YES H-Termination proof of ../tpdb/FP/full_haskell/FiniteMap_fmToList_GE_10.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ LR

mainModule Main
  ((FiniteMap.fmToList_GE :: (Ord a, Ord b) => FiniteMap.FiniteMap (Either b a) c  ->  Either b a  ->  [(Either b a,c)]) :: (Ord a, Ord b) => FiniteMap.FiniteMap (Either b a) c  ->  Either b a  ->  [(Either b a,c)])

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

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

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

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

  foldFM_GE :: Ord 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

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


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

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


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

is transformed to
fmToList_GE0 key elt rest = (key,elt) : rest

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

mainModule Main
  ((FiniteMap.fmToList_GE :: (Ord a, Ord c) => FiniteMap.FiniteMap (Either a c) b  ->  Either a c  ->  [(Either a c,b)]) :: (Ord a, Ord c) => FiniteMap.FiniteMap (Either a c) b  ->  Either a c  ->  [(Either a c,b)])

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

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

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

  fmToList_GE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 key elt rest = (key,elt) : rest

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

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

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


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

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


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

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



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

mainModule Main
  ((FiniteMap.fmToList_GE :: (Ord a, Ord c) => FiniteMap.FiniteMap (Either a c) b  ->  Either a c  ->  [(Either a c,b)]) :: (Ord a, Ord c) => FiniteMap.FiniteMap (Either a c) b  ->  Either a c  ->  [(Either a c,b)])

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

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

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

  fmToList_GE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 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

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


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

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


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

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

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

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



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

mainModule Main
  ((FiniteMap.fmToList_GE :: (Ord c, Ord b) => FiniteMap.FiniteMap (Either c b) a  ->  Either c b  ->  [(Either c b,a)]) :: (Ord c, Ord b) => FiniteMap.FiniteMap (Either c b) a  ->  Either c b  ->  [(Either c b,a)])

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

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

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

  fmToList_GE :: Ord b => FiniteMap b a  ->  b  ->  [(b,a)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 key elt rest = (key,elt) : rest

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

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

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


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

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


Replaced joker patterns by fresh variables and removed binding patterns.

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

mainModule Main
  ((FiniteMap.fmToList_GE :: (Ord a, Ord c) => FiniteMap.FiniteMap (Either c a) b  ->  Either c a  ->  [(Either c a,b)]) :: (Ord a, Ord c) => FiniteMap.FiniteMap (Either c a) b  ->  Either c a  ->  [(Either c a,b)])

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

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

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

  fmToList_GE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 key elt rest = (key,elt) : rest

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

  foldFM_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 wv fm_l fm_r) 
 | key >= fr = 
foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
 | otherwise = 
foldFM_GE k z fr fm_r

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


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

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


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

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

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

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

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

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

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

The following Function with conditions
reduce x y
 | y == 0
 = error []
 | otherwise
 = x `quot` d :% (y `quot` d)
where 
d  = gcd x y

is transformed to
reduce x y = reduce2 x y

reduce2 x y = 
reduce1 x y (y == 0)
where 
d  = gcd x y
reduce0 x y True = x `quot` d :% (y `quot` d)
reduce1 x y True = error []
reduce1 x y False = reduce0 x y otherwise

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

is transformed to
compare x y = compare3 x y

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

compare0 x y True = GT

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

compare3 x y = compare2 x y (x == y)



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

mainModule Main
  ((FiniteMap.fmToList_GE :: (Ord a, Ord c) => FiniteMap.FiniteMap (Either c a) b  ->  Either c a  ->  [(Either c a,b)]) :: (Ord c, Ord a) => FiniteMap.FiniteMap (Either c a) b  ->  Either c a  ->  [(Either c a,b)])

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

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

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

  fmToList_GE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 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 b => (b  ->  a  ->  c  ->  c)  ->  c  ->  b  ->  FiniteMap b a  ->  c
foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM
foldFM_GE k z fr (Branch key elt wv fm_l fm_r) = foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r)

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

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

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

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

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


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

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


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

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

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

reduce2D vyw vyx = gcd vyw vyx

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

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

gcd0Gcd'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



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

mainModule Main
  ((FiniteMap.fmToList_GE :: (Ord b, Ord a) => FiniteMap.FiniteMap (Either a b) c  ->  Either a b  ->  [(Either a b,c)]) :: (Ord a, Ord b) => FiniteMap.FiniteMap (Either a b) c  ->  Either a b  ->  [(Either a b,c)])

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

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

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

  fmToList_GE :: Ord b => FiniteMap b a  ->  b  ->  [(b,a)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 key elt rest = (key,elt) : rest

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

  foldFM_GE :: Ord 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

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


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

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


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

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

mainModule Main
  (FiniteMap.fmToList_GE :: (Ord b, Ord c) => FiniteMap.FiniteMap (Either c b) a  ->  Either c b  ->  [(Either c b,a)])

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

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

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

  fmToList_GE :: Ord a => FiniteMap a b  ->  a  ->  [(a,b)]
fmToList_GE fm fr = foldFM_GE fmToList_GE0 [] fr fm

  
fmToList_GE0 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 b => (b  ->  a  ->  c  ->  c)  ->  c  ->  b  ->  FiniteMap b a  ->  c
foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM
foldFM_GE k z fr (Branch key elt wv fm_l fm_r) = foldFM_GE2 k z fr (Branch key elt wv fm_l fm_r)

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

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

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

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

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


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

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


Haskell To QDPs


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

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

new_primMulNat(Succ(vyy300100), Succ(vyy40100)) → new_primMulNat(vyy300100, Succ(vyy40100))

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

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



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

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

new_primPlusNat(Succ(vyy14800), Succ(vyy401000)) → new_primPlusNat(vyy14800, vyy401000)

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

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



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

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

new_ltEs2(Right(vyy9700), Right(vyy9800), ec, app(ty_Maybe, bae)) → new_ltEs(vyy9700, vyy9800, bae)
new_ltEs0(:(vyy970, vyy971), :(vyy980, vyy981), h) → new_compare(vyy971, vyy981, h)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), eg, app(app(app(ty_@3, fb), fc), fd), dg) → new_lt1(vyy971, vyy981, fb, fc, fd)
new_ltEs3(@2(vyy970, vyy971), @2(vyy980, vyy981), app(app(app(ty_@3, bbh), bca), bcb), bbf) → new_lt1(vyy970, vyy980, bbh, bca, bcb)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), eg, df, app(app(ty_@2, ha), hb)) → new_ltEs3(vyy972, vyy982, ha, hb)
new_compare2(vyy970, vyy980, dh, ea, eb) → new_compare21(vyy970, vyy980, new_esEs5(vyy970, vyy980, dh, ea, eb), dh, ea, eb)
new_ltEs3(@2(vyy970, vyy971), @2(vyy980, vyy981), app(app(ty_Either, bcc), bcd), bbf) → new_lt2(vyy970, vyy980, bcc, bcd)
new_ltEs3(@2(vyy970, vyy971), @2(vyy980, vyy981), app(ty_[], bbe), bbf) → new_lt(vyy970, vyy980, bbe)
new_ltEs3(@2(vyy970, vyy971), @2(vyy980, vyy981), bcg, app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs1(vyy971, vyy981, bdb, bdc, bdd)
new_ltEs2(Left(vyy9700), Left(vyy9800), app(app(ty_Either, hh), baa), ed) → new_ltEs2(vyy9700, vyy9800, hh, baa)
new_ltEs(Just(vyy970), Just(vyy980), app(ty_[], cc)) → new_ltEs0(vyy970, vyy980, cc)
new_compare21(vyy970, vyy980, False, dh, ea, eb) → new_ltEs1(vyy970, vyy980, dh, ea, eb)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), app(app(ty_Either, ec), ed), df, dg) → new_compare22(vyy970, vyy980, new_esEs6(vyy970, vyy980, ec, ed), ec, ed)
new_ltEs2(Left(vyy9700), Left(vyy9800), app(ty_Maybe, hd), ed) → new_ltEs(vyy9700, vyy9800, hd)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), eg, app(ty_Maybe, fa), dg) → new_lt0(vyy971, vyy981, fa)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), app(ty_[], de), df, dg) → new_compare(vyy970, vyy980, de)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), eg, app(app(ty_@2, fh), ga), dg) → new_lt3(vyy971, vyy981, fh, ga)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), app(app(app(ty_@3, dh), ea), eb), df, dg) → new_compare21(vyy970, vyy980, new_esEs5(vyy970, vyy980, dh, ea, eb), dh, ea, eb)
new_compare3(vyy970, vyy980, ec, ed) → new_compare22(vyy970, vyy980, new_esEs6(vyy970, vyy980, ec, ed), ec, ed)
new_ltEs(Just(vyy970), Just(vyy980), app(app(app(ty_@3, ce), cf), cg)) → new_ltEs1(vyy970, vyy980, ce, cf, cg)
new_compare22(Right(vyy9700), Right(vyy9800), False, ec, app(app(ty_Either, bba), bbb)) → new_ltEs2(vyy9700, vyy9800, bba, bbb)
new_ltEs(Just(vyy970), Just(vyy980), app(ty_Maybe, cd)) → new_ltEs(vyy970, vyy980, cd)
new_primCompAux(vyy970, vyy980, vyy170, app(ty_[], ba)) → new_compare(vyy970, vyy980, ba)
new_ltEs2(Left(vyy9700), Left(vyy9800), app(app(ty_@2, bab), bac), ed) → new_ltEs3(vyy9700, vyy9800, bab, bac)
new_ltEs2(Left(vyy9700), Left(vyy9800), app(app(app(ty_@3, he), hf), hg), ed) → new_ltEs1(vyy9700, vyy9800, he, hf, hg)
new_ltEs3(@2(vyy970, vyy971), @2(vyy980, vyy981), bcg, app(ty_Maybe, bda)) → new_ltEs(vyy971, vyy981, bda)
new_lt3(vyy970, vyy980, ee, ef) → new_compare23(vyy970, vyy980, new_esEs7(vyy970, vyy980, ee, ef), ee, ef)
new_lt(vyy970, vyy980, de) → new_compare(vyy970, vyy980, de)
new_compare22(Left(vyy9700), Left(vyy9800), False, app(ty_[], hc), ed) → new_ltEs0(vyy9700, vyy9800, hc)
new_ltEs3(@2(vyy970, vyy971), @2(vyy980, vyy981), bcg, app(app(ty_@2, bdg), bdh)) → new_ltEs3(vyy971, vyy981, bdg, bdh)
new_ltEs2(Right(vyy9700), Right(vyy9800), ec, app(app(app(ty_@3, baf), bag), bah)) → new_ltEs1(vyy9700, vyy9800, baf, bag, bah)
new_ltEs2(Right(vyy9700), Right(vyy9800), ec, app(app(ty_@2, bbc), bbd)) → new_ltEs3(vyy9700, vyy9800, bbc, bbd)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), eg, app(app(ty_Either, ff), fg), dg) → new_lt2(vyy971, vyy981, ff, fg)
new_compare22(Left(vyy9700), Left(vyy9800), False, app(app(ty_@2, bab), bac), ed) → new_ltEs3(vyy9700, vyy9800, bab, bac)
new_compare22(Right(vyy9700), Right(vyy9800), False, ec, app(ty_Maybe, bae)) → new_ltEs(vyy9700, vyy9800, bae)
new_ltEs2(Right(vyy9700), Right(vyy9800), ec, app(app(ty_Either, bba), bbb)) → new_ltEs2(vyy9700, vyy9800, bba, bbb)
new_ltEs0(:(vyy970, vyy971), :(vyy980, vyy981), h) → new_primCompAux(vyy970, vyy980, new_compare0(vyy971, vyy981, h), h)
new_ltEs2(Right(vyy9700), Right(vyy9800), ec, app(ty_[], bad)) → new_ltEs0(vyy9700, vyy9800, bad)
new_ltEs(Just(vyy970), Just(vyy980), app(app(ty_Either, da), db)) → new_ltEs2(vyy970, vyy980, da, db)
new_ltEs3(@2(vyy970, vyy971), @2(vyy980, vyy981), app(ty_Maybe, bbg), bbf) → new_lt0(vyy970, vyy980, bbg)
new_lt1(vyy970, vyy980, dh, ea, eb) → new_compare21(vyy970, vyy980, new_esEs5(vyy970, vyy980, dh, ea, eb), dh, ea, eb)
new_compare23(vyy970, vyy980, False, ee, ef) → new_ltEs3(vyy970, vyy980, ee, ef)
new_ltEs3(@2(vyy970, vyy971), @2(vyy980, vyy981), app(app(ty_@2, bce), bcf), bbf) → new_lt3(vyy970, vyy980, bce, bcf)
new_ltEs(Just(vyy970), Just(vyy980), app(app(ty_@2, dc), dd)) → new_ltEs3(vyy970, vyy980, dc, dd)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), app(ty_Maybe, cb), df, dg) → new_compare20(vyy970, vyy980, new_esEs4(vyy970, vyy980, cb), cb)
new_compare(:(vyy970, vyy971), :(vyy980, vyy981), h) → new_compare(vyy971, vyy981, h)
new_primCompAux(vyy970, vyy980, vyy170, app(ty_Maybe, bb)) → new_compare1(vyy970, vyy980, bb)
new_primCompAux(vyy970, vyy980, vyy170, app(app(ty_Either, bf), bg)) → new_compare3(vyy970, vyy980, bf, bg)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), eg, df, app(ty_Maybe, gc)) → new_ltEs(vyy972, vyy982, gc)
new_compare(:(vyy970, vyy971), :(vyy980, vyy981), h) → new_primCompAux(vyy970, vyy980, new_compare0(vyy971, vyy981, h), h)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), eg, df, app(app(app(ty_@3, gd), ge), gf)) → new_ltEs1(vyy972, vyy982, gd, ge, gf)
new_primCompAux(vyy970, vyy980, vyy170, app(app(ty_@2, bh), ca)) → new_compare4(vyy970, vyy980, bh, ca)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), eg, app(ty_[], eh), dg) → new_lt(vyy971, vyy981, eh)
new_compare1(vyy970, vyy980, cb) → new_compare20(vyy970, vyy980, new_esEs4(vyy970, vyy980, cb), cb)
new_compare22(Left(vyy9700), Left(vyy9800), False, app(ty_Maybe, hd), ed) → new_ltEs(vyy9700, vyy9800, hd)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), app(app(ty_@2, ee), ef), df, dg) → new_compare23(vyy970, vyy980, new_esEs7(vyy970, vyy980, ee, ef), ee, ef)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), eg, df, app(ty_[], gb)) → new_ltEs0(vyy972, vyy982, gb)
new_primCompAux(vyy970, vyy980, vyy170, app(app(app(ty_@3, bc), bd), be)) → new_compare2(vyy970, vyy980, bc, bd, be)
new_compare22(Right(vyy9700), Right(vyy9800), False, ec, app(app(ty_@2, bbc), bbd)) → new_ltEs3(vyy9700, vyy9800, bbc, bbd)
new_compare22(Right(vyy9700), Right(vyy9800), False, ec, app(app(app(ty_@3, baf), bag), bah)) → new_ltEs1(vyy9700, vyy9800, baf, bag, bah)
new_compare22(Right(vyy9700), Right(vyy9800), False, ec, app(ty_[], bad)) → new_ltEs0(vyy9700, vyy9800, bad)
new_ltEs3(@2(vyy970, vyy971), @2(vyy980, vyy981), bcg, app(app(ty_Either, bde), bdf)) → new_ltEs2(vyy971, vyy981, bde, bdf)
new_lt2(vyy970, vyy980, ec, ed) → new_compare22(vyy970, vyy980, new_esEs6(vyy970, vyy980, ec, ed), ec, ed)
new_lt0(vyy970, vyy980, cb) → new_compare20(vyy970, vyy980, new_esEs4(vyy970, vyy980, cb), cb)
new_compare4(vyy970, vyy980, ee, ef) → new_compare23(vyy970, vyy980, new_esEs7(vyy970, vyy980, ee, ef), ee, ef)
new_ltEs3(@2(vyy970, vyy971), @2(vyy980, vyy981), bcg, app(ty_[], bch)) → new_ltEs0(vyy971, vyy981, bch)
new_ltEs1(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), eg, df, app(app(ty_Either, gg), gh)) → new_ltEs2(vyy972, vyy982, gg, gh)
new_compare22(Left(vyy9700), Left(vyy9800), False, app(app(app(ty_@3, he), hf), hg), ed) → new_ltEs1(vyy9700, vyy9800, he, hf, hg)
new_compare20(vyy970, vyy980, False, cb) → new_ltEs(vyy970, vyy980, cb)
new_compare22(Left(vyy9700), Left(vyy9800), False, app(app(ty_Either, hh), baa), ed) → new_ltEs2(vyy9700, vyy9800, hh, baa)
new_ltEs2(Left(vyy9700), Left(vyy9800), app(ty_[], hc), ed) → new_ltEs0(vyy9700, vyy9800, hc)

