) → new_esEs15(vyy3000, vyy400, cdf)
new_esEs9(vyy2130010, vyy1510, ty_Bool) → new_esEs13(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, app(ty_Ratio, fh)) → new_ltEs13(vyy2130011, vyy1511, fh)
new_primCmpInt(Pos(Succ(vyy21300000)), Pos(vyy1500)) → new_primCmpNat0(Succ(vyy21300000), vyy1500)
new_primPlusNat0(Zero, vyy40000) → Succ(vyy40000)
new_esEs19(vyy2130011, vyy1511, app(app(ty_@2, bed), bee)) → new_esEs7(vyy2130011, vyy1511, bed, bee)
new_compare5(vyy213000, vyy150, bc, bd, be) → new_compare26(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, bc, bd, be), bc, bd, be)
new_lt6(vyy2130010, vyy1510, app(app(app(ty_@3, ge), gf), gg)) → new_lt4(vyy2130010, vyy1510, ge, gf, gg)
new_ltEs17(vyy213001, vyy151) → new_fsEs(new_compare12(vyy213001, vyy151))
new_esEs24(vyy3001, vyy401, app(app(ty_Either, cfc), cfd)) → new_esEs6(vyy3001, vyy401, cfc, cfd)
new_lt16(vyy213000, vyy150) → new_esEs8(new_compare28(vyy213000, vyy150), LT)
new_foldFM_GE11(vyy67, vyy15, vyy16, vyy210, vyy211, vyy212, EmptyFM, vyy214, False, h, ba, bb) → new_keysFM_GE0(vyy210, vyy211, new_foldFM_GE0(vyy67, vyy15, vyy16, vyy214, h, ba, bb), h, ba, bb)
new_esEs20(vyy2130010, vyy1510, ty_Float) → new_esEs14(vyy2130010, vyy1510)
new_esEs9(vyy2130010, vyy1510, app(ty_Ratio, hb)) → new_esEs15(vyy2130010, vyy1510, hb)
new_lt21(vyy213000, vyy150, ty_Ordering) → new_lt12(vyy213000, vyy150)
new_lt19(vyy2130011, vyy1511, ty_Bool) → new_lt11(vyy2130011, vyy1511)
new_esEs20(vyy2130010, vyy1510, app(ty_[], bef)) → new_esEs11(vyy2130010, vyy1510, bef)
new_ltEs14(vyy213001, vyy151) → new_fsEs(new_compare28(vyy213001, vyy151))
new_esEs26(vyy3002, vyy402, ty_Int) → new_esEs18(vyy3002, vyy402)
new_lt6(vyy2130010, vyy1510, ty_Bool) → new_lt11(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, app(ty_Maybe, fa)) → new_ltEs7(vyy2130011, vyy1511, fa)
new_esEs19(vyy2130011, vyy1511, ty_Int) → new_esEs18(vyy2130011, vyy1511)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, bgf) → new_esEs13(vyy3000, vyy400)
new_esEs21(vyy213000, vyy150, app(ty_Ratio, bgc)) → new_esEs15(vyy213000, vyy150, bgc)
new_ltEs11(GT, GT) → True
new_esEs27(vyy3001, vyy401, app(app(ty_Either, dbd), dbe)) → new_esEs6(vyy3001, vyy401, dbd, dbe)
new_esEs29(vyy3000, vyy400, app(ty_Ratio, ddh)) → new_esEs15(vyy3000, vyy400, ddh)
new_esEs6(Right(vyy3000), Right(vyy400), caa, app(ty_[], cag)) → new_esEs11(vyy3000, vyy400, cag)
new_esEs20(vyy2130010, vyy1510, ty_Int) → new_esEs18(vyy2130010, vyy1510)
new_ltEs20(vyy213001, vyy151, app(app(app(ty_@3, bbg), bbh), bca)) → new_ltEs8(vyy213001, vyy151, bbg, bbh, bca)
new_esEs20(vyy2130010, vyy1510, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs5(vyy2130010, vyy1510, beh, bfa, bfb)
new_ltEs7(Just(vyy2130010), Just(vyy1510), app(ty_Maybe, hg)) → new_ltEs7(vyy2130010, vyy1510, hg)
new_primCmpInt(Pos(Succ(vyy21300000)), Neg(vyy1500)) → GT
new_esEs21(vyy213000, vyy150, app(app(app(ty_@3, bc), bd), be)) → new_esEs5(vyy213000, vyy150, bc, bd, be)
new_esEs9(vyy2130010, vyy1510, ty_Char) → new_esEs12(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, ty_Ordering) → new_ltEs11(vyy2130011, vyy1511)
new_primMulInt(Pos(vyy30000), Pos(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_esEs26(vyy3002, vyy402, ty_@0) → new_esEs10(vyy3002, vyy402)
new_esEs6(Right(vyy3000), Right(vyy400), caa, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs19(vyy2130011, vyy1511, ty_Bool) → new_esEs13(vyy2130011, vyy1511)
new_primMulInt(Neg(vyy30000), Neg(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_compare110(vyy213000, vyy150, True) → LT
new_compare9(:%(vyy2130000, vyy2130001), :%(vyy1500, vyy1501), ty_Integer) → new_compare6(new_sr(vyy2130000, vyy1501), new_sr(vyy1500, vyy2130001))
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_esEs21(vyy213000, vyy150, ty_@0) → new_esEs10(vyy213000, vyy150)
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Integer) → new_ltEs16(vyy2130010, vyy1510)
new_lt20(vyy2130010, vyy1510, app(ty_Ratio, bfe)) → new_lt15(vyy2130010, vyy1510, bfe)
new_esEs26(vyy3002, vyy402, app(app(ty_@2, che), chf)) → new_esEs7(vyy3002, vyy402, che, chf)
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Char) → new_ltEs9(vyy2130010, vyy1510)
new_esEs9(vyy2130010, vyy1510, app(app(app(ty_@3, ge), gf), gg)) → new_esEs5(vyy2130010, vyy1510, ge, gf, gg)
new_compare25(vyy21300, vyy15, True, bga, bgb) → EQ
new_compare110(vyy213000, vyy150, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, ccf) → True
new_esEs25(vyy3000, vyy400, app(ty_[], cgb)) → new_esEs11(vyy3000, vyy400, cgb)
new_esEs6(Right(vyy3000), Right(vyy400), caa, ty_Float) → new_esEs14(vyy3000, vyy400)
new_lt18(vyy213000, vyy150) → new_esEs8(new_compare12(vyy213000, vyy150), LT)
new_compare210(vyy213000, vyy150, True) → EQ
new_esEs20(vyy2130010, vyy1510, app(app(ty_Either, bfc), bfd)) → new_esEs6(vyy2130010, vyy1510, bfc, bfd)
new_ltEs19(vyy2130012, vyy1512, app(app(app(ty_@3, bcd), bce), bcf)) → new_ltEs8(vyy2130012, vyy1512, bcd, bce, bcf)
new_ltEs19(vyy2130012, vyy1512, ty_Ordering) → new_ltEs11(vyy2130012, vyy1512)
new_esEs29(vyy3000, vyy400, app(app(ty_Either, dea), deb)) → new_esEs6(vyy3000, vyy400, dea, deb)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs13(vyy3000, vyy400)
new_ltEs7(Nothing, Nothing, he) → True
new_ltEs19(vyy2130012, vyy1512, ty_Bool) → new_ltEs10(vyy2130012, vyy1512)
new_esEs27(vyy3001, vyy401, app(ty_Maybe, dbb)) → new_esEs4(vyy3001, vyy401, dbb)
new_ltEs20(vyy213001, vyy151, ty_Int) → new_ltEs17(vyy213001, vyy151)
new_ltEs19(vyy2130012, vyy1512, ty_Char) → new_ltEs9(vyy2130012, vyy1512)
new_esEs29(vyy3000, vyy400, app(app(app(ty_@3, dda), ddb), ddc)) → new_esEs5(vyy3000, vyy400, dda, ddb, ddc)
new_ltEs20(vyy213001, vyy151, ty_@0) → new_ltEs5(vyy213001, vyy151)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy15000))) → new_primCmpNat0(Succ(vyy15000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy15000))) → GT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, bgf) → new_esEs8(vyy3000, vyy400)
new_lt21(vyy213000, vyy150, ty_Integer) → new_lt5(vyy213000, vyy150)
new_lt20(vyy2130010, vyy1510, app(ty_Maybe, beg)) → new_lt9(vyy2130010, vyy1510, beg)
new_compare31(vyy2130000, vyy1500, app(ty_[], cbd)) → new_compare(vyy2130000, vyy1500, cbd)
new_sr0(vyy3000, vyy400) → new_primMulInt(vyy3000, vyy400)
new_compare11(vyy177, vyy178, vyy179, vyy180, False, bbb, bbc) → GT
new_ltEs18(vyy2130011, vyy1511, ty_Float) → new_ltEs12(vyy2130011, vyy1511)
new_foldFM_GE12(vyy125, vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, h, ba, bb) → new_foldFM_GE11(vyy125, vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, new_esEs8(new_compare25(vyy2130, @2(vyy15, vyy16), new_esEs7(vyy2130, @2(vyy15, vyy16), h, ba), h, ba), LT), h, ba, bb)
new_ltEs20(vyy213001, vyy151, ty_Ordering) → new_ltEs11(vyy213001, vyy151)
new_compare25(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, bga, bgb) → new_compare10(vyy213000, vyy213001, vyy150, vyy151, new_lt21(vyy213000, vyy150, bga), new_asAs(new_esEs21(vyy213000, vyy150, bga), new_ltEs20(vyy213001, vyy151, bgb)), bga, bgb)
new_ltEs7(Just(vyy2130010), Just(vyy1510), app(ty_Ratio, bae)) → new_ltEs13(vyy2130010, vyy1510, bae)
new_lt20(vyy2130010, vyy1510, ty_Double) → new_lt16(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, app(ty_[], eh)) → new_ltEs6(vyy2130011, vyy1511, eh)
new_esEs21(vyy213000, vyy150, app(ty_Maybe, bfh)) → new_esEs4(vyy213000, vyy150, bfh)
new_ltEs11(EQ, EQ) → True
new_lt20(vyy2130010, vyy1510, ty_Char) → new_lt10(vyy2130010, vyy1510)