The TRS R consists of the following rules:

new_esEs25(vyy3000, vyy400, app(ty_[], cga)) → new_esEs14(vyy3000, vyy400, cga)
new_esEs6(Right(vyy3000), Right(vyy400), cdg, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, cbd)) → new_esEs4(vyy3000, vyy400, cbd)
new_esEs28(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_ltEs6(vyy972, vyy982, ty_Float) → new_ltEs11(vyy972, vyy982)
new_ltEs6(vyy972, vyy982, app(app(ty_@2, ha), hb)) → new_ltEs15(vyy972, vyy982, ha, hb)
new_primCmpNat0(vyy9700, Succ(vyy9800)) → new_primCmpNat2(vyy9700, vyy9800)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt20(vyy970, vyy980, ty_Int) → new_lt16(vyy970, vyy980)
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, app(app(ty_@2, bbc), bbd)) → new_ltEs15(vyy9700, vyy9800, bbc, bbd)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Float) → new_ltEs11(vyy970, vyy980)
new_esEs25(vyy3000, vyy400, ty_Bool) → new_esEs15(vyy3000, vyy400)
new_ltEs6(vyy972, vyy982, ty_Int) → new_ltEs16(vyy972, vyy982)
new_lt4(vyy970, vyy980, ty_Int) → new_lt16(vyy970, vyy980)
new_esEs24(vyy3002, vyy402, app(app(app(ty_@3, cad), cae), caf)) → new_esEs5(vyy3002, vyy402, cad, cae, caf)
new_esEs28(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, ccd) → new_esEs17(vyy3000, vyy400)
new_compare110(vyy970, vyy980, True, ec, ed) → LT
new_esEs27(vyy3000, vyy400, app(ty_Ratio, daa)) → new_esEs18(vyy3000, vyy400, daa)
new_esEs13(vyy971, vyy981, ty_Float) → new_esEs10(vyy971, vyy981)
new_compare10(vyy970, vyy980, True, ee, ef) → LT
new_esEs26(vyy970, vyy980, ty_Float) → new_esEs10(vyy970, vyy980)
new_esEs24(vyy3002, vyy402, ty_Char) → new_esEs9(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, app(ty_Maybe, caa)) → new_esEs4(vyy3002, vyy402, caa)
new_esEs4(Nothing, Just(vyy400), cag) → False
new_esEs4(Just(vyy3000), Nothing, cag) → False
new_lt20(vyy970, vyy980, app(app(app(ty_@3, bbh), bca), bcb)) → new_lt8(vyy970, vyy980, bbh, bca, bcb)
new_ltEs14(vyy97, vyy98) → new_not(new_esEs8(new_compare11(vyy97, vyy98), GT))
new_ltEs19(vyy971, vyy981, ty_Float) → new_ltEs11(vyy971, vyy981)
new_ltEs8(Just(vyy970), Just(vyy980), app(ty_Ratio, ccc)) → new_ltEs4(vyy970, vyy980, ccc)
new_compare7(Double(vyy970, vyy971), Double(vyy980, vyy981)) → new_compare8(new_sr(vyy970, vyy980), new_sr(vyy971, vyy981))
new_primCompAux1(vyy970, vyy980, vyy170, h) → new_primCompAux0(vyy170, new_compare18(vyy970, vyy980, h))
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, ty_Double) → new_ltEs18(vyy9700, vyy9800)
new_ltEs8(Just(vyy970), Just(vyy980), ty_@0) → new_ltEs10(vyy970, vyy980)
new_compare19(vyy970, vyy980, cb) → new_compare212(vyy970, vyy980, new_esEs4(vyy970, vyy980, cb), cb)
new_esEs13(vyy971, vyy981, app(ty_[], eh)) → new_esEs14(vyy971, vyy981, eh)
new_lt4(vyy970, vyy980, ty_Float) → new_lt11(vyy970, vyy980)
new_lt16(vyy970, vyy980) → new_esEs8(new_compare8(vyy970, vyy980), LT)
new_primMulNat0(Zero, Zero) → Zero
new_esEs13(vyy971, vyy981, ty_Integer) → new_esEs17(vyy971, vyy981)
new_esEs6(Right(vyy3000), Right(vyy400), cdg, ty_Bool) → new_esEs15(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), cdg, app(app(ty_@2, ceb), cec)) → new_esEs7(vyy3000, vyy400, ceb, cec)
new_ltEs6(vyy972, vyy982, app(app(ty_Either, gg), gh)) → new_ltEs12(vyy972, vyy982, gg, gh)
new_esEs25(vyy3000, vyy400, app(app(ty_Either, cfc), cfd)) → new_esEs6(vyy3000, vyy400, cfc, cfd)
new_ltEs6(vyy972, vyy982, app(app(app(ty_@3, gd), ge), gf)) → new_ltEs5(vyy972, vyy982, gd, ge, gf)
new_esEs12(vyy970, vyy980, ty_Bool) → new_esEs15(vyy970, vyy980)
new_esEs22(vyy3000, vyy400, ty_Char) → new_esEs9(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, ccd) → new_esEs19(vyy3000, vyy400)
new_compare18(vyy970, vyy980, app(ty_Ratio, cgg)) → new_compare5(vyy970, vyy980, cgg)
new_esEs13(vyy971, vyy981, ty_Int) → new_esEs11(vyy971, vyy981)
new_esEs13(vyy971, vyy981, ty_Double) → new_esEs19(vyy971, vyy981)
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, ty_Integer) → new_ltEs17(vyy9700, vyy9800)
new_compare24(vyy970, vyy980, False) → new_compare16(vyy970, vyy980, new_ltEs13(vyy970, vyy980))
new_ltEs12(Left(vyy9700), Left(vyy9800), app(app(ty_@2, bab), bac), ed) → new_ltEs15(vyy9700, vyy9800, bab, bac)
new_lt20(vyy970, vyy980, app(app(ty_Either, bcc), bcd)) → new_lt12(vyy970, vyy980, bcc, bcd)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Integer) → new_ltEs17(vyy970, vyy980)
new_lt20(vyy970, vyy980, app(ty_[], bbe)) → new_lt6(vyy970, vyy980, bbe)
new_esEs25(vyy3000, vyy400, app(ty_Ratio, cfh)) → new_esEs18(vyy3000, vyy400, cfh)
new_ltEs9(True, False) → False
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, ccd) → new_esEs10(vyy3000, vyy400)
new_lt5(vyy971, vyy981, ty_Ordering) → new_lt13(vyy971, vyy981)
new_ltEs5(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), eg, df, dg) → new_pePe(new_lt4(vyy970, vyy980, eg), new_asAs(new_esEs12(vyy970, vyy980, eg), new_pePe(new_lt5(vyy971, vyy981, df), new_asAs(new_esEs13(vyy971, vyy981, df), new_ltEs6(vyy972, vyy982, dg)))))
new_esEs23(vyy3001, vyy401, app(ty_Maybe, bgg)) → new_esEs4(vyy3001, vyy401, bgg)
new_compare18(vyy970, vyy980, app(app(app(ty_@3, bc), bd), be)) → new_compare14(vyy970, vyy980, bc, bd, be)
new_esEs6(Right(vyy3000), Right(vyy400), cdg, ty_Char) → new_esEs9(vyy3000, vyy400)
new_lt4(vyy970, vyy980, ty_Char) → new_lt14(vyy970, vyy980)
new_lt5(vyy971, vyy981, ty_Integer) → new_lt17(vyy971, vyy981)
new_ltEs13(LT, EQ) → True
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, ccd) → new_esEs11(vyy3000, vyy400)
new_compare18(vyy970, vyy980, ty_Ordering) → new_compare6(vyy970, vyy980)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs17(vyy3000, vyy400)
new_compare17(vyy970, vyy980, True, dh, ea, eb) → LT
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_ltEs6(vyy972, vyy982, ty_Bool) → new_ltEs9(vyy972, vyy982)
new_lt11(vyy970, vyy980) → new_esEs8(new_compare27(vyy970, vyy980), LT)
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, app(ty_Maybe, bae)) → new_ltEs8(vyy9700, vyy9800, bae)
new_esEs26(vyy970, vyy980, app(ty_Maybe, bbg)) → new_esEs4(vyy970, vyy980, bbg)
new_compare15(vyy970, vyy980, False, cb) → GT
new_ltEs19(vyy971, vyy981, ty_Bool) → new_ltEs9(vyy971, vyy981)
new_esEs22(vyy3000, vyy400, app(ty_[], bfg)) → new_esEs14(vyy3000, vyy400, bfg)
new_esEs28(vyy3001, vyy401, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs5(vyy3001, vyy401, dbe, dbf, dbg)
new_esEs22(vyy3000, vyy400, app(ty_Ratio, bff)) → new_esEs18(vyy3000, vyy400, bff)
new_esEs17(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_lt17(vyy970, vyy980) → new_esEs8(new_compare9(vyy970, vyy980), LT)
new_pePe(False, vyy169) → vyy169
new_esEs14([], [], cfb) → True
new_esEs25(vyy3000, vyy400, app(app(ty_@2, cfe), cff)) → new_esEs7(vyy3000, vyy400, cfe, cff)
new_esEs15(False, True) → False
new_esEs15(True, False) → False
new_esEs27(vyy3000, vyy400, ty_@0) → new_esEs16(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), app(ty_[], hc), ed) → new_ltEs7(vyy9700, vyy9800, hc)
new_esEs13(vyy971, vyy981, app(ty_Maybe, fa)) → new_esEs4(vyy971, vyy981, fa)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Ordering, ed) → new_ltEs13(vyy9700, vyy9800)
new_esEs26(vyy970, vyy980, ty_Int) → new_esEs11(vyy970, vyy980)
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, ty_Int) → new_ltEs16(vyy9700, vyy9800)
new_esEs14(:(vyy3000, vyy3001), :(vyy400, vyy401), cfb) → new_asAs(new_esEs25(vyy3000, vyy400, cfb), new_esEs14(vyy3001, vyy401, cfb))
new_esEs22(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Float, ed) → new_ltEs11(vyy9700, vyy9800)
new_ltEs13(EQ, GT) → True
new_esEs22(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare18(vyy970, vyy980, app(ty_Maybe, bb)) → new_compare19(vyy970, vyy980, bb)
new_esEs20(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_lt5(vyy971, vyy981, ty_Double) → new_lt19(vyy971, vyy981)
new_primCmpInt(Neg(Succ(vyy9700)), Neg(vyy980)) → new_primCmpNat1(vyy980, vyy9700)
new_esEs12(vyy970, vyy980, ty_Float) → new_esEs10(vyy970, vyy980)
new_esEs12(vyy970, vyy980, ty_Char) → new_esEs9(vyy970, vyy980)
new_esEs19(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt4(vyy970, vyy980, ty_@0) → new_lt10(vyy970, vyy980)
new_ltEs8(Nothing, Just(vyy980), ccb) → True
new_esEs6(Right(vyy3000), Left(vyy400), cdg, ccd) → False
new_esEs6(Left(vyy3000), Right(vyy400), cdg, ccd) → False
new_esEs8(LT, LT) → True
new_ltEs11(vyy97, vyy98) → new_not(new_esEs8(new_compare27(vyy97, vyy98), GT))
new_compare25(vyy970, vyy980, True, dh, ea, eb) → EQ
new_esEs23(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_ltEs12(Left(vyy9700), Left(vyy9800), app(ty_Ratio, cgh), ed) → new_ltEs4(vyy9700, vyy9800, cgh)
new_esEs25(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs28(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_ltEs8(Just(vyy970), Just(vyy980), app(ty_[], cc)) → new_ltEs7(vyy970, vyy980, cc)
new_compare0([], [], h) → EQ
new_esEs23(vyy3001, vyy401, ty_@0) → new_esEs16(vyy3001, vyy401)
new_pePe(True, vyy169) → True
new_primEqNat0(Zero, Zero) → True
new_esEs20(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, app(app(ty_Either, bgc), bgd)) → new_esEs6(vyy3001, vyy401, bgc, bgd)
new_esEs6(Right(vyy3000), Right(vyy400), cdg, ty_@0) → new_esEs16(vyy3000, vyy400)
new_esEs28(vyy3001, vyy401, ty_@0) → new_esEs16(vyy3001, vyy401)
new_ltEs6(vyy972, vyy982, ty_@0) → new_ltEs10(vyy972, vyy982)
new_esEs26(vyy970, vyy980, ty_@0) → new_esEs16(vyy970, vyy980)
new_esEs22(vyy3000, vyy400, app(app(ty_@2, bfc), bfd)) → new_esEs7(vyy3000, vyy400, bfc, bfd)
new_esEs6(Right(vyy3000), Right(vyy400), cdg, app(app(ty_Either, cdh), cea)) → new_esEs6(vyy3000, vyy400, cdh, cea)
new_esEs26(vyy970, vyy980, ty_Bool) → new_esEs15(vyy970, vyy980)
new_compare110(vyy970, vyy980, False, ec, ed) → GT
new_esEs12(vyy970, vyy980, app(app(ty_@2, ee), ef)) → new_esEs7(vyy970, vyy980, ee, ef)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs28(vyy3001, vyy401, app(app(ty_Either, daf), dag)) → new_esEs6(vyy3001, vyy401, daf, dag)
new_compare28(vyy970, vyy980, ec, ed) → new_compare210(vyy970, vyy980, new_esEs6(vyy970, vyy980, ec, ed), ec, ed)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs9(vyy3000, vyy400)
new_ltEs6(vyy972, vyy982, ty_Integer) → new_ltEs17(vyy972, vyy982)
new_esEs24(vyy3002, vyy402, app(app(ty_@2, bhg), bhh)) → new_esEs7(vyy3002, vyy402, bhg, bhh)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy9800))) → new_primCmpNat0(vyy9800, Zero)
new_esEs26(vyy970, vyy980, ty_Ordering) → new_esEs8(vyy970, vyy980)
new_esEs8(GT, GT) → True
new_esEs9(Char(vyy3000), Char(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy1480), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1480, vyy40100)))
new_primCmpInt(Pos(Zero), Pos(Succ(vyy9800))) → new_primCmpNat1(Zero, vyy9800)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_lt20(vyy970, vyy980, ty_Bool) → new_lt9(vyy970, vyy980)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, cbe)) → new_esEs18(vyy3000, vyy400, cbe)
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, app(app(app(ty_@3, baf), bag), bah)) → new_ltEs5(vyy9700, vyy9800, baf, bag, bah)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs15(True, True) → True
new_esEs23(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs12(Left(vyy9700), Left(vyy9800), app(ty_Maybe, hd), ed) → new_ltEs8(vyy9700, vyy9800, hd)
new_primPlusNat1(Succ(vyy14800), Zero) → Succ(vyy14800)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_compare27(Float(vyy970, vyy971), Float(vyy980, vyy981)) → new_compare8(new_sr(vyy970, vyy980), new_sr(vyy971, vyy981))
new_compare13(vyy970, vyy980, False) → GT
new_ltEs12(Left(vyy9700), Left(vyy9800), app(app(app(ty_@3, he), hf), hg), ed) → new_ltEs5(vyy9700, vyy9800, he, hf, hg)
new_esEs28(vyy3001, vyy401, app(ty_Maybe, dbb)) → new_esEs4(vyy3001, vyy401, dbb)
new_compare18(vyy970, vyy980, ty_Float) → new_compare27(vyy970, vyy980)
new_ltEs13(LT, GT) → True
new_compare16(vyy970, vyy980, True) → LT
new_esEs14([], :(vyy400, vyy401), cfb) → False
new_esEs14(:(vyy3000, vyy3001), [], cfb) → False
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], cdc), ccd) → new_esEs14(vyy3000, vyy400, cdc)
new_primCmpNat1(Zero, vyy9700) → LT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bef, beg, beh) → new_asAs(new_esEs22(vyy3000, vyy400, bef), new_asAs(new_esEs23(vyy3001, vyy401, beg), new_esEs24(vyy3002, vyy402, beh)))
new_ltEs8(Just(vyy970), Just(vyy980), ty_Char) → new_ltEs14(vyy970, vyy980)
new_lt4(vyy970, vyy980, app(app(ty_@2, ee), ef)) → new_lt15(vyy970, vyy980, ee, ef)
new_esEs26(vyy970, vyy980, app(ty_[], bbe)) → new_esEs14(vyy970, vyy980, bbe)
new_lt5(vyy971, vyy981, ty_Int) → new_lt16(vyy971, vyy981)
new_compare8(vyy97, vyy98) → new_primCmpInt(vyy97, vyy98)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primCompAux0(vyy174, GT) → GT
new_esEs18(:%(vyy3000, vyy3001), :%(vyy400, vyy401), bee) → new_asAs(new_esEs20(vyy3000, vyy400, bee), new_esEs21(vyy3001, vyy401, bee))
new_esEs8(EQ, EQ) → True
new_ltEs8(Just(vyy970), Just(vyy980), ty_Double) → new_ltEs18(vyy970, vyy980)
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, app(ty_[], bad)) → new_ltEs7(vyy9700, vyy9800, bad)
new_lt20(vyy970, vyy980, ty_@0) → new_lt10(vyy970, vyy980)
new_lt5(vyy971, vyy981, app(app(app(ty_@3, fb), fc), fd)) → new_lt8(vyy971, vyy981, fb, fc, fd)
new_lt20(vyy970, vyy980, ty_Ordering) → new_lt13(vyy970, vyy980)
new_esEs6(Right(vyy3000), Right(vyy400), cdg, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Int, ed) → new_ltEs16(vyy9700, vyy9800)
new_esEs28(vyy3001, vyy401, app(ty_[], dbd)) → new_esEs14(vyy3001, vyy401, dbd)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Char, ed) → new_ltEs14(vyy9700, vyy9800)
new_esEs22(vyy3000, vyy400, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs5(vyy3000, vyy400, bfh, bga, bgb)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_compare18(vyy970, vyy980, ty_Int) → new_compare8(vyy970, vyy980)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, cdb), ccd) → new_esEs18(vyy3000, vyy400, cdb)
new_esEs28(vyy3001, vyy401, app(app(ty_@2, dah), dba)) → new_esEs7(vyy3001, vyy401, dah, dba)
new_ltEs19(vyy971, vyy981, app(ty_Ratio, cgf)) → new_ltEs4(vyy971, vyy981, cgf)
new_esEs23(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_esEs22(vyy3000, vyy400, app(ty_Maybe, bfe)) → new_esEs4(vyy3000, vyy400, bfe)
new_esEs25(vyy3000, vyy400, app(ty_Maybe, cfg)) → new_esEs4(vyy3000, vyy400, cfg)
new_esEs26(vyy970, vyy980, ty_Integer) → new_esEs17(vyy970, vyy980)
new_ltEs13(GT, LT) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs12(vyy970, vyy980, app(app(app(ty_@3, dh), ea), eb)) → new_esEs5(vyy970, vyy980, dh, ea, eb)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs15(vyy3000, vyy400)
new_compare10(vyy970, vyy980, False, ee, ef) → GT
new_ltEs19(vyy971, vyy981, ty_Integer) → new_ltEs17(vyy971, vyy981)
new_ltEs13(EQ, EQ) → True
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, cah), cba)) → new_esEs6(vyy3000, vyy400, cah, cba)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, cdd), cde), cdf), ccd) → new_esEs5(vyy3000, vyy400, cdd, cde, cdf)
new_esEs22(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs7(@2(vyy3000, vyy3001), @2(vyy400, vyy401), chb, chc) → new_asAs(new_esEs27(vyy3000, vyy400, chb), new_esEs28(vyy3001, vyy401, chc))
new_esEs6(Right(vyy3000), Right(vyy400), cdg, app(ty_Maybe, ced)) → new_esEs4(vyy3000, vyy400, ced)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, ccd) → new_esEs16(vyy3000, vyy400)
new_primEqNat0(Succ(vyy300000), Succ(vyy40000)) → new_primEqNat0(vyy300000, vyy40000)
new_esEs24(vyy3002, vyy402, ty_@0) → new_esEs16(vyy3002, vyy402)
new_esEs27(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs27(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, ccd) → new_esEs9(vyy3000, vyy400)
new_esEs24(vyy3002, vyy402, app(ty_Ratio, cab)) → new_esEs18(vyy3002, vyy402, cab)
new_esEs13(vyy971, vyy981, app(app(app(ty_@3, fb), fc), fd)) → new_esEs5(vyy971, vyy981, fb, fc, fd)
new_lt13(vyy970, vyy980) → new_esEs8(new_compare6(vyy970, vyy980), LT)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, cbg), cbh), cca)) → new_esEs5(vyy3000, vyy400, cbg, cbh, cca)
new_ltEs8(Just(vyy970), Just(vyy980), app(app(ty_Either, da), db)) → new_ltEs12(vyy970, vyy980, da, db)
new_lt5(vyy971, vyy981, ty_Float) → new_lt11(vyy971, vyy981)
new_lt20(vyy970, vyy980, ty_Integer) → new_lt17(vyy970, vyy980)
new_esEs28(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_compare212(vyy970, vyy980, True, cb) → EQ
new_ltEs6(vyy972, vyy982, app(ty_Ratio, bed)) → new_ltEs4(vyy972, vyy982, bed)
new_esEs24(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_ltEs8(Just(vyy970), Nothing, ccb) → False
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, ty_Char) → new_ltEs14(vyy9700, vyy9800)
new_esEs23(vyy3001, vyy401, ty_Bool) → new_esEs15(vyy3001, vyy401)