new_esEs21(vyy213000, vyy150, ty_Integer) → new_esEs17(vyy213000, vyy150)
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, app(ty_[], dc)) → new_ltEs6(vyy2130010, vyy1510, dc)
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, app(ty_Ratio, eb)) → new_ltEs13(vyy2130010, vyy1510, eb)
new_esEs15(:%(vyy3000, vyy3001), :%(vyy400, vyy401), bge) → new_asAs(new_esEs23(vyy3000, vyy400, bge), new_esEs22(vyy3001, vyy401, bge))
new_esEs10(@0, @0) → True
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Int) → new_ltEs17(vyy2130010, vyy1510)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt6(vyy2130010, vyy1510, app(ty_Maybe, gd)) → new_lt9(vyy2130010, vyy1510, gd)
new_esEs28(vyy3000, vyy400, ty_@0) → new_esEs10(vyy3000, vyy400)
new_esEs19(vyy2130011, vyy1511, ty_Double) → new_esEs16(vyy2130011, vyy1511)
new_ltEs10(True, False) → False
new_asAs(False, vyy123) → False
new_primMulInt(Neg(vyy30000), Pos(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulInt(Pos(vyy30000), Neg(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40000)) → Zero
new_esEs29(vyy3000, vyy400, ty_Char) → new_esEs12(vyy3000, vyy400)
new_esEs21(vyy213000, vyy150, ty_Ordering) → new_esEs8(vyy213000, vyy150)
new_ltEs11(EQ, LT) → False
new_esEs21(vyy213000, vyy150, ty_Bool) → new_esEs13(vyy213000, vyy150)
new_esEs9(vyy2130010, vyy1510, app(ty_Maybe, gd)) → new_esEs4(vyy2130010, vyy1510, gd)
new_esEs19(vyy2130011, vyy1511, app(ty_[], bdd)) → new_esEs11(vyy2130011, vyy1511, bdd)
new_lt8(vyy213000, vyy150, ee) → new_esEs8(new_compare(vyy213000, vyy150, ee), LT)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_esEs13(False, False) → True
new_esEs29(vyy3000, vyy400, ty_Float) → new_esEs14(vyy3000, vyy400)
new_ltEs18(vyy2130011, vyy1511, ty_Int) → new_ltEs17(vyy2130011, vyy1511)
new_lt20(vyy2130010, vyy1510, ty_Float) → new_lt13(vyy2130010, vyy1510)
new_lt21(vyy213000, vyy150, ty_Double) → new_lt16(vyy213000, vyy150)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs16(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, bgf) → new_esEs18(vyy3000, vyy400)
new_ltEs7(Just(vyy2130010), Just(vyy1510), ty_Bool) → new_ltEs10(vyy2130010, vyy1510)
new_compare17(vyy213000, vyy150) → new_compare210(vyy213000, vyy150, new_esEs8(vyy213000, vyy150))
new_lt5(vyy213000, vyy150) → new_esEs8(new_compare6(vyy213000, vyy150), LT)
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs10(vyy3000, vyy400)
new_ltEs7(Just(vyy2130010), Nothing, he) → False
new_lt20(vyy2130010, vyy1510, ty_Integer) → new_lt5(vyy2130010, vyy1510)
new_esEs27(vyy3001, vyy401, app(ty_[], dba)) → new_esEs11(vyy3001, vyy401, dba)
new_compare9(:%(vyy2130000, vyy2130001), :%(vyy1500, vyy1501), ty_Int) → new_compare12(new_sr0(vyy2130000, vyy1501), new_sr0(vyy1500, vyy2130001))
new_ltEs18(vyy2130011, vyy1511, ty_Double) → new_ltEs14(vyy2130011, vyy1511)
new_compare31(vyy2130000, vyy1500, ty_Ordering) → new_compare17(vyy2130000, vyy1500)
new_ltEs19(vyy2130012, vyy1512, app(app(ty_@2, bdb), bdc)) → new_ltEs15(vyy2130012, vyy1512, bdb, bdc)
new_lt11(vyy213000, vyy150) → new_esEs8(new_compare7(vyy213000, vyy150), LT)
new_ltEs19(vyy2130012, vyy1512, app(ty_Maybe, bcc)) → new_ltEs7(vyy2130012, vyy1512, bcc)
new_esEs25(vyy3000, vyy400, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs5(vyy3000, vyy400, cfe, cff, cfg)
new_ltEs19(vyy2130012, vyy1512, app(ty_[], bcb)) → new_ltEs6(vyy2130012, vyy1512, bcb)
new_lt12(vyy213000, vyy150) → new_esEs8(new_compare17(vyy213000, vyy150), LT)
new_ltEs4(Right(vyy2130010), Right(vyy1510), db, ty_Char) → new_ltEs9(vyy2130010, vyy1510)
new_esEs28(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_ltEs4(Left(vyy2130010), Left(vyy1510), app(ty_Maybe, bh), bf) → new_ltEs7(vyy2130010, vyy1510, bh)
new_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_esEs21(vyy213000, vyy150, app(ty_[], ee)) → new_esEs11(vyy213000, vyy150, ee)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, cdb), cdc)) → new_esEs7(vyy3000, vyy400, cdb, cdc)
new_compare112(vyy213000, vyy150, False, bfh) → GT
new_esEs19(vyy2130011, vyy1511, ty_Integer) → new_esEs17(vyy2130011, vyy1511)
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cgg, cgh, cha) → new_asAs(new_esEs28(vyy3000, vyy400, cgg), new_asAs(new_esEs27(vyy3001, vyy401, cgh), new_esEs26(vyy3002, vyy402, cha)))
new_compare27(vyy213000, vyy150, True, bfh) → EQ
new_lt6(vyy2130010, vyy1510, ty_Float) → new_lt13(vyy2130010, vyy1510)
new_lt19(vyy2130011, vyy1511, ty_Ordering) → new_lt12(vyy2130011, vyy1511)
new_lt9(vyy213000, vyy150, bfh) → new_esEs8(new_compare18(vyy213000, vyy150, bfh), LT)
new_compare11(vyy177, vyy178, vyy179, vyy180, True, bbb, bbc) → LT
new_esEs20(vyy2130010, vyy1510, app(app(ty_@2, bff), bfg)) → new_esEs7(vyy2130010, vyy1510, bff, bfg)
new_compare26(vyy213000, vyy150, True, bc, bd, be) → EQ
new_lt13(vyy213000, vyy150) → new_esEs8(new_compare14(vyy213000, vyy150), LT)
new_esEs29(vyy3000, vyy400, ty_@0) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy3002, vyy402, app(app(ty_Either, dab), dac)) → new_esEs6(vyy3002, vyy402, dab, dac)
new_compare111(vyy213000, vyy150, True, bbe, bbf) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs10(True, True) → True
new_lt21(vyy213000, vyy150, app(app(ty_Either, bbe), bbf)) → new_lt14(vyy213000, vyy150, bbe, bbf)
new_asAs(True, vyy123) → vyy123
new_esEs26(vyy3002, vyy402, ty_Float) → new_esEs14(vyy3002, vyy402)
new_primMulNat0(Succ(vyy300000), Succ(vyy40000)) → new_primPlusNat0(new_primMulNat0(vyy300000, Succ(vyy40000)), vyy40000)
new_esEs26(vyy3002, vyy402, app(app(app(ty_@3, chb), chc), chd)) → new_esEs5(vyy3002, vyy402, chb, chc, chd)
new_compare30(Char(vyy2130000), Char(vyy1500)) → new_primCmpNat0(vyy2130000, vyy1500)
new_esEs13(True, True) → True
new_ltEs19(vyy2130012, vyy1512, ty_Float) → new_ltEs12(vyy2130012, vyy1512)
new_esEs14(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs18(new_sr0(vyy3000, vyy400), new_sr0(vyy3001, vyy401))
new_esEs6(Right(vyy3000), Right(vyy400), caa, ty_Int) → new_esEs18(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], cdd)) → new_esEs11(vyy3000, vyy400, cdd)
new_fsEs(vyy183) → new_not(new_esEs8(vyy183, GT))
new_primCompAux0(vyy2130000, vyy1500, vyy192, ee) → new_primCompAux00(vyy192, new_compare31(vyy2130000, vyy1500, ee))
new_esEs19(vyy2130011, vyy1511, ty_@0) → new_esEs10(vyy2130011, vyy1511)
new_esEs19(vyy2130011, vyy1511, ty_Ordering) → new_esEs8(vyy2130011, vyy1511)
new_esEs26(vyy3002, vyy402, ty_Double) → new_esEs16(vyy3002, vyy402)
new_esEs27(vyy3001, vyy401, ty_Float) → new_esEs14(vyy3001, vyy401)
new_lt21(vyy213000, vyy150, app(ty_Ratio, bgc)) → new_lt15(vyy213000, vyy150, bgc)
new_esEs29(vyy3000, vyy400, app(ty_Maybe, ddg)) → new_esEs4(vyy3000, vyy400, ddg)
new_ltEs20(vyy213001, vyy151, app(ty_Maybe, he)) → new_ltEs7(vyy213001, vyy151, he)
new_lt19(vyy2130011, vyy1511, app(app(ty_@2, bed), bee)) → new_lt17(vyy2130011, vyy1511, bed, bee)
new_compare13(vyy213000, vyy150, True, bc, bd, be) → LT
new_ltEs15(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), ef, eg) → new_pePe(new_lt6(vyy2130010, vyy1510, ef), new_asAs(new_esEs9(vyy2130010, vyy1510, ef), new_ltEs18(vyy2130011, vyy1511, eg)))
new_compare31(vyy2130000, vyy1500, ty_Float) → new_compare14(vyy2130000, vyy1500)
new_compare31(vyy2130000, vyy1500, ty_@0) → new_compare19(vyy2130000, vyy1500)
new_lt21(vyy213000, vyy150, ty_Int) → new_lt18(vyy213000, vyy150)
new_primCompAux00(vyy201, GT) → GT
new_lt15(vyy213000, vyy150, bgc) → new_esEs8(new_compare9(vyy213000, vyy150, bgc), LT)