new_esEs27(vyy3000, vyy400, app(app(app(ty_@3, dac), dad), dae)) → new_esEs5(vyy3000, vyy400, dac, dad, dae)
new_compare5(:%(vyy970, vyy971), :%(vyy980, vyy981), ty_Integer) → new_compare9(new_sr0(vyy970, vyy981), new_sr0(vyy980, vyy971))
new_esEs12(vyy970, vyy980, app(ty_Ratio, beb)) → new_esEs18(vyy970, vyy980, beb)
new_esEs10(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare17(vyy970, vyy980, False, dh, ea, eb) → GT
new_esEs21(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_esEs28(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs25(vyy3000, vyy400, ty_Char) → new_esEs9(vyy3000, vyy400)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_ltEs16(vyy97, vyy98) → new_not(new_esEs8(new_compare8(vyy97, vyy98), GT))
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_@0, ed) → new_ltEs10(vyy9700, vyy9800)
new_ltEs6(vyy972, vyy982, ty_Ordering) → new_ltEs13(vyy972, vyy982)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy9800))) → LT
new_sr0(Integer(vyy9800), Integer(vyy9710)) → Integer(new_primMulInt(vyy9800, vyy9710))
new_lt15(vyy970, vyy980, ee, ef) → new_esEs8(new_compare29(vyy970, vyy980, ee, ef), LT)
new_compare13(vyy970, vyy980, True) → LT
new_lt4(vyy970, vyy980, app(ty_Maybe, cb)) → new_lt7(vyy970, vyy980, cb)
new_primPlusNat1(Succ(vyy14800), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy14800, vyy401000)))
new_lt6(vyy970, vyy980, de) → new_esEs8(new_compare0(vyy970, vyy980, de), LT)
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_ltEs12(Left(vyy9700), Right(vyy9800), ec, ed) → True
new_compare213(vyy970, vyy980, False, ee, ef) → new_compare10(vyy970, vyy980, new_ltEs15(vyy970, vyy980, ee, ef), ee, ef)
new_esEs13(vyy971, vyy981, ty_Bool) → new_esEs15(vyy971, vyy981)
new_compare211(vyy970, vyy980, False) → new_compare13(vyy970, vyy980, new_ltEs9(vyy970, vyy980))
new_lt5(vyy971, vyy981, app(ty_Ratio, bec)) → new_lt18(vyy971, vyy981, bec)
new_esEs13(vyy971, vyy981, ty_@0) → new_esEs16(vyy971, vyy981)
new_compare18(vyy970, vyy980, ty_Double) → new_compare7(vyy970, vyy980)
new_lt5(vyy971, vyy981, ty_Bool) → new_lt9(vyy971, vyy981)
new_ltEs6(vyy972, vyy982, app(ty_Maybe, gc)) → new_ltEs8(vyy972, vyy982, gc)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, cda), ccd) → new_esEs4(vyy3000, vyy400, cda)
new_primCmpNat2(Zero, Succ(vyy98000)) → LT
new_lt7(vyy970, vyy980, cb) → new_esEs8(new_compare19(vyy970, vyy980, cb), LT)
new_compare18(vyy970, vyy980, ty_Bool) → new_compare12(vyy970, vyy980)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_lt5(vyy971, vyy981, app(app(ty_@2, fh), ga)) → new_lt15(vyy971, vyy981, fh, ga)
new_lt8(vyy970, vyy980, dh, ea, eb) → new_esEs8(new_compare14(vyy970, vyy980, dh, ea, eb), LT)
new_compare24(vyy970, vyy980, True) → EQ
new_esEs27(vyy3000, vyy400, app(app(ty_@2, chf), chg)) → new_esEs7(vyy3000, vyy400, chf, chg)
new_lt5(vyy971, vyy981, ty_Char) → new_lt14(vyy971, vyy981)
new_ltEs19(vyy971, vyy981, ty_Double) → new_ltEs18(vyy971, vyy981)
new_ltEs13(GT, EQ) → False
new_ltEs13(EQ, LT) → False
new_esEs22(vyy3000, vyy400, ty_@0) → new_esEs16(vyy3000, vyy400)
new_esEs27(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_lt19(vyy970, vyy980) → new_esEs8(new_compare7(vyy970, vyy980), LT)
new_primCompAux0(vyy174, LT) → LT
new_ltEs4(vyy97, vyy98, bea) → new_not(new_esEs8(new_compare5(vyy97, vyy98, bea), GT))
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, ccg), cch), ccd) → new_esEs7(vyy3000, vyy400, ccg, cch)
new_esEs12(vyy970, vyy980, ty_Integer) → new_esEs17(vyy970, vyy980)
new_esEs11(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_not(False) → True
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, cce), ccf), ccd) → new_esEs6(vyy3000, vyy400, cce, ccf)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, ccd) → new_esEs15(vyy3000, vyy400)
new_compare210(vyy970, vyy980, True, ec, ed) → EQ
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_ltEs19(vyy971, vyy981, app(app(ty_Either, bde), bdf)) → new_ltEs12(vyy971, vyy981, bde, bdf)
new_esEs24(vyy3002, vyy402, app(app(ty_Either, bhe), bhf)) → new_esEs6(vyy3002, vyy402, bhe, bhf)
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, app(app(ty_Either, bba), bbb)) → new_ltEs12(vyy9700, vyy9800, bba, bbb)
new_esEs26(vyy970, vyy980, app(ty_Ratio, cge)) → new_esEs18(vyy970, vyy980, cge)
new_ltEs12(Right(vyy9700), Left(vyy9800), ec, ed) → False
new_esEs28(vyy3001, vyy401, ty_Char) → new_esEs9(vyy3001, vyy401)
new_esEs25(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs24(vyy3002, vyy402, app(ty_[], cac)) → new_esEs14(vyy3002, vyy402, cac)
new_compare0(:(vyy970, vyy971), [], h) → GT
new_ltEs6(vyy972, vyy982, ty_Double) → new_ltEs18(vyy972, vyy982)
new_esEs27(vyy3000, vyy400, app(app(ty_Either, chd), che)) → new_esEs6(vyy3000, vyy400, chd, che)
new_esEs13(vyy971, vyy981, ty_Char) → new_esEs9(vyy971, vyy981)
new_esEs27(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_lt4(vyy970, vyy980, ty_Double) → new_lt19(vyy970, vyy980)
new_compare18(vyy970, vyy980, app(ty_[], ba)) → new_compare0(vyy970, vyy980, ba)
new_primCmpInt(Pos(Succ(vyy9700)), Neg(vyy980)) → GT
new_esEs13(vyy971, vyy981, app(app(ty_Either, ff), fg)) → new_esEs6(vyy971, vyy981, ff, fg)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare5(:%(vyy970, vyy971), :%(vyy980, vyy981), ty_Int) → new_compare8(new_sr(vyy970, vyy981), new_sr(vyy980, vyy971))
new_ltEs6(vyy972, vyy982, ty_Char) → new_ltEs14(vyy972, vyy982)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Ordering) → new_ltEs13(vyy970, vyy980)
new_ltEs9(True, True) → True
new_esEs6(Right(vyy3000), Right(vyy400), cdg, ty_Double) → new_esEs19(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs19(vyy971, vyy981, app(ty_Maybe, bda)) → new_ltEs8(vyy971, vyy981, bda)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs24(vyy3002, vyy402, ty_Bool) → new_esEs15(vyy3002, vyy402)
new_compare12(vyy970, vyy980) → new_compare211(vyy970, vyy980, new_esEs15(vyy970, vyy980))
new_primEqNat0(Zero, Succ(vyy40000)) → False
new_primEqNat0(Succ(vyy300000), Zero) → False
new_esEs26(vyy970, vyy980, app(app(ty_@2, bce), bcf)) → new_esEs7(vyy970, vyy980, bce, bcf)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs9(False, False) → True
new_esEs23(vyy3001, vyy401, app(ty_Ratio, bgh)) → new_esEs18(vyy3001, vyy401, bgh)
new_ltEs10(vyy97, vyy98) → new_not(new_esEs8(new_compare26(vyy97, vyy98), GT))
new_esEs4(Nothing, Nothing, cag) → True
new_esEs12(vyy970, vyy980, ty_Double) → new_esEs19(vyy970, vyy980)
new_primCmpInt(Pos(Succ(vyy9700)), Pos(vyy980)) → new_primCmpNat0(vyy9700, vyy980)
new_primCmpNat2(Succ(vyy97000), Succ(vyy98000)) → new_primCmpNat2(vyy97000, vyy98000)
new_esEs13(vyy971, vyy981, app(app(ty_@2, fh), ga)) → new_esEs7(vyy971, vyy981, fh, ga)
new_ltEs12(Left(vyy9700), Left(vyy9800), app(app(ty_Either, hh), baa), ed) → new_ltEs12(vyy9700, vyy9800, hh, baa)
new_primCmpNat0(vyy9700, Zero) → GT
new_esEs23(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_lt20(vyy970, vyy980, ty_Char) → new_lt14(vyy970, vyy980)
new_esEs27(vyy3000, vyy400, app(ty_Maybe, chh)) → new_esEs4(vyy3000, vyy400, chh)
new_lt4(vyy970, vyy980, app(ty_Ratio, beb)) → new_lt18(vyy970, vyy980, beb)
new_compare6(vyy970, vyy980) → new_compare24(vyy970, vyy980, new_esEs8(vyy970, vyy980))
new_lt4(vyy970, vyy980, app(ty_[], de)) → new_lt6(vyy970, vyy980, de)
new_esEs23(vyy3001, vyy401, app(ty_[], bha)) → new_esEs14(vyy3001, vyy401, bha)
new_esEs24(vyy3002, vyy402, ty_Double) → new_esEs19(vyy3002, vyy402)
new_lt12(vyy970, vyy980, ec, ed) → new_esEs8(new_compare28(vyy970, vyy980, ec, ed), LT)
new_esEs12(vyy970, vyy980, ty_@0) → new_esEs16(vyy970, vyy980)
new_ltEs15(@2(vyy970, vyy971), @2(vyy980, vyy981), bcg, bbf) → new_pePe(new_lt20(vyy970, vyy980, bcg), new_asAs(new_esEs26(vyy970, vyy980, bcg), new_ltEs19(vyy971, vyy981, bbf)))
new_primCmpInt(Pos(Zero), Neg(Succ(vyy9800))) → GT
new_lt20(vyy970, vyy980, app(app(ty_@2, bce), bcf)) → new_lt15(vyy970, vyy980, bce, bcf)
new_esEs6(Right(vyy3000), Right(vyy400), cdg, app(ty_[], cef)) → new_esEs14(vyy3000, vyy400, cef)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, ccd) → new_esEs8(vyy3000, vyy400)
new_lt9(vyy970, vyy980) → new_esEs8(new_compare12(vyy970, vyy980), LT)
new_compare0(:(vyy970, vyy971), :(vyy980, vyy981), h) → new_primCompAux1(vyy970, vyy980, new_compare0(vyy971, vyy981, h), h)
new_ltEs19(vyy971, vyy981, app(ty_[], bch)) → new_ltEs7(vyy971, vyy981, bch)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], cbf)) → new_esEs14(vyy3000, vyy400, cbf)
new_ltEs19(vyy971, vyy981, ty_Char) → new_ltEs14(vyy971, vyy981)
new_esEs24(vyy3002, vyy402, ty_Int) → new_esEs11(vyy3002, vyy402)
new_esEs13(vyy971, vyy981, app(ty_Ratio, bec)) → new_esEs18(vyy971, vyy981, bec)
new_lt5(vyy971, vyy981, app(ty_Maybe, fa)) → new_lt7(vyy971, vyy981, fa)
new_ltEs17(vyy97, vyy98) → new_not(new_esEs8(new_compare9(vyy97, vyy98), GT))
new_lt4(vyy970, vyy980, ty_Ordering) → new_lt13(vyy970, vyy980)
new_esEs21(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Bool) → new_ltEs9(vyy970, vyy980)
new_esEs6(Right(vyy3000), Right(vyy400), cdg, ty_Int) → new_esEs11(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Integer, ed) → new_ltEs17(vyy9700, vyy9800)
new_compare18(vyy970, vyy980, app(app(ty_Either, bf), bg)) → new_compare28(vyy970, vyy980, bf, bg)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare18(vyy970, vyy980, app(app(ty_@2, bh), ca)) → new_compare29(vyy970, vyy980, bh, ca)
new_ltEs18(vyy97, vyy98) → new_not(new_esEs8(new_compare7(vyy97, vyy98), GT))
new_esEs12(vyy970, vyy980, app(app(ty_Either, ec), ed)) → new_esEs6(vyy970, vyy980, ec, ed)
new_ltEs8(Just(vyy970), Just(vyy980), app(ty_Maybe, cd)) → new_ltEs8(vyy970, vyy980, cd)
new_lt20(vyy970, vyy980, app(ty_Maybe, bbg)) → new_lt7(vyy970, vyy980, bbg)
new_ltEs13(GT, GT) → True
new_esEs12(vyy970, vyy980, app(ty_Maybe, cb)) → new_esEs4(vyy970, vyy980, cb)
new_compare9(Integer(vyy970), Integer(vyy980)) → new_primCmpInt(vyy970, vyy980)
new_asAs(False, vyy137) → False
new_lt4(vyy970, vyy980, ty_Integer) → new_lt17(vyy970, vyy980)
new_lt20(vyy970, vyy980, ty_Double) → new_lt19(vyy970, vyy980)
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, ty_Bool) → new_ltEs9(vyy9700, vyy9800)
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, app(ty_Ratio, cha)) → new_ltEs4(vyy9700, vyy9800, cha)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_compare14(vyy970, vyy980, dh, ea, eb) → new_compare25(vyy970, vyy980, new_esEs5(vyy970, vyy980, dh, ea, eb), dh, ea, eb)
new_esEs25(vyy3000, vyy400, ty_@0) → new_esEs16(vyy3000, vyy400)
new_lt5(vyy971, vyy981, ty_@0) → new_lt10(vyy971, vyy981)
new_esEs6(Right(vyy3000), Right(vyy400), cdg, app(ty_Ratio, cee)) → new_esEs18(vyy3000, vyy400, cee)
new_esEs24(vyy3002, vyy402, ty_Float) → new_esEs10(vyy3002, vyy402)
new_esEs23(vyy3001, vyy401, app(app(ty_@2, bge), bgf)) → new_esEs7(vyy3001, vyy401, bge, bgf)
new_ltEs19(vyy971, vyy981, ty_@0) → new_ltEs10(vyy971, vyy981)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Double, ed) → new_ltEs18(vyy9700, vyy9800)
new_primCmpNat1(Succ(vyy9800), vyy9700) → new_primCmpNat2(vyy9800, vyy9700)
new_esEs24(vyy3002, vyy402, ty_Integer) → new_esEs17(vyy3002, vyy402)
new_primCmpNat2(Succ(vyy97000), Zero) → GT
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs19(vyy3000, vyy400)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Int) → new_ltEs16(vyy970, vyy980)
new_compare11(Char(vyy970), Char(vyy980)) → new_primCmpInt(vyy970, vyy980)
new_ltEs9(False, True) → True
new_esEs23(vyy3001, vyy401, ty_Char) → new_esEs9(vyy3001, vyy401)
new_esEs16(@0, @0) → True
new_lt20(vyy970, vyy980, app(ty_Ratio, cge)) → new_lt18(vyy970, vyy980, cge)
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, ty_@0) → new_ltEs10(vyy9700, vyy9800)
new_ltEs19(vyy971, vyy981, ty_Int) → new_ltEs16(vyy971, vyy981)
new_esEs26(vyy970, vyy980, ty_Double) → new_esEs19(vyy970, vyy980)
new_lt18(vyy970, vyy980, beb) → new_esEs8(new_compare5(vyy970, vyy980, beb), LT)
new_lt14(vyy970, vyy980) → new_esEs8(new_compare11(vyy970, vyy980), LT)
new_esEs22(vyy3000, vyy400, ty_Bool) → new_esEs15(vyy3000, vyy400)
new_ltEs6(vyy972, vyy982, app(ty_[], gb)) → new_ltEs7(vyy972, vyy982, gb)
new_esEs28(vyy3001, vyy401, ty_Bool) → new_esEs15(vyy3001, vyy401)
new_ltEs19(vyy971, vyy981, app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs5(vyy971, vyy981, bdb, bdc, bdd)
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, ty_Ordering) → new_ltEs13(vyy9700, vyy9800)
new_compare26(@0, @0) → EQ
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs11(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Bool, ed) → new_ltEs9(vyy9700, vyy9800)
new_compare29(vyy970, vyy980, ee, ef) → new_compare213(vyy970, vyy980, new_esEs7(vyy970, vyy980, ee, ef), ee, ef)
new_ltEs8(Nothing, Nothing, ccb) → True
new_lt20(vyy970, vyy980, ty_Float) → new_lt11(vyy970, vyy980)
new_ltEs19(vyy971, vyy981, app(app(ty_@2, bdg), bdh)) → new_ltEs15(vyy971, vyy981, bdg, bdh)
new_esEs25(vyy3000, vyy400, app(app(app(ty_@3, cgb), cgc), cgd)) → new_esEs5(vyy3000, vyy400, cgb, cgc, cgd)
new_compare25(vyy970, vyy980, False, dh, ea, eb) → new_compare17(vyy970, vyy980, new_ltEs5(vyy970, vyy980, dh, ea, eb), dh, ea, eb)
new_esEs22(vyy3000, vyy400, app(app(ty_Either, bfa), bfb)) → new_esEs6(vyy3000, vyy400, bfa, bfb)
new_lt5(vyy971, vyy981, app(app(ty_Either, ff), fg)) → new_lt12(vyy971, vyy981, ff, fg)
new_esEs22(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_lt4(vyy970, vyy980, ty_Bool) → new_lt9(vyy970, vyy980)
new_esEs12(vyy970, vyy980, ty_Int) → new_esEs11(vyy970, vyy980)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, cbb), cbc)) → new_esEs7(vyy3000, vyy400, cbb, cbc)
new_ltEs8(Just(vyy970), Just(vyy980), app(app(ty_@2, dc), dd)) → new_ltEs15(vyy970, vyy980, dc, dd)
new_esEs26(vyy970, vyy980, ty_Char) → new_esEs9(vyy970, vyy980)
new_ltEs13(LT, LT) → True
new_esEs22(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs26(vyy970, vyy980, app(app(ty_Either, bcc), bcd)) → new_esEs6(vyy970, vyy980, bcc, bcd)
new_compare213(vyy970, vyy980, True, ee, ef) → EQ
new_compare0([], :(vyy980, vyy981), h) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_compare15(vyy970, vyy980, True, cb) → LT
new_esEs12(vyy970, vyy980, ty_Ordering) → new_esEs8(vyy970, vyy980)
new_esEs27(vyy3000, vyy400, app(ty_[], dab)) → new_esEs14(vyy3000, vyy400, dab)
new_lt4(vyy970, vyy980, app(app(app(ty_@3, dh), ea), eb)) → new_lt8(vyy970, vyy980, dh, ea, eb)
new_esEs13(vyy971, vyy981, ty_Ordering) → new_esEs8(vyy971, vyy981)
new_esEs12(vyy970, vyy980, app(ty_[], de)) → new_esEs14(vyy970, vyy980, de)
new_asAs(True, vyy137) → vyy137
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs26(vyy970, vyy980, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs5(vyy970, vyy980, bbh, bca, bcb)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs28(vyy3001, vyy401, app(ty_Ratio, dbc)) → new_esEs18(vyy3001, vyy401, dbc)
new_compare18(vyy970, vyy980, ty_Integer) → new_compare9(vyy970, vyy980)
new_esEs27(vyy3000, vyy400, ty_Bool) → new_esEs15(vyy3000, vyy400)
new_ltEs12(Right(vyy9700), Right(vyy9800), ec, ty_Float) → new_ltEs11(vyy9700, vyy9800)
new_compare211(vyy970, vyy980, True) → EQ
new_ltEs8(Just(vyy970), Just(vyy980), app(app(app(ty_@3, ce), cf), cg)) → new_ltEs5(vyy970, vyy980, ce, cf, cg)
new_esEs23(vyy3001, vyy401, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs5(vyy3001, vyy401, bhb, bhc, bhd)
new_lt4(vyy970, vyy980, app(app(ty_Either, ec), ed)) → new_lt12(vyy970, vyy980, ec, ed)
new_ltEs7(vyy97, vyy98, h) → new_not(new_esEs8(new_compare0(vyy97, vyy98, h), GT))
new_compare210(vyy970, vyy980, False, ec, ed) → new_compare110(vyy970, vyy980, new_ltEs12(vyy970, vyy980, ec, ed), ec, ed)
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs16(vyy3000, vyy400)
new_compare18(vyy970, vyy980, ty_@0) → new_compare26(vyy970, vyy980)
new_lt5(vyy971, vyy981, app(ty_[], eh)) → new_lt6(vyy971, vyy981, eh)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), cdg, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare212(vyy970, vyy980, False, cb) → new_compare15(vyy970, vyy980, new_ltEs8(vyy970, vyy980, cb), cb)
new_esEs6(Right(vyy3000), Right(vyy400), cdg, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs5(vyy3000, vyy400, ceg, ceh, cfa)
new_primCompAux0(vyy174, EQ) → vyy174
new_lt10(vyy970, vyy980) → new_esEs8(new_compare26(vyy970, vyy980), LT)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_compare18(vyy970, vyy980, ty_Char) → new_compare11(vyy970, vyy980)
new_esEs27(vyy3000, vyy400, ty_Char) → new_esEs9(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy9700)), Pos(vyy980)) → LT
new_ltEs19(vyy971, vyy981, ty_Ordering) → new_ltEs13(vyy971, vyy981)
new_not(True) → False
new_compare16(vyy970, vyy980, False) → GT
new_esEs15(False, False) → True
new_esEs27(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)