new_compare27(vyy213000, vyy150, False, bfh) → new_compare112(vyy213000, vyy150, new_ltEs7(vyy213000, vyy150, bfh), bfh)
new_esEs25(vyy3000, vyy400, ty_Float) → new_esEs14(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), caa, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs26(vyy3002, vyy402, ty_Bool) → new_esEs13(vyy3002, vyy402)
new_esEs6(Right(vyy3000), Right(vyy400), caa, app(app(app(ty_@3, cab), cac), cad)) → new_esEs5(vyy3000, vyy400, cab, cac, cad)
new_esEs29(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs11(EQ, GT) → True
new_ltEs20(vyy213001, vyy151, app(ty_Ratio, bgd)) → new_ltEs13(vyy213001, vyy151, bgd)
new_lt21(vyy213000, vyy150, app(app(app(ty_@3, bc), bd), be)) → new_lt4(vyy213000, vyy150, bc, bd, be)
new_esEs28(vyy3000, vyy400, ty_Char) → new_esEs12(vyy3000, vyy400)
new_ltEs7(Just(vyy2130010), Just(vyy1510), app(app(ty_Either, bac), bad)) → new_ltEs4(vyy2130010, vyy1510, bac, bad)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(vyy21300000)), Pos(vyy1500)) → LT
new_esEs19(vyy2130011, vyy1511, ty_Char) → new_esEs12(vyy2130011, vyy1511)
new_compare16(vyy213000, vyy150, False) → GT
new_not(True) → False

The set Q consists of the following terms:

new_lt21(x0, x1, ty_Char)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True)
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Nothing, Just(x0), x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_compare31(x0, x1, ty_Int)
new_compare5(x0, x1, x2, x3, x4)
new_ltEs11(EQ, GT)
new_ltEs11(GT, EQ)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_lt6(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_asAs(True, x0)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Integer)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs26(x0, x1, ty_Integer)
new_ltEs11(EQ, EQ)
new_compare30(Char(x0), Char(x1))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs9(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt16(x0, x1)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs11(:(x0, x1), [], x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs25(x0, x1, ty_Ordering)
new_lt15(x0, x1, x2)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primCompAux00(x0, GT)
new_esEs28(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, ty_Float)
new_lt6(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_compare210(x0, x1, False)
new_ltEs7(Nothing, Nothing, x0)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_primCompAux00(x0, LT)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_compare210(x0, x1, True)
new_lt21(x0, x1, ty_Integer)
new_compare31(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Integer)
new_compare112(x0, x1, True, x2)
new_esEs19(x0, x1, ty_Int)
new_ltEs7(Nothing, Just(x0), x1)
new_esEs8(GT, GT)
new_ltEs6(x0, x1, x2)
new_lt21(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_esEs9(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Integer)
new_lt21(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs9(x0, x1, ty_Integer)
new_ltEs8(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(LT, LT)
new_compare24(x0, x1, True)
new_ltEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_ltEs7(Just(x0), Just(x1), ty_Bool)
new_lt21(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2, x3)
new_lt6(x0, x1, ty_Float)
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare13(x0, x1, False, x2, x3, x4)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs11(LT, GT)
new_compare([], [], x0)
new_ltEs11(GT, LT)
new_ltEs20(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Ordering)
new_ltEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_sr(Integer(x0), Integer(x1))
new_primEqNat0(Succ(x0), Succ(x1))
new_asAs(False, x0)
new_foldFM_GE11(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9, x10)
new_esEs23(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, x2, x3, True, x4, x5)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare17(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_primEqNat0(Zero, Zero)
new_esEs18(x0, x1)
new_lt18(x0, x1)
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_compare31(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, ty_Bool)
new_esEs11([], :(x0, x1), x2)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt6(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs13(False, False)
new_primMulNat0(Zero, Zero)
new_compare16(x0, x1, False)
new_esEs19(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Char)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_compare6(Integer(x0), Integer(x1))
new_ltEs14(x0, x1)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs19(x0, x1, app(ty_[], x2))
new_lt4(x0, x1, x2, x3, x4)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Zero, x0)
new_compare7(x0, x1)
new_esEs19(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare31(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare(:(x0, x1), [], x2)
new_lt11(x0, x1)
new_primCmpNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare112(x0, x1, False, x2)
new_esEs29(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs4(Nothing, Nothing, x0)
new_lt17(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_compare14(Float(x0, x1), Float(x2, x3))
new_ltEs7(Just(x0), Nothing, x1)
new_primPlusNat1(Zero, Zero)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_compare18(x0, x1, x2)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs18(x0, x1, ty_Int)
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_esEs21(x0, x1, ty_Integer)
new_lt6(x0, x1, ty_Bool)
new_compare111(x0, x1, False, x2, x3)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs15(:%(x0, x1), :%(x2, x3), x4)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs10(False, False)
new_lt20(x0, x1, ty_Char)
new_lt7(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_compare10(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs17(x0, x1)
new_esEs21(x0, x1, ty_Float)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_@0)
new_ltEs7(Just(x0), Just(x1), app(ty_[], x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Integer)
new_esEs11([], [], x0)
new_ltEs18(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare26(x0, x1, True, x2, x3, x4)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, True, x2)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt6(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs20(x0, x1, ty_@0)
new_compare8(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs10(@0, @0)
new_compare10(x0, x1, x2, x3, False, x4, x5, x6)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs18(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_compare27(x0, x1, False, x2)
new_lt9(x0, x1, x2)
new_lt19(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Nothing, x1)
new_primPlusNat0(Succ(x0), x1)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_@0)
new_compare29(x0, x1, True, x2, x3)
new_esEs25(x0, x1, ty_Char)
new_compare12(x0, x1)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, True, x2, x3, x4)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, EQ)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs18(x0, x1, ty_Ordering)
new_primCompAux00(x0, EQ)
new_lt21(x0, x1, ty_Double)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs21(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_esEs28(x0, x1, ty_Integer)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Float)
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_compare31(x0, x1, ty_Float)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs7(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_foldFM_GE11(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, False, x12, x13, x14)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs28(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(x0, x1)