The set Q consists of the following terms:

new_compare210(x0, x1, True, x2, x3)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Float)
new_compare5(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare18(x0, x1, app(ty_Ratio, x2))
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs28(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs12(x0, x1, ty_@0)
new_ltEs12(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_compare6(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Left(x0), Left(x1), ty_@0, x2)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_@0)
new_primCmpNat2(Zero, Succ(x0))
new_esEs12(x0, x1, ty_Bool)
new_esEs12(x0, x1, ty_Int)
new_compare0([], [], x0)
new_ltEs18(x0, x1)
new_lt20(x0, x1, ty_Float)
new_esEs4(Nothing, Nothing, x0)
new_esEs13(x0, x1, ty_Double)
new_ltEs17(x0, x1)
new_ltEs12(Left(x0), Right(x1), x2, x3)
new_ltEs12(Right(x0), Left(x1), x2, x3)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs12(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs15(True, True)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Nothing, Nothing, x0)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_primEqNat0(Zero, Succ(x0))
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs25(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, True)
new_esEs24(x0, x1, ty_Char)
new_lt7(x0, x1, x2)
new_esEs28(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(:(x0, x1), [], x2)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_lt4(x0, x1, ty_Float)
new_esEs15(False, False)
new_compare0([], :(x0, x1), x2)
new_compare15(x0, x1, False, x2)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(x0, x1, x2, x3)
new_compare25(x0, x1, False, x2, x3, x4)
new_compare19(x0, x1, x2)
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Integer)
new_esEs12(x0, x1, ty_Float)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_@0)
new_esEs8(LT, LT)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs16(@0, @0)
new_ltEs12(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, ty_@0)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(True, x0)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Just(x0), Nothing, x1)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs19(Double(x0, x1), Double(x2, x3))
new_esEs13(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs12(Right(x0), Right(x1), x2, ty_Double)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_compare16(x0, x1, True)
new_compare18(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs8(Nothing, Just(x0), x1)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, app(ty_[], x2))
new_primEqNat0(Zero, Zero)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_compare17(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, ty_Char)
new_lt6(x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs13(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Int)
new_ltEs13(EQ, EQ)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Float)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_ltEs9(False, False)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_asAs(False, x0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare18(x0, x1, ty_Float)
new_primPlusNat1(Zero, Succ(x0))
new_compare110(x0, x1, True, x2, x3)
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs11(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_ltEs12(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs12(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_lt5(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Char)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs13(x0, x1, app(ty_Ratio, x2))
new_ltEs13(LT, EQ)
new_ltEs13(EQ, LT)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Left(x0), Left(x1), ty_Char, x2)
new_lt5(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_ltEs6(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt12(x0, x1, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare10(x0, x1, False, x2, x3)
new_ltEs6(x0, x1, ty_Ordering)
new_lt5(x0, x1, ty_Int)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Int)
new_compare17(x0, x1, True, x2, x3, x4)
new_lt9(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare213(x0, x1, False, x2, x3)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs13(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Integer)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_esEs24(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs19(x0, x1, ty_Float)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_ltEs12(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs26(x0, x1, ty_Char)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare211(x0, x1, False)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs10(x0, x1)
new_compare18(x0, x1, ty_Int)
new_primPlusNat1(Zero, Zero)
new_primCmpNat1(Zero, x0)
new_primCmpNat2(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare27(Float(x0, x1), Float(x2, x3))
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_asAs(True, x0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs11(x0, x1)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, ty_Double)
new_primCmpNat1(Succ(x0), x1)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs12(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, ty_Int)
new_compare0(:(x0, x1), [], x2)
new_compare15(x0, x1, True, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, ty_@0)
new_lt5(x0, x1, ty_Ordering)
new_ltEs9(False, True)
new_ltEs9(True, False)
new_compare9(Integer(x0), Integer(x1))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs12(Right(x0), Right(x1), x2, ty_Float)
new_ltEs9(True, True)
new_ltEs12(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs12(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_ltEs13(EQ, GT)
new_esEs28(x0, x1, ty_Int)
new_ltEs13(GT, EQ)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs19(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs22(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Bool)
new_ltEs12(Right(x0), Right(x1), x2, ty_Bool)
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_esEs23(x0, x1, ty_Bool)
new_primCompAux0(x0, EQ)
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14([], :(x0, x1), x2)
new_ltEs12(Left(x0), Left(x1), ty_Bool, x2)
new_compare10(x0, x1, True, x2, x3)
new_esEs27(x0, x1, ty_Ordering)
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_ltEs12(Left(x0), Left(x1), ty_Int, x2)
new_compare16(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt8(x0, x1, x2, x3, x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt20(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, ty_Int)
new_ltEs12(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs13(LT, GT)
new_ltEs13(GT, LT)
new_esEs25(x0, x1, ty_Char)
new_compare212(x0, x1, False, x2)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs15(True, False)
new_esEs15(False, True)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt5(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare11(Char(x0), Char(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, ty_Float)
new_esEs12(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs19(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs13(x0, x1, ty_Char)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, app(ty_[], x2))
new_compare18(x0, x1, ty_Double)
new_sr0(Integer(x0), Integer(x1))
new_primCompAux1(x0, x1, x2, x3)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, ty_Int)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, False)
new_lt15(x0, x1, x2, x3)
new_esEs13(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare8(x0, x1)
new_esEs13(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs6(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs13(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Int)
new_compare210(x0, x1, False, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs9(Char(x0), Char(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_esEs12(x0, x1, ty_Ordering)
new_lt17(x0, x1)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, x2, x3)
new_primPlusNat0(Zero, x0)
new_lt18(x0, x1, x2)
new_esEs23(x0, x1, ty_@0)
new_compare18(x0, x1, ty_Char)
new_esEs17(Integer(x0), Integer(x1))
new_compare24(x0, x1, True)
new_esEs24(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_ltEs12(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, ty_@0)
new_ltEs13(LT, LT)
new_ltEs6(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Int)
new_lt5(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Double)
new_compare5(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare18(x0, x1, ty_Ordering)
new_ltEs7(x0, x1, x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs12(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Ordering)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt11(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs6(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Int)
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt4(x0, x1, ty_Char)
new_primCmpNat2(Succ(x0), Zero)
new_esEs27(x0, x1, ty_@0)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs13(GT, GT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs12(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt19(x0, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_esEs14([], [], x0)
new_esEs27(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs12(Right(x0), Right(x1), x2, ty_Int)
new_pePe(False, x0)
new_compare212(x0, x1, True, x2)
new_primCmpNat2(Succ(x0), Succ(x1))
new_not(True)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_esEs13(x0, x1, ty_Int)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare18(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare110(x0, x1, False, x2, x3)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs14(x0, x1)
new_ltEs12(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare25(x0, x1, True, x2, x3, x4)
new_ltEs4(x0, x1, x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Double)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs12(Left(x0), Left(x1), ty_Double, x2)
new_lt10(x0, x1)
new_ltEs16(x0, x1)
new_esEs27(x0, x1, ty_Double)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare213(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Double)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Char)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1)
new_compare26(@0, @0)
new_primCmpNat0(x0, Zero)
new_esEs12(x0, x1, app(ty_[], x2))
new_compare211(x0, x1, True)
new_primCmpNat0(x0, Succ(x1))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_lt14(x0, x1)
new_esEs12(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs27(x0, x1, ty_Integer)
new_primCompAux0(x0, GT)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs13(x0, x1, ty_@0)
new_compare12(x0, x1)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, False)
new_primCompAux0(x0, LT)
new_compare18(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Double)

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

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



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

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

new_primCmpNat(Succ(vyy97000), Succ(vyy98000)) → new_primCmpNat(vyy97000, vyy98000)

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
                                  ↳ QDP

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

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

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

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



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

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

new_foldFM_GE2(vyy330, vyy331, vyy110, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb) → new_foldFM_GE1(new_fmToList_GE0(vyy330, vyy331, vyy110, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, h, ba), h, ba, bb)
new_foldFM_GE1(vyy85, vyy40, vyy330, vyy331, vyy332, vyy333, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), False, h, ba, bb) → new_foldFM_GE1(vyy85, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h, ba), h, ba, bb)
new_foldFM_GE(vyy85, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba, bb) → new_foldFM_GE1(vyy85, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h, ba), h, ba, bb)
new_foldFM_GE1(vyy85, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba, bb) → new_foldFM_GE(vyy85, vyy40, vyy334, h, ba, bb)
new_foldFM_GE1(vyy85, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba, bb) → new_foldFM_GE(vyy85, vyy40, vyy334, h, ba, bb)
new_foldFM_GE1(vyy85, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba, bb) → new_foldFM_GE2(vyy330, vyy331, new_foldFM_GE0(vyy85, vyy40, vyy334, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb)

The TRS R consists of the following rules:

new_esEs25(vyy3000, vyy400, app(ty_[], cad)) → new_esEs14(vyy3000, vyy400, cad)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, bcf)) → new_esEs4(vyy3000, vyy400, bcf)
new_esEs28(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_ltEs6(vyy972, vyy982, ty_Float) → new_ltEs11(vyy972, vyy982)
new_primCmpNat0(vyy9700, Succ(vyy9800)) → new_primCmpNat2(vyy9700, vyy9800)
new_ltEs6(vyy972, vyy982, app(app(ty_@2, fc), fd)) → new_ltEs15(vyy972, vyy982, fc, fd)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_gtEs(vyy3330, vyy40, h, ba) → new_not(new_esEs8(new_compare210(vyy3330, Right(vyy40), new_esEs6(vyy3330, Right(vyy40), h, ba), h, ba), LT))
new_lt20(vyy970, vyy980, ty_Int) → new_lt16(vyy970, vyy980)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, app(app(ty_@2, che), chf)) → new_ltEs15(vyy9700, vyy9800, che, chf)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Float) → new_ltEs11(vyy970, vyy980)
new_esEs25(vyy3000, vyy400, ty_Bool) → new_esEs15(vyy3000, vyy400)
new_ltEs6(vyy972, vyy982, ty_Int) → new_ltEs16(vyy972, vyy982)
new_lt4(vyy970, vyy980, ty_Int) → new_lt16(vyy970, vyy980)
new_esEs24(vyy3002, vyy402, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs5(vyy3002, vyy402, bbf, bbg, bbh)
new_esEs28(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, beg) → new_esEs17(vyy3000, vyy400)
new_compare110(vyy970, vyy980, True, cf, cg) → LT
new_esEs27(vyy3000, vyy400, app(ty_Ratio, dag)) → new_esEs18(vyy3000, vyy400, dag)
new_esEs13(vyy971, vyy981, ty_Float) → new_esEs10(vyy971, vyy981)
new_compare10(vyy970, vyy980, True, bd, be) → LT
new_esEs26(vyy970, vyy980, ty_Float) → new_esEs10(vyy970, vyy980)
new_esEs24(vyy3002, vyy402, ty_Char) → new_esEs9(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, app(ty_Maybe, bbc)) → new_esEs4(vyy3002, vyy402, bbc)
new_esEs4(Nothing, Just(vyy400), bca) → False
new_esEs4(Just(vyy3000), Nothing, bca) → False
new_lt20(vyy970, vyy980, app(app(app(ty_@3, cbd), cbe), cbf)) → new_lt8(vyy970, vyy980, cbd, cbe, cbf)
new_ltEs14(vyy97, vyy98) → new_not(new_esEs8(new_compare11(vyy97, vyy98), GT))
new_ltEs19(vyy971, vyy981, ty_Float) → new_ltEs11(vyy971, vyy981)
new_ltEs8(Just(vyy970), Just(vyy980), app(ty_Ratio, bef)) → new_ltEs4(vyy970, vyy980, bef)
new_compare7(Double(vyy970, vyy971), Double(vyy980, vyy981)) → new_compare8(new_sr(vyy970, vyy980), new_sr(vyy971, vyy981))
new_primCompAux1(vyy970, vyy980, vyy170, cdf) → new_primCompAux0(vyy170, new_compare18(vyy970, vyy980, cdf))
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Double) → new_ltEs18(vyy9700, vyy9800)
new_fmToList_GE0(vyy170, vyy171, vyy107, cfa, cfb, cfc) → :(@2(vyy170, vyy171), vyy107)
new_ltEs8(Just(vyy970), Just(vyy980), ty_@0) → new_ltEs10(vyy970, vyy980)
new_compare19(vyy970, vyy980, cb) → new_compare212(vyy970, vyy980, new_esEs4(vyy970, vyy980, cb), cb)
new_esEs13(vyy971, vyy981, app(ty_[], db)) → new_esEs14(vyy971, vyy981, db)
new_lt4(vyy970, vyy980, ty_Float) → new_lt11(vyy970, vyy980)
new_lt16(vyy970, vyy980) → new_esEs8(new_compare8(vyy970, vyy980), LT)
new_primMulNat0(Zero, Zero) → Zero
new_esEs13(vyy971, vyy981, ty_Integer) → new_esEs17(vyy971, vyy981)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Bool) → new_esEs15(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, app(app(ty_@2, bge), bgf)) → new_esEs7(vyy3000, vyy400, bge, bgf)
new_ltEs6(vyy972, vyy982, app(app(ty_Either, fa), fb)) → new_ltEs12(vyy972, vyy982, fa, fb)
new_esEs25(vyy3000, vyy400, app(app(ty_Either, bhf), bhg)) → new_esEs6(vyy3000, vyy400, bhf, bhg)
new_ltEs6(vyy972, vyy982, app(app(app(ty_@3, ef), eg), eh)) → new_ltEs5(vyy972, vyy982, ef, eg, eh)
new_esEs12(vyy970, vyy980, ty_Bool) → new_esEs15(vyy970, vyy980)
new_esEs22(vyy3000, vyy400, ty_Char) → new_esEs9(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, beg) → new_esEs19(vyy3000, vyy400)
new_compare18(vyy970, vyy980, app(ty_Ratio, ceh)) → new_compare5(vyy970, vyy980, ceh)
new_esEs13(vyy971, vyy981, ty_Int) → new_esEs11(vyy971, vyy981)
new_esEs13(vyy971, vyy981, ty_Double) → new_esEs19(vyy971, vyy981)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Integer) → new_ltEs17(vyy9700, vyy9800)
new_compare24(vyy970, vyy980, False) → new_compare16(vyy970, vyy980, new_ltEs13(vyy970, vyy980))
new_ltEs12(Left(vyy9700), Left(vyy9800), app(app(ty_@2, cgc), cgd), cg) → new_ltEs15(vyy9700, vyy9800, cgc, cgd)
new_lt20(vyy970, vyy980, app(app(ty_Either, cbg), cbh)) → new_lt12(vyy970, vyy980, cbg, cbh)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Integer) → new_ltEs17(vyy970, vyy980)
new_lt20(vyy970, vyy980, app(ty_[], cbb)) → new_lt6(vyy970, vyy980, cbb)
new_esEs25(vyy3000, vyy400, app(ty_Ratio, cac)) → new_esEs18(vyy3000, vyy400, cac)
new_ltEs9(True, False) → False
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, beg) → new_esEs10(vyy3000, vyy400)
new_lt5(vyy971, vyy981, ty_Ordering) → new_lt13(vyy971, vyy981)
new_ltEs5(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), bf, bg, bh) → new_pePe(new_lt4(vyy970, vyy980, bf), new_asAs(new_esEs12(vyy970, vyy980, bf), new_pePe(new_lt5(vyy971, vyy981, bg), new_asAs(new_esEs13(vyy971, vyy981, bg), new_ltEs6(vyy972, vyy982, bh)))))
new_esEs23(vyy3001, vyy401, app(ty_Maybe, baa)) → new_esEs4(vyy3001, vyy401, baa)
new_compare18(vyy970, vyy980, app(app(app(ty_@3, cea), ceb), cec)) → new_compare14(vyy970, vyy980, cea, ceb, cec)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Char) → new_esEs9(vyy3000, vyy400)
new_lt4(vyy970, vyy980, ty_Char) → new_lt14(vyy970, vyy980)
new_lt5(vyy971, vyy981, ty_Integer) → new_lt17(vyy971, vyy981)
new_ltEs13(LT, EQ) → True
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, beg) → new_esEs11(vyy3000, vyy400)
new_compare18(vyy970, vyy980, ty_Ordering) → new_compare6(vyy970, vyy980)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs17(vyy3000, vyy400)
new_compare17(vyy970, vyy980, True, cc, cd, ce) → LT
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_ltEs6(vyy972, vyy982, ty_Bool) → new_ltEs9(vyy972, vyy982)
new_lt11(vyy970, vyy980) → new_esEs8(new_compare27(vyy970, vyy980), LT)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, app(ty_Maybe, cgg)) → new_ltEs8(vyy9700, vyy9800, cgg)
new_esEs26(vyy970, vyy980, app(ty_Maybe, cbc)) → new_esEs4(vyy970, vyy980, cbc)
new_compare15(vyy970, vyy980, False, cb) → GT
new_ltEs19(vyy971, vyy981, ty_Bool) → new_ltEs9(vyy971, vyy981)
new_esEs22(vyy3000, vyy400, app(ty_[], ha)) → new_esEs14(vyy3000, vyy400, ha)
new_esEs28(vyy3001, vyy401, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs5(vyy3001, vyy401, dcc, dcd, dce)
new_esEs22(vyy3000, vyy400, app(ty_Ratio, gh)) → new_esEs18(vyy3000, vyy400, gh)
new_esEs17(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_lt17(vyy970, vyy980) → new_esEs8(new_compare9(vyy970, vyy980), LT)
new_pePe(False, vyy169) → vyy169
new_esEs14([], [], bhe) → True
new_esEs25(vyy3000, vyy400, app(app(ty_@2, bhh), caa)) → new_esEs7(vyy3000, vyy400, bhh, caa)
new_esEs15(False, True) → False
new_esEs15(True, False) → False
new_esEs27(vyy3000, vyy400, ty_@0) → new_esEs16(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), app(ty_[], cfd), cg) → new_ltEs7(vyy9700, vyy9800, cfd)
new_esEs13(vyy971, vyy981, app(ty_Maybe, dc)) → new_esEs4(vyy971, vyy981, dc)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Ordering, cg) → new_ltEs13(vyy9700, vyy9800)
new_esEs26(vyy970, vyy980, ty_Int) → new_esEs11(vyy970, vyy980)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Int) → new_ltEs16(vyy9700, vyy9800)
new_esEs14(:(vyy3000, vyy3001), :(vyy400, vyy401), bhe) → new_asAs(new_esEs25(vyy3000, vyy400, bhe), new_esEs14(vyy3001, vyy401, bhe))
new_esEs22(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Float, cg) → new_ltEs11(vyy9700, vyy9800)
new_ltEs13(EQ, GT) → True
new_esEs22(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare18(vyy970, vyy980, app(ty_Maybe, cdh)) → new_compare19(vyy970, vyy980, cdh)
new_esEs20(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_lt5(vyy971, vyy981, ty_Double) → new_lt19(vyy971, vyy981)
new_primCmpInt(Neg(Succ(vyy9700)), Neg(vyy980)) → new_primCmpNat1(vyy980, vyy9700)
new_esEs12(vyy970, vyy980, ty_Float) → new_esEs10(vyy970, vyy980)
new_esEs12(vyy970, vyy980, ty_Char) → new_esEs9(vyy970, vyy980)
new_esEs19(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt4(vyy970, vyy980, ty_@0) → new_lt10(vyy970, vyy980)
new_ltEs8(Nothing, Just(vyy980), bdd) → True
new_esEs6(Right(vyy3000), Left(vyy400), bgb, beg) → False
new_esEs6(Left(vyy3000), Right(vyy400), bgb, beg) → False
new_esEs8(LT, LT) → True
new_ltEs11(vyy97, vyy98) → new_not(new_esEs8(new_compare27(vyy97, vyy98), GT))
new_compare25(vyy970, vyy980, True, cc, cd, ce) → EQ
new_esEs23(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs25(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), app(ty_Ratio, cge), cg) → new_ltEs4(vyy9700, vyy9800, cge)
new_foldFM_GE0(vyy85, vyy40, Branch(vyy3340, vyy3341, vyy3342, vyy3343, vyy3344), h, ba, bb) → new_foldFM_GE10(vyy85, vyy40, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, new_gtEs(vyy3340, vyy40, h, ba), h, ba, bb)
new_esEs28(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_ltEs8(Just(vyy970), Just(vyy980), app(ty_[], bde)) → new_ltEs7(vyy970, vyy980, bde)
new_compare0([], [], cdf) → EQ
new_esEs23(vyy3001, vyy401, ty_@0) → new_esEs16(vyy3001, vyy401)
new_pePe(True, vyy169) → True
new_primEqNat0(Zero, Zero) → True
new_esEs20(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, app(app(ty_Either, he), hf)) → new_esEs6(vyy3001, vyy401, he, hf)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_@0) → new_esEs16(vyy3000, vyy400)
new_esEs28(vyy3001, vyy401, ty_@0) → new_esEs16(vyy3001, vyy401)
new_ltEs6(vyy972, vyy982, ty_@0) → new_ltEs10(vyy972, vyy982)
new_esEs26(vyy970, vyy980, ty_@0) → new_esEs16(vyy970, vyy980)
new_esEs22(vyy3000, vyy400, app(app(ty_@2, ge), gf)) → new_esEs7(vyy3000, vyy400, ge, gf)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, app(app(ty_Either, bgc), bgd)) → new_esEs6(vyy3000, vyy400, bgc, bgd)
new_foldFM_GE10(vyy85, vyy40, vyy330, vyy331, vyy332, EmptyFM, vyy334, True, h, ba, bb) → new_foldFM_GE3(vyy330, vyy331, new_foldFM_GE0(vyy85, vyy40, vyy334, h, ba, bb), vyy40, h, ba, bb)
new_esEs26(vyy970, vyy980, ty_Bool) → new_esEs15(vyy970, vyy980)
new_compare110(vyy970, vyy980, False, cf, cg) → GT
new_esEs12(vyy970, vyy980, app(app(ty_@2, bd), be)) → new_esEs7(vyy970, vyy980, bd, be)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs28(vyy3001, vyy401, app(app(ty_Either, dbd), dbe)) → new_esEs6(vyy3001, vyy401, dbd, dbe)
new_compare28(vyy970, vyy980, cf, cg) → new_compare210(vyy970, vyy980, new_esEs6(vyy970, vyy980, cf, cg), cf, cg)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs9(vyy3000, vyy400)
new_ltEs6(vyy972, vyy982, ty_Integer) → new_ltEs17(vyy972, vyy982)
new_esEs24(vyy3002, vyy402, app(app(ty_@2, bba), bbb)) → new_esEs7(vyy3002, vyy402, bba, bbb)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy9800))) → new_primCmpNat0(vyy9800, Zero)
new_esEs26(vyy970, vyy980, ty_Ordering) → new_esEs8(vyy970, vyy980)
new_esEs8(GT, GT) → True
new_esEs9(Char(vyy3000), Char(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy1480), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1480, vyy40100)))
new_primCmpInt(Pos(Zero), Pos(Succ(vyy9800))) → new_primCmpNat1(Zero, vyy9800)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_lt20(vyy970, vyy980, ty_Bool) → new_lt9(vyy970, vyy980)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, bcg)) → new_esEs18(vyy3000, vyy400, bcg)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, app(app(app(ty_@3, cgh), cha), chb)) → new_ltEs5(vyy9700, vyy9800, cgh, cha, chb)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs15(True, True) → True
new_esEs23(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs12(Left(vyy9700), Left(vyy9800), app(ty_Maybe, cfe), cg) → new_ltEs8(vyy9700, vyy9800, cfe)
new_primPlusNat1(Succ(vyy14800), Zero) → Succ(vyy14800)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_compare27(Float(vyy970, vyy971), Float(vyy980, vyy981)) → new_compare8(new_sr(vyy970, vyy980), new_sr(vyy971, vyy981))
new_compare13(vyy970, vyy980, False) → GT
new_ltEs12(Left(vyy9700), Left(vyy9800), app(app(app(ty_@3, cff), cfg), cfh), cg) → new_ltEs5(vyy9700, vyy9800, cff, cfg, cfh)
new_esEs28(vyy3001, vyy401, app(ty_Maybe, dbh)) → new_esEs4(vyy3001, vyy401, dbh)
new_compare18(vyy970, vyy980, ty_Float) → new_compare27(vyy970, vyy980)
new_foldFM_GE10(vyy85, vyy40, vyy330, vyy331, vyy332, vyy333, vyy334, False, h, ba, bb) → new_foldFM_GE0(vyy85, vyy40, vyy334, h, ba, bb)
new_ltEs13(LT, GT) → True
new_compare16(vyy970, vyy980, True) → LT
new_esEs14([], :(vyy400, vyy401), bhe) → False
new_esEs14(:(vyy3000, vyy3001), [], bhe) → False
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], bff), beg) → new_esEs14(vyy3000, vyy400, bff)
new_primCmpNat1(Zero, vyy9700) → LT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), fh, ga, gb) → new_asAs(new_esEs22(vyy3000, vyy400, fh), new_asAs(new_esEs23(vyy3001, vyy401, ga), new_esEs24(vyy3002, vyy402, gb)))
new_ltEs8(Just(vyy970), Just(vyy980), ty_Char) → new_ltEs14(vyy970, vyy980)
new_lt4(vyy970, vyy980, app(app(ty_@2, bd), be)) → new_lt15(vyy970, vyy980, bd, be)
new_esEs26(vyy970, vyy980, app(ty_[], cbb)) → new_esEs14(vyy970, vyy980, cbb)
new_lt5(vyy971, vyy981, ty_Int) → new_lt16(vyy971, vyy981)
new_compare8(vyy97, vyy98) → new_primCmpInt(vyy97, vyy98)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primCompAux0(vyy174, GT) → GT
new_esEs18(:%(vyy3000, vyy3001), :%(vyy400, vyy401), fg) → new_asAs(new_esEs20(vyy3000, vyy400, fg), new_esEs21(vyy3001, vyy401, fg))
new_esEs8(EQ, EQ) → True
new_ltEs8(Just(vyy970), Just(vyy980), ty_Double) → new_ltEs18(vyy970, vyy980)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, app(ty_[], cgf)) → new_ltEs7(vyy9700, vyy9800, cgf)
new_lt20(vyy970, vyy980, ty_@0) → new_lt10(vyy970, vyy980)
new_lt5(vyy971, vyy981, app(app(app(ty_@3, dd), de), df)) → new_lt8(vyy971, vyy981, dd, de, df)
new_lt20(vyy970, vyy980, ty_Ordering) → new_lt13(vyy970, vyy980)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Int, cg) → new_ltEs16(vyy9700, vyy9800)
new_esEs28(vyy3001, vyy401, app(ty_[], dcb)) → new_esEs14(vyy3001, vyy401, dcb)
new_esEs22(vyy3000, vyy400, app(app(app(ty_@3, hb), hc), hd)) → new_esEs5(vyy3000, vyy400, hb, hc, hd)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Char, cg) → new_ltEs14(vyy9700, vyy9800)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_compare18(vyy970, vyy980, ty_Int) → new_compare8(vyy970, vyy980)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, bfe), beg) → new_esEs18(vyy3000, vyy400, bfe)
new_esEs28(vyy3001, vyy401, app(app(ty_@2, dbf), dbg)) → new_esEs7(vyy3001, vyy401, dbf, dbg)
new_ltEs19(vyy971, vyy981, app(ty_Ratio, cde)) → new_ltEs4(vyy971, vyy981, cde)
new_esEs23(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_esEs22(vyy3000, vyy400, app(ty_Maybe, gg)) → new_esEs4(vyy3000, vyy400, gg)
new_esEs25(vyy3000, vyy400, app(ty_Maybe, cab)) → new_esEs4(vyy3000, vyy400, cab)
new_esEs26(vyy970, vyy980, ty_Integer) → new_esEs17(vyy970, vyy980)
new_ltEs13(GT, LT) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs12(vyy970, vyy980, app(app(app(ty_@3, cc), cd), ce)) → new_esEs5(vyy970, vyy980, cc, cd, ce)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs15(vyy3000, vyy400)
new_compare10(vyy970, vyy980, False, bd, be) → GT
new_ltEs19(vyy971, vyy981, ty_Integer) → new_ltEs17(vyy971, vyy981)
new_ltEs13(EQ, EQ) → True
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, bcb), bcc)) → new_esEs6(vyy3000, vyy400, bcb, bcc)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bfg), bfh), bga), beg) → new_esEs5(vyy3000, vyy400, bfg, bfh, bga)
new_esEs22(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs7(@2(vyy3000, vyy3001), @2(vyy400, vyy401), chh, daa) → new_asAs(new_esEs27(vyy3000, vyy400, chh), new_esEs28(vyy3001, vyy401, daa))
new_esEs6(Right(vyy3000), Right(vyy400), bgb, app(ty_Maybe, bgg)) → new_esEs4(vyy3000, vyy400, bgg)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, beg) → new_esEs16(vyy3000, vyy400)
new_primEqNat0(Succ(vyy300000), Succ(vyy40000)) → new_primEqNat0(vyy300000, vyy40000)
new_esEs24(vyy3002, vyy402, ty_@0) → new_esEs16(vyy3002, vyy402)
new_esEs27(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs27(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, beg) → new_esEs9(vyy3000, vyy400)
new_esEs24(vyy3002, vyy402, app(ty_Ratio, bbd)) → new_esEs18(vyy3002, vyy402, bbd)
new_esEs13(vyy971, vyy981, app(app(app(ty_@3, dd), de), df)) → new_esEs5(vyy971, vyy981, dd, de, df)
new_lt13(vyy970, vyy980) → new_esEs8(new_compare6(vyy970, vyy980), LT)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs5(vyy3000, vyy400, bda, bdb, bdc)
new_ltEs8(Just(vyy970), Just(vyy980), app(app(ty_Either, beb), bec)) → new_ltEs12(vyy970, vyy980, beb, bec)
new_lt5(vyy971, vyy981, ty_Float) → new_lt11(vyy971, vyy981)
new_lt20(vyy970, vyy980, ty_Integer) → new_lt17(vyy970, vyy980)
new_esEs28(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_compare212(vyy970, vyy980, True, cb) → EQ
new_ltEs6(vyy972, vyy982, app(ty_Ratio, ff)) → new_ltEs4(vyy972, vyy982, ff)
new_esEs24(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_ltEs8(Just(vyy970), Nothing, bdd) → False
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Char) → new_ltEs14(vyy9700, vyy9800)
new_esEs23(vyy3001, vyy401, ty_Bool) → new_esEs15(vyy3001, vyy401)
new_esEs27(vyy3000, vyy400, app(app(app(ty_@3, dba), dbb), dbc)) → new_esEs5(vyy3000, vyy400, dba, dbb, dbc)
new_compare5(:%(vyy970, vyy971), :%(vyy980, vyy981), ty_Integer) → new_compare9(new_sr0(vyy970, vyy981), new_sr0(vyy980, vyy971))
new_esEs12(vyy970, vyy980, app(ty_Ratio, da)) → new_esEs18(vyy970, vyy980, da)
new_esEs10(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare17(vyy970, vyy980, False, cc, cd, ce) → GT
new_esEs21(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_esEs28(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs25(vyy3000, vyy400, ty_Char) → new_esEs9(vyy3000, vyy400)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_ltEs16(vyy97, vyy98) → new_not(new_esEs8(new_compare8(vyy97, vyy98), GT))
new_ltEs6(vyy972, vyy982, ty_Ordering) → new_ltEs13(vyy972, vyy982)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_@0, cg) → new_ltEs10(vyy9700, vyy9800)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy9800))) → LT
new_sr0(Integer(vyy9800), Integer(vyy9710)) → Integer(new_primMulInt(vyy9800, vyy9710))
new_lt15(vyy970, vyy980, bd, be) → new_esEs8(new_compare29(vyy970, vyy980, bd, be), LT)
new_compare13(vyy970, vyy980, True) → LT
new_lt4(vyy970, vyy980, app(ty_Maybe, cb)) → new_lt7(vyy970, vyy980, cb)
new_primPlusNat1(Succ(vyy14800), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy14800, vyy401000)))
new_lt6(vyy970, vyy980, ca) → new_esEs8(new_compare0(vyy970, vyy980, ca), LT)
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_ltEs12(Left(vyy9700), Right(vyy9800), cf, cg) → True
new_compare213(vyy970, vyy980, False, bd, be) → new_compare10(vyy970, vyy980, new_ltEs15(vyy970, vyy980, bd, be), bd, be)
new_esEs13(vyy971, vyy981, ty_Bool) → new_esEs15(vyy971, vyy981)
new_compare211(vyy970, vyy980, False) → new_compare13(vyy970, vyy980, new_ltEs9(vyy970, vyy980))
new_lt5(vyy971, vyy981, app(ty_Ratio, ec)) → new_lt18(vyy971, vyy981, ec)
new_esEs13(vyy971, vyy981, ty_@0) → new_esEs16(vyy971, vyy981)
new_compare18(vyy970, vyy980, ty_Double) → new_compare7(vyy970, vyy980)
new_lt5(vyy971, vyy981, ty_Bool) → new_lt9(vyy971, vyy981)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, bfd), beg) → new_esEs4(vyy3000, vyy400, bfd)
new_ltEs6(vyy972, vyy982, app(ty_Maybe, ee)) → new_ltEs8(vyy972, vyy982, ee)
new_primCmpNat2(Zero, Succ(vyy98000)) → LT
new_lt7(vyy970, vyy980, cb) → new_esEs8(new_compare19(vyy970, vyy980, cb), LT)
new_compare18(vyy970, vyy980, ty_Bool) → new_compare12(vyy970, vyy980)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_lt5(vyy971, vyy981, app(app(ty_@2, ea), eb)) → new_lt15(vyy971, vyy981, ea, eb)
new_lt8(vyy970, vyy980, cc, cd, ce) → new_esEs8(new_compare14(vyy970, vyy980, cc, cd, ce), LT)
new_compare24(vyy970, vyy980, True) → EQ
new_esEs27(vyy3000, vyy400, app(app(ty_@2, dad), dae)) → new_esEs7(vyy3000, vyy400, dad, dae)
new_foldFM_GE10(vyy85, vyy40, vyy330, vyy331, vyy332, Branch(vyy3330, vyy3331, vyy3332, vyy3333, vyy3334), vyy334, True, h, ba, bb) → new_foldFM_GE20(vyy330, vyy331, new_foldFM_GE0(vyy85, vyy40, vyy334, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb)
new_lt5(vyy971, vyy981, ty_Char) → new_lt14(vyy971, vyy981)
new_ltEs19(vyy971, vyy981, ty_Double) → new_ltEs18(vyy971, vyy981)
new_ltEs13(GT, EQ) → False
new_ltEs13(EQ, LT) → False
new_esEs22(vyy3000, vyy400, ty_@0) → new_esEs16(vyy3000, vyy400)
new_esEs27(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_lt19(vyy970, vyy980) → new_esEs8(new_compare7(vyy970, vyy980), LT)
new_primCompAux0(vyy174, LT) → LT
new_ltEs4(vyy97, vyy98, bc) → new_not(new_esEs8(new_compare5(vyy97, vyy98, bc), GT))
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, bfb), bfc), beg) → new_esEs7(vyy3000, vyy400, bfb, bfc)
new_esEs12(vyy970, vyy980, ty_Integer) → new_esEs17(vyy970, vyy980)
new_esEs11(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_not(False) → True
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, beh), bfa), beg) → new_esEs6(vyy3000, vyy400, beh, bfa)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, beg) → new_esEs15(vyy3000, vyy400)
new_compare210(vyy970, vyy980, True, cf, cg) → EQ
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_ltEs19(vyy971, vyy981, app(app(ty_Either, cda), cdb)) → new_ltEs12(vyy971, vyy981, cda, cdb)
new_esEs24(vyy3002, vyy402, app(app(ty_Either, bag), bah)) → new_esEs6(vyy3002, vyy402, bag, bah)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, app(app(ty_Either, chc), chd)) → new_ltEs12(vyy9700, vyy9800, chc, chd)
new_esEs26(vyy970, vyy980, app(ty_Ratio, ccc)) → new_esEs18(vyy970, vyy980, ccc)
new_ltEs12(Right(vyy9700), Left(vyy9800), cf, cg) → False
new_esEs28(vyy3001, vyy401, ty_Char) → new_esEs9(vyy3001, vyy401)
new_esEs25(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs24(vyy3002, vyy402, app(ty_[], bbe)) → new_esEs14(vyy3002, vyy402, bbe)
new_compare0(:(vyy970, vyy971), [], cdf) → GT
new_ltEs6(vyy972, vyy982, ty_Double) → new_ltEs18(vyy972, vyy982)
new_esEs27(vyy3000, vyy400, app(app(ty_Either, dab), dac)) → new_esEs6(vyy3000, vyy400, dab, dac)
new_esEs13(vyy971, vyy981, ty_Char) → new_esEs9(vyy971, vyy981)
new_esEs27(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_lt4(vyy970, vyy980, ty_Double) → new_lt19(vyy970, vyy980)
new_compare18(vyy970, vyy980, app(ty_[], cdg)) → new_compare0(vyy970, vyy980, cdg)
new_primCmpInt(Pos(Succ(vyy9700)), Neg(vyy980)) → GT
new_esEs13(vyy971, vyy981, app(app(ty_Either, dg), dh)) → new_esEs6(vyy971, vyy981, dg, dh)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare5(:%(vyy970, vyy971), :%(vyy980, vyy981), ty_Int) → new_compare8(new_sr(vyy970, vyy981), new_sr(vyy980, vyy971))
new_ltEs6(vyy972, vyy982, ty_Char) → new_ltEs14(vyy972, vyy982)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Ordering) → new_ltEs13(vyy970, vyy980)
new_ltEs9(True, True) → True
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Double) → new_esEs19(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs19(vyy971, vyy981, app(ty_Maybe, cce)) → new_ltEs8(vyy971, vyy981, cce)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs24(vyy3002, vyy402, ty_Bool) → new_esEs15(vyy3002, vyy402)
new_compare12(vyy970, vyy980) → new_compare211(vyy970, vyy980, new_esEs15(vyy970, vyy980))
new_primEqNat0(Zero, Succ(vyy40000)) → False
new_primEqNat0(Succ(vyy300000), Zero) → False
new_esEs26(vyy970, vyy980, app(app(ty_@2, cca), ccb)) → new_esEs7(vyy970, vyy980, cca, ccb)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs9(False, False) → True
new_esEs23(vyy3001, vyy401, app(ty_Ratio, bab)) → new_esEs18(vyy3001, vyy401, bab)
new_ltEs10(vyy97, vyy98) → new_not(new_esEs8(new_compare26(vyy97, vyy98), GT))
new_esEs4(Nothing, Nothing, bca) → True
new_esEs12(vyy970, vyy980, ty_Double) → new_esEs19(vyy970, vyy980)
new_primCmpInt(Pos(Succ(vyy9700)), Pos(vyy980)) → new_primCmpNat0(vyy9700, vyy980)
new_primCmpNat2(Succ(vyy97000), Succ(vyy98000)) → new_primCmpNat2(vyy97000, vyy98000)
new_esEs13(vyy971, vyy981, app(app(ty_@2, ea), eb)) → new_esEs7(vyy971, vyy981, ea, eb)
new_ltEs12(Left(vyy9700), Left(vyy9800), app(app(ty_Either, cga), cgb), cg) → new_ltEs12(vyy9700, vyy9800, cga, cgb)
new_primCmpNat0(vyy9700, Zero) → GT
new_esEs23(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_lt20(vyy970, vyy980, ty_Char) → new_lt14(vyy970, vyy980)
new_esEs27(vyy3000, vyy400, app(ty_Maybe, daf)) → new_esEs4(vyy3000, vyy400, daf)
new_lt4(vyy970, vyy980, app(ty_[], ca)) → new_lt6(vyy970, vyy980, ca)
new_compare6(vyy970, vyy980) → new_compare24(vyy970, vyy980, new_esEs8(vyy970, vyy980))
new_lt4(vyy970, vyy980, app(ty_Ratio, da)) → new_lt18(vyy970, vyy980, da)
new_esEs23(vyy3001, vyy401, app(ty_[], bac)) → new_esEs14(vyy3001, vyy401, bac)
new_esEs24(vyy3002, vyy402, ty_Double) → new_esEs19(vyy3002, vyy402)
new_lt12(vyy970, vyy980, cf, cg) → new_esEs8(new_compare28(vyy970, vyy980, cf, cg), LT)
new_esEs12(vyy970, vyy980, ty_@0) → new_esEs16(vyy970, vyy980)
new_ltEs15(@2(vyy970, vyy971), @2(vyy980, vyy981), cah, cba) → new_pePe(new_lt20(vyy970, vyy980, cah), new_asAs(new_esEs26(vyy970, vyy980, cah), new_ltEs19(vyy971, vyy981, cba)))
new_primCmpInt(Pos(Zero), Neg(Succ(vyy9800))) → GT
new_lt20(vyy970, vyy980, app(app(ty_@2, cca), ccb)) → new_lt15(vyy970, vyy980, cca, ccb)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, app(ty_[], bha)) → new_esEs14(vyy3000, vyy400, bha)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, beg) → new_esEs8(vyy3000, vyy400)
new_lt9(vyy970, vyy980) → new_esEs8(new_compare12(vyy970, vyy980), LT)
new_compare0(:(vyy970, vyy971), :(vyy980, vyy981), cdf) → new_primCompAux1(vyy970, vyy980, new_compare0(vyy971, vyy981, cdf), cdf)
new_ltEs19(vyy971, vyy981, app(ty_[], ccd)) → new_ltEs7(vyy971, vyy981, ccd)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], bch)) → new_esEs14(vyy3000, vyy400, bch)
new_ltEs19(vyy971, vyy981, ty_Char) → new_ltEs14(vyy971, vyy981)
new_esEs24(vyy3002, vyy402, ty_Int) → new_esEs11(vyy3002, vyy402)
new_esEs13(vyy971, vyy981, app(ty_Ratio, ec)) → new_esEs18(vyy971, vyy981, ec)
new_lt5(vyy971, vyy981, app(ty_Maybe, dc)) → new_lt7(vyy971, vyy981, dc)
new_ltEs17(vyy97, vyy98) → new_not(new_esEs8(new_compare9(vyy97, vyy98), GT))
new_lt4(vyy970, vyy980, ty_Ordering) → new_lt13(vyy970, vyy980)
new_esEs21(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Bool) → new_ltEs9(vyy970, vyy980)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Int) → new_esEs11(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Integer, cg) → new_ltEs17(vyy9700, vyy9800)
new_compare18(vyy970, vyy980, app(app(ty_Either, ced), cee)) → new_compare28(vyy970, vyy980, ced, cee)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare18(vyy970, vyy980, app(app(ty_@2, cef), ceg)) → new_compare29(vyy970, vyy980, cef, ceg)
new_ltEs18(vyy97, vyy98) → new_not(new_esEs8(new_compare7(vyy97, vyy98), GT))
new_esEs12(vyy970, vyy980, app(app(ty_Either, cf), cg)) → new_esEs6(vyy970, vyy980, cf, cg)
new_ltEs8(Just(vyy970), Just(vyy980), app(ty_Maybe, bdf)) → new_ltEs8(vyy970, vyy980, bdf)
new_lt20(vyy970, vyy980, app(ty_Maybe, cbc)) → new_lt7(vyy970, vyy980, cbc)
new_ltEs13(GT, GT) → True
new_foldFM_GE20(vyy330, vyy331, vyy110, vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, h, ba, bb) → new_foldFM_GE10(new_fmToList_GE0(vyy330, vyy331, vyy110, h, ba, bb), vyy40, vyy3330, vyy3331, vyy3332, vyy3333, vyy3334, new_gtEs(vyy3330, vyy40, h, ba), h, ba, bb)
new_esEs12(vyy970, vyy980, app(ty_Maybe, cb)) → new_esEs4(vyy970, vyy980, cb)
new_compare9(Integer(vyy970), Integer(vyy980)) → new_primCmpInt(vyy970, vyy980)
new_asAs(False, vyy137) → False
new_lt4(vyy970, vyy980, ty_Integer) → new_lt17(vyy970, vyy980)
new_lt20(vyy970, vyy980, ty_Double) → new_lt19(vyy970, vyy980)
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Bool) → new_ltEs9(vyy9700, vyy9800)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, app(ty_Ratio, chg)) → new_ltEs4(vyy9700, vyy9800, chg)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_compare14(vyy970, vyy980, cc, cd, ce) → new_compare25(vyy970, vyy980, new_esEs5(vyy970, vyy980, cc, cd, ce), cc, cd, ce)
new_esEs25(vyy3000, vyy400, ty_@0) → new_esEs16(vyy3000, vyy400)
new_lt5(vyy971, vyy981, ty_@0) → new_lt10(vyy971, vyy981)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, app(ty_Ratio, bgh)) → new_esEs18(vyy3000, vyy400, bgh)
new_esEs24(vyy3002, vyy402, ty_Float) → new_esEs10(vyy3002, vyy402)
new_esEs23(vyy3001, vyy401, app(app(ty_@2, hg), hh)) → new_esEs7(vyy3001, vyy401, hg, hh)
new_ltEs19(vyy971, vyy981, ty_@0) → new_ltEs10(vyy971, vyy981)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Double, cg) → new_ltEs18(vyy9700, vyy9800)
new_primCmpNat1(Succ(vyy9800), vyy9700) → new_primCmpNat2(vyy9800, vyy9700)
new_esEs24(vyy3002, vyy402, ty_Integer) → new_esEs17(vyy3002, vyy402)
new_primCmpNat2(Succ(vyy97000), Zero) → GT
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs19(vyy3000, vyy400)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Int) → new_ltEs16(vyy970, vyy980)
new_compare11(Char(vyy970), Char(vyy980)) → new_primCmpInt(vyy970, vyy980)
new_ltEs9(False, True) → True
new_esEs23(vyy3001, vyy401, ty_Char) → new_esEs9(vyy3001, vyy401)
new_foldFM_GE3(vyy330, vyy331, vyy109, vyy40, h, ba, bb) → new_fmToList_GE0(vyy330, vyy331, vyy109, h, ba, bb)
new_esEs16(@0, @0) → True
new_lt20(vyy970, vyy980, app(ty_Ratio, ccc)) → new_lt18(vyy970, vyy980, ccc)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_@0) → new_ltEs10(vyy9700, vyy9800)
new_ltEs19(vyy971, vyy981, ty_Int) → new_ltEs16(vyy971, vyy981)
new_esEs26(vyy970, vyy980, ty_Double) → new_esEs19(vyy970, vyy980)
new_lt18(vyy970, vyy980, da) → new_esEs8(new_compare5(vyy970, vyy980, da), LT)
new_lt14(vyy970, vyy980) → new_esEs8(new_compare11(vyy970, vyy980), LT)
new_ltEs6(vyy972, vyy982, app(ty_[], ed)) → new_ltEs7(vyy972, vyy982, ed)
new_esEs22(vyy3000, vyy400, ty_Bool) → new_esEs15(vyy3000, vyy400)
new_esEs28(vyy3001, vyy401, ty_Bool) → new_esEs15(vyy3001, vyy401)
new_ltEs19(vyy971, vyy981, app(app(app(ty_@3, ccf), ccg), cch)) → new_ltEs5(vyy971, vyy981, ccf, ccg, cch)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Ordering) → new_ltEs13(vyy9700, vyy9800)
new_compare26(@0, @0) → EQ
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs11(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Bool, cg) → new_ltEs9(vyy9700, vyy9800)
new_compare29(vyy970, vyy980, bd, be) → new_compare213(vyy970, vyy980, new_esEs7(vyy970, vyy980, bd, be), bd, be)
new_ltEs8(Nothing, Nothing, bdd) → True
new_lt20(vyy970, vyy980, ty_Float) → new_lt11(vyy970, vyy980)
new_ltEs19(vyy971, vyy981, app(app(ty_@2, cdc), cdd)) → new_ltEs15(vyy971, vyy981, cdc, cdd)
new_esEs25(vyy3000, vyy400, app(app(app(ty_@3, cae), caf), cag)) → new_esEs5(vyy3000, vyy400, cae, caf, cag)
new_compare25(vyy970, vyy980, False, cc, cd, ce) → new_compare17(vyy970, vyy980, new_ltEs5(vyy970, vyy980, cc, cd, ce), cc, cd, ce)
new_esEs22(vyy3000, vyy400, app(app(ty_Either, gc), gd)) → new_esEs6(vyy3000, vyy400, gc, gd)
new_lt5(vyy971, vyy981, app(app(ty_Either, dg), dh)) → new_lt12(vyy971, vyy981, dg, dh)
new_esEs22(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_lt4(vyy970, vyy980, ty_Bool) → new_lt9(vyy970, vyy980)
new_esEs12(vyy970, vyy980, ty_Int) → new_esEs11(vyy970, vyy980)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, bcd), bce)) → new_esEs7(vyy3000, vyy400, bcd, bce)
new_ltEs8(Just(vyy970), Just(vyy980), app(app(ty_@2, bed), bee)) → new_ltEs15(vyy970, vyy980, bed, bee)
new_esEs26(vyy970, vyy980, ty_Char) → new_esEs9(vyy970, vyy980)
new_ltEs13(LT, LT) → True
new_esEs22(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs26(vyy970, vyy980, app(app(ty_Either, cbg), cbh)) → new_esEs6(vyy970, vyy980, cbg, cbh)
new_compare213(vyy970, vyy980, True, bd, be) → EQ
new_compare0([], :(vyy980, vyy981), cdf) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_compare15(vyy970, vyy980, True, cb) → LT
new_esEs12(vyy970, vyy980, ty_Ordering) → new_esEs8(vyy970, vyy980)
new_esEs27(vyy3000, vyy400, app(ty_[], dah)) → new_esEs14(vyy3000, vyy400, dah)
new_lt4(vyy970, vyy980, app(app(app(ty_@3, cc), cd), ce)) → new_lt8(vyy970, vyy980, cc, cd, ce)
new_esEs13(vyy971, vyy981, ty_Ordering) → new_esEs8(vyy971, vyy981)
new_esEs12(vyy970, vyy980, app(ty_[], ca)) → new_esEs14(vyy970, vyy980, ca)
new_asAs(True, vyy137) → vyy137
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs26(vyy970, vyy980, app(app(app(ty_@3, cbd), cbe), cbf)) → new_esEs5(vyy970, vyy980, cbd, cbe, cbf)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs28(vyy3001, vyy401, app(ty_Ratio, dca)) → new_esEs18(vyy3001, vyy401, dca)
new_compare18(vyy970, vyy980, ty_Integer) → new_compare9(vyy970, vyy980)
new_esEs27(vyy3000, vyy400, ty_Bool) → new_esEs15(vyy3000, vyy400)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Float) → new_ltEs11(vyy9700, vyy9800)
new_compare211(vyy970, vyy980, True) → EQ
new_ltEs8(Just(vyy970), Just(vyy980), app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs5(vyy970, vyy980, bdg, bdh, bea)
new_esEs23(vyy3001, vyy401, app(app(app(ty_@3, bad), bae), baf)) → new_esEs5(vyy3001, vyy401, bad, bae, baf)
new_lt4(vyy970, vyy980, app(app(ty_Either, cf), cg)) → new_lt12(vyy970, vyy980, cf, cg)
new_ltEs7(vyy97, vyy98, cdf) → new_not(new_esEs8(new_compare0(vyy97, vyy98, cdf), GT))
new_compare210(vyy970, vyy980, False, cf, cg) → new_compare110(vyy970, vyy980, new_ltEs12(vyy970, vyy980, cf, cg), cf, cg)
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs16(vyy3000, vyy400)
new_compare18(vyy970, vyy980, ty_@0) → new_compare26(vyy970, vyy980)
new_lt5(vyy971, vyy981, app(ty_[], db)) → new_lt6(vyy971, vyy981, db)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare212(vyy970, vyy980, False, cb) → new_compare15(vyy970, vyy980, new_ltEs8(vyy970, vyy980, cb), cb)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs5(vyy3000, vyy400, bhb, bhc, bhd)
new_primCompAux0(vyy174, EQ) → vyy174
new_lt10(vyy970, vyy980) → new_esEs8(new_compare26(vyy970, vyy980), LT)
new_foldFM_GE0(vyy85, vyy40, EmptyFM, h, ba, bb) → vyy85
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_compare18(vyy970, vyy980, ty_Char) → new_compare11(vyy970, vyy980)
new_esEs27(vyy3000, vyy400, ty_Char) → new_esEs9(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy9700)), Pos(vyy980)) → LT
new_ltEs19(vyy971, vyy981, ty_Ordering) → new_ltEs13(vyy971, vyy981)
new_not(True) → False
new_compare16(vyy970, vyy980, False) → GT
new_esEs15(False, False) → True
new_esEs27(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)

The set Q consists of the following terms:

new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Float)
new_compare5(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_compare110(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_@0)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, ty_@0)
new_compare6(x0, x1)
new_ltEs12(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_compare213(x0, x1, True, x2, x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_fmToList_GE0(x0, x1, x2, x3, x4, x5)
new_lt6(x0, x1, x2)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs8(Just(x0), Nothing, x1)
new_esEs24(x0, x1, ty_@0)
new_primCmpNat2(Zero, Succ(x0))
new_esEs12(x0, x1, ty_Bool)
new_esEs12(x0, x1, ty_Int)
new_ltEs18(x0, x1)
new_lt20(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs12(Left(x0), Left(x1), ty_Double, x2)
new_esEs13(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs17(x0, x1)
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs15(True, True)
new_ltEs7(x0, x1, x2)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Zero, Succ(x0))
new_compare18(x0, x1, app(ty_Maybe, x2))
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs25(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primMulNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, True)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs24(x0, x1, ty_Char)
new_lt7(x0, x1, x2)
new_esEs28(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_gtEs(x0, x1, x2, x3)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_lt4(x0, x1, ty_Float)
new_esEs15(False, False)
new_compare15(x0, x1, False, x2)
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, x2)
new_ltEs12(Left(x0), Left(x1), ty_Ordering, x2)
new_lt4(x0, x1, ty_Integer)
new_ltEs12(Left(x0), Left(x1), ty_Float, x2)
new_esEs12(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs12(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs6(x0, x1, ty_@0)
new_esEs8(LT, LT)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs16(@0, @0)
new_foldFM_GE10(x0, x1, x2, x3, x4, EmptyFM, x5, True, x6, x7, x8)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs26(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(True, x0)
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_esEs13(x0, x1, ty_Integer)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_compare0([], [], x0)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare16(x0, x1, True)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, ty_Char)
new_esEs14([], [], x0)
new_esEs28(x0, x1, ty_Integer)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, ty_Char)
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_ltEs13(EQ, EQ)
new_ltEs19(x0, x1, ty_Ordering)
new_compare0([], :(x0, x1), x2)
new_esEs26(x0, x1, ty_Float)
new_ltEs9(False, False)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_foldFM_GE20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs22(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_compare18(x0, x1, ty_Float)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs11(x0, x1)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_lt18(x0, x1, x2)
new_ltEs12(Left(x0), Left(x1), ty_@0, x2)
new_esEs22(x0, x1, ty_Bool)
new_lt5(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(x0, x1, ty_Bool)
new_compare18(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs28(x0, x1, ty_Char)
new_esEs14(:(x0, x1), [], x2)
new_ltEs13(LT, EQ)
new_ltEs13(EQ, LT)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_lt5(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_ltEs6(x0, x1, ty_Char)
new_esEs14([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs6(x0, x1, ty_Ordering)
new_lt5(x0, x1, ty_Int)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_foldFM_GE10(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, True, x11, x12, x13)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_compare18(x0, x1, ty_Bool)
new_ltEs12(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_ltEs8(Nothing, Nothing, x0)
new_lt9(x0, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, ty_Bool)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs12(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, ty_Float)
new_ltEs12(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare0(:(x0, x1), [], x2)
new_ltEs4(x0, x1, x2)
new_ltEs19(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Char)
new_ltEs12(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare10(x0, x1, True, x2, x3)
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_compare211(x0, x1, False)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(x0, x1)
new_compare18(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_primPlusNat1(Zero, Zero)
new_primCmpNat1(Zero, x0)
new_primCmpNat2(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare27(Float(x0, x1), Float(x2, x3))
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_asAs(True, x0)
new_primPlusNat1(Succ(x0), Zero)
new_compare29(x0, x1, x2, x3)
new_ltEs11(x0, x1)
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs24(x0, x1, ty_Double)
new_primCmpNat1(Succ(x0), x1)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Int)
new_compare15(x0, x1, True, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare18(x0, x1, ty_@0)
new_lt5(x0, x1, ty_Ordering)
new_ltEs9(False, True)
new_ltEs9(True, False)
new_compare9(Integer(x0), Integer(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs9(True, True)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_ltEs13(EQ, GT)
new_esEs28(x0, x1, ty_Int)
new_ltEs13(GT, EQ)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs19(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt4(x0, x1, ty_@0)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs12(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs23(x0, x1, ty_Bool)
new_primCompAux0(x0, EQ)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs13(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Ordering)
new_compare16(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs12(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, ty_Int)
new_esEs12(x0, x1, app(ty_[], x2))
new_ltEs13(LT, GT)
new_ltEs13(GT, LT)
new_compare213(x0, x1, False, x2, x3)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare212(x0, x1, False, x2)
new_ltEs12(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs15(True, False)
new_esEs15(False, True)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, ty_Bool)
new_compare11(Char(x0), Char(x1))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare210(x0, x1, False, x2, x3)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, ty_Float)
new_ltEs12(Right(x0), Right(x1), x2, ty_Float)
new_esEs12(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs13(x0, x1, ty_Char)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare14(x0, x1, x2, x3, x4)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare18(x0, x1, ty_Double)
new_sr0(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_foldFM_GE10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_esEs21(x0, x1, ty_Int)
new_compare210(x0, x1, True, x2, x3)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare24(x0, x1, False)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare8(x0, x1)
new_esEs13(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs13(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs20(x0, x1, ty_Int)
new_primCompAux1(x0, x1, x2, x3)
new_lt8(x0, x1, x2, x3, x4)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs9(Char(x0), Char(x1))
new_lt5(x0, x1, app(ty_[], x2))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_lt16(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Integer)
new_esEs12(x0, x1, ty_Ordering)
new_lt17(x0, x1)
new_ltEs12(Right(x0), Right(x1), x2, ty_Bool)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Zero, x0)
new_esEs23(x0, x1, ty_@0)
new_compare18(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs17(Integer(x0), Integer(x1))
new_compare24(x0, x1, True)
new_esEs24(x0, x1, ty_Ordering)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_esEs13(x0, x1, app(ty_Ratio, x2))
new_ltEs13(LT, LT)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Int)
new_compare28(x0, x1, x2, x3)
new_lt5(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Double)
new_compare5(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_compare18(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Ordering)
new_lt11(x0, x1)
new_ltEs12(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Bool)
new_compare17(x0, x1, False, x2, x3, x4)
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_[], x2))
new_primCmpNat2(Succ(x0), Zero)
new_ltEs12(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_@0)
new_ltEs13(GT, GT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt19(x0, x1)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs27(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, False, x2, x3)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(False, x0)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare212(x0, x1, True, x2)
new_primCmpNat2(Succ(x0), Succ(x1))
new_not(True)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_esEs13(x0, x1, ty_Int)
new_foldFM_GE3(x0, x1, x2, x3, x4, x5, x6)
new_compare18(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs19(x0, x1, ty_Double)
new_esEs13(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Nothing, Just(x0), x1)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare17(x0, x1, True, x2, x3, x4)
new_lt20(x0, x1, app(ty_[], x2))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs14(x0, x1)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(Nothing, Just(x0), x1)
new_foldFM_GE0(x0, x1, EmptyFM, x2, x3, x4)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Double)
new_primEqNat0(Succ(x0), Succ(x1))
new_lt15(x0, x1, x2, x3)
new_lt10(x0, x1)
new_ltEs16(x0, x1)
new_esEs27(x0, x1, ty_Double)
new_ltEs12(Right(x0), Right(x1), x2, ty_Double)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Left(x0), Right(x1), x2, x3)
new_ltEs12(Right(x0), Left(x1), x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Just(x0), Nothing, x1)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Bool)
new_lt4(x0, x1, ty_Bool)
new_compare110(x0, x1, True, x2, x3)
new_lt20(x0, x1, ty_Double)
new_esEs13(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Double)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_Char)
new_lt13(x0, x1)
new_compare26(@0, @0)
new_primCmpNat0(x0, Zero)
new_compare211(x0, x1, True)
new_primCmpNat0(x0, Succ(x1))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs4(Nothing, Nothing, x0)
new_ltEs12(Right(x0), Right(x1), x2, ty_@0)
new_lt14(x0, x1)
new_ltEs12(Left(x0), Left(x1), ty_Int, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, ty_Double)
new_primEqNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_compare25(x0, x1, False, x2, x3, x4)
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_primCompAux0(x0, GT)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs13(x0, x1, ty_@0)
new_compare12(x0, x1)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, False)
new_foldFM_GE0(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_primCompAux0(x0, LT)
new_esEs22(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Double)

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

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



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

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

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

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

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



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

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

new_foldFM_GE21(vyy170, vyy171, vyy108, vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb) → new_foldFM_GE11(new_fmToList_GE0(vyy170, vyy171, vyy108, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, new_gtEs0(vyy1730, vyy13, h, ba), h, ba, bb)
new_foldFM_GE11(vyy84, vyy13, vyy170, vyy171, vyy172, Branch(vyy1730, vyy1731, vyy1732, vyy1733, vyy1734), vyy174, True, h, ba, bb) → new_foldFM_GE4(vyy84, vyy13, vyy174, h, ba, bb)
new_foldFM_GE11(vyy84, vyy13, vyy170, vyy171, vyy172, Branch(vyy1730, vyy1731, vyy1732, vyy1733, vyy1734), vyy174, True, h, ba, bb) → new_foldFM_GE21(vyy170, vyy171, new_foldFM_GE5(vyy84, vyy13, vyy174, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb)
new_foldFM_GE4(vyy84, vyy13, Branch(vyy1740, vyy1741, vyy1742, vyy1743, vyy1744), h, ba, bb) → new_foldFM_GE11(vyy84, vyy13, vyy1740, vyy1741, vyy1742, vyy1743, vyy1744, new_gtEs0(vyy1740, vyy13, h, ba), h, ba, bb)
new_foldFM_GE11(vyy84, vyy13, vyy170, vyy171, vyy172, vyy173, Branch(vyy1740, vyy1741, vyy1742, vyy1743, vyy1744), False, h, ba, bb) → new_foldFM_GE11(vyy84, vyy13, vyy1740, vyy1741, vyy1742, vyy1743, vyy1744, new_gtEs0(vyy1740, vyy13, h, ba), h, ba, bb)
new_foldFM_GE11(vyy84, vyy13, vyy170, vyy171, vyy172, EmptyFM, vyy174, True, h, ba, bb) → new_foldFM_GE4(vyy84, vyy13, vyy174, h, ba, bb)

The TRS R consists of the following rules:

new_esEs25(vyy3000, vyy400, app(ty_[], cad)) → new_esEs14(vyy3000, vyy400, cad)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, bcf)) → new_esEs4(vyy3000, vyy400, bcf)
new_esEs28(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_ltEs6(vyy972, vyy982, ty_Float) → new_ltEs11(vyy972, vyy982)
new_primCmpNat0(vyy9700, Succ(vyy9800)) → new_primCmpNat2(vyy9700, vyy9800)
new_ltEs6(vyy972, vyy982, app(app(ty_@2, fc), fd)) → new_ltEs15(vyy972, vyy982, fc, fd)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_lt20(vyy970, vyy980, ty_Int) → new_lt16(vyy970, vyy980)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, app(app(ty_@2, chb), chc)) → new_ltEs15(vyy9700, vyy9800, chb, chc)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Float) → new_ltEs11(vyy970, vyy980)
new_esEs25(vyy3000, vyy400, ty_Bool) → new_esEs15(vyy3000, vyy400)
new_ltEs6(vyy972, vyy982, ty_Int) → new_ltEs16(vyy972, vyy982)
new_lt4(vyy970, vyy980, ty_Int) → new_lt16(vyy970, vyy980)
new_esEs24(vyy3002, vyy402, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs5(vyy3002, vyy402, bbf, bbg, bbh)
new_esEs28(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, beg) → new_esEs17(vyy3000, vyy400)
new_compare110(vyy970, vyy980, True, cf, cg) → LT
new_esEs27(vyy3000, vyy400, app(ty_Ratio, dad)) → new_esEs18(vyy3000, vyy400, dad)
new_esEs13(vyy971, vyy981, ty_Float) → new_esEs10(vyy971, vyy981)
new_compare10(vyy970, vyy980, True, bd, be) → LT
new_esEs26(vyy970, vyy980, ty_Float) → new_esEs10(vyy970, vyy980)
new_esEs24(vyy3002, vyy402, ty_Char) → new_esEs9(vyy3002, vyy402)
new_esEs24(vyy3002, vyy402, app(ty_Maybe, bbc)) → new_esEs4(vyy3002, vyy402, bbc)
new_esEs4(Nothing, Just(vyy400), bca) → False
new_esEs4(Just(vyy3000), Nothing, bca) → False
new_lt20(vyy970, vyy980, app(app(app(ty_@3, cbd), cbe), cbf)) → new_lt8(vyy970, vyy980, cbd, cbe, cbf)
new_ltEs14(vyy97, vyy98) → new_not(new_esEs8(new_compare11(vyy97, vyy98), GT))
new_ltEs19(vyy971, vyy981, ty_Float) → new_ltEs11(vyy971, vyy981)
new_ltEs8(Just(vyy970), Just(vyy980), app(ty_Ratio, bef)) → new_ltEs4(vyy970, vyy980, bef)
new_compare7(Double(vyy970, vyy971), Double(vyy980, vyy981)) → new_compare8(new_sr(vyy970, vyy980), new_sr(vyy971, vyy981))
new_primCompAux1(vyy970, vyy980, vyy170, cdf) → new_primCompAux0(vyy170, new_compare18(vyy970, vyy980, cdf))
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Double) → new_ltEs18(vyy9700, vyy9800)
new_fmToList_GE0(vyy170, vyy171, vyy107, h, ba, bb) → :(@2(vyy170, vyy171), vyy107)
new_ltEs8(Just(vyy970), Just(vyy980), ty_@0) → new_ltEs10(vyy970, vyy980)
new_foldFM_GE12(vyy84, vyy13, vyy170, vyy171, vyy172, Branch(vyy1730, vyy1731, vyy1732, vyy1733, vyy1734), vyy174, True, h, ba, bb) → new_foldFM_GE22(vyy170, vyy171, new_foldFM_GE5(vyy84, vyy13, vyy174, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb)
new_compare19(vyy970, vyy980, cb) → new_compare212(vyy970, vyy980, new_esEs4(vyy970, vyy980, cb), cb)
new_esEs13(vyy971, vyy981, app(ty_[], db)) → new_esEs14(vyy971, vyy981, db)
new_lt4(vyy970, vyy980, ty_Float) → new_lt11(vyy970, vyy980)
new_lt16(vyy970, vyy980) → new_esEs8(new_compare8(vyy970, vyy980), LT)
new_primMulNat0(Zero, Zero) → Zero
new_esEs13(vyy971, vyy981, ty_Integer) → new_esEs17(vyy971, vyy981)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Bool) → new_esEs15(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, app(app(ty_@2, bge), bgf)) → new_esEs7(vyy3000, vyy400, bge, bgf)
new_ltEs6(vyy972, vyy982, app(app(ty_Either, fa), fb)) → new_ltEs12(vyy972, vyy982, fa, fb)
new_esEs25(vyy3000, vyy400, app(app(ty_Either, bhf), bhg)) → new_esEs6(vyy3000, vyy400, bhf, bhg)
new_ltEs6(vyy972, vyy982, app(app(app(ty_@3, ef), eg), eh)) → new_ltEs5(vyy972, vyy982, ef, eg, eh)
new_esEs12(vyy970, vyy980, ty_Bool) → new_esEs15(vyy970, vyy980)
new_esEs22(vyy3000, vyy400, ty_Char) → new_esEs9(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, beg) → new_esEs19(vyy3000, vyy400)
new_compare18(vyy970, vyy980, app(ty_Ratio, ceh)) → new_compare5(vyy970, vyy980, ceh)
new_esEs13(vyy971, vyy981, ty_Int) → new_esEs11(vyy971, vyy981)
new_esEs13(vyy971, vyy981, ty_Double) → new_esEs19(vyy971, vyy981)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Integer) → new_ltEs17(vyy9700, vyy9800)
new_compare24(vyy970, vyy980, False) → new_compare16(vyy970, vyy980, new_ltEs13(vyy970, vyy980))
new_ltEs12(Left(vyy9700), Left(vyy9800), app(app(ty_@2, cfh), cga), cg) → new_ltEs15(vyy9700, vyy9800, cfh, cga)
new_lt20(vyy970, vyy980, app(app(ty_Either, cbg), cbh)) → new_lt12(vyy970, vyy980, cbg, cbh)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Integer) → new_ltEs17(vyy970, vyy980)
new_lt20(vyy970, vyy980, app(ty_[], cbb)) → new_lt6(vyy970, vyy980, cbb)
new_esEs25(vyy3000, vyy400, app(ty_Ratio, cac)) → new_esEs18(vyy3000, vyy400, cac)
new_ltEs9(True, False) → False
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, beg) → new_esEs10(vyy3000, vyy400)
new_lt5(vyy971, vyy981, ty_Ordering) → new_lt13(vyy971, vyy981)
new_ltEs5(@3(vyy970, vyy971, vyy972), @3(vyy980, vyy981, vyy982), bf, bg, bh) → new_pePe(new_lt4(vyy970, vyy980, bf), new_asAs(new_esEs12(vyy970, vyy980, bf), new_pePe(new_lt5(vyy971, vyy981, bg), new_asAs(new_esEs13(vyy971, vyy981, bg), new_ltEs6(vyy972, vyy982, bh)))))
new_esEs23(vyy3001, vyy401, app(ty_Maybe, baa)) → new_esEs4(vyy3001, vyy401, baa)
new_compare18(vyy970, vyy980, app(app(app(ty_@3, cea), ceb), cec)) → new_compare14(vyy970, vyy980, cea, ceb, cec)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Char) → new_esEs9(vyy3000, vyy400)
new_lt4(vyy970, vyy980, ty_Char) → new_lt14(vyy970, vyy980)
new_lt5(vyy971, vyy981, ty_Integer) → new_lt17(vyy971, vyy981)
new_foldFM_GE22(vyy170, vyy171, vyy108, vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, h, ba, bb) → new_foldFM_GE12(new_fmToList_GE0(vyy170, vyy171, vyy108, h, ba, bb), vyy13, vyy1