new_esEs24(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_compare28(Double(x0, x1), Double(x2, x3))
new_compare16(x0, x1, True)
new_ltEs11(LT, LT)
new_ltEs5(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Just(x0), Just(x1), ty_Integer)
new_compare110(x0, x1, False)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_ltEs19(x0, x1, ty_Char)
new_ltEs11(EQ, LT)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs11(LT, EQ)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_lt21(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_compare25(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_ltEs13(x0, x1, x2)
new_primCmpNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs17(Integer(x0), Integer(x1))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Just(x0), Just(x1), ty_Float)
new_esEs25(x0, x1, ty_@0)
new_compare29(x0, x1, False, x2, x3)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs10(True, True)
new_ltEs20(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs7(Just(x0), Just(x1), ty_Char)
new_ltEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_pePe(False, x0)
new_esEs27(x0, x1, ty_Double)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_GE0(x0, x1, x2, EmptyFM, x3, x4, x5)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_@0)
new_compare15(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Bool)
new_ltEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Int)
new_esEs13(True, False)
new_esEs13(False, True)
new_compare26(x0, x1, False, x2, x3, x4)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), Zero)
new_foldFM_GE11(x0, x1, x2, x3, x4, x5, EmptyFM, x6, False, x7, x8, x9)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_not(True)
new_esEs24(x0, x1, ty_Float)
new_esEs13(True, True)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs29(x0, x1, ty_@0)
new_keysFM_GE0(x0, x1, x2, x3, x4, x5)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs19(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Integer)
new_lt5(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs29(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Char)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Char)
new_lt8(x0, x1, x2)
new_compare31(x0, x1, ty_Bool)
new_ltEs12(x0, x1)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_compare19(@0, @0)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primMulNat0(Succ(x0), Zero)
new_compare11(x0, x1, x2, x3, False, x4, x5)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_foldFM_GE0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10)
new_ltEs10(True, False)
new_ltEs10(False, True)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_foldFM_GE12(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_lt20(x0, x1, ty_@0)
new_sr0(x0, x1)
new_pePe(True, x0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare([], :(x0, x1), x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt10(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Succ(x0), Zero)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Just(x0), Just(x1), ty_Double)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_Ordering)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, ty_Double)
new_esEs9(x0, x1, ty_Ordering)
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(x0, x1, ty_Float)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs21(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_esEs12(Char(x0), Char(x1))
new_fsEs(x0)
new_esEs25(x0, x1, ty_Float)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs11(GT, GT)

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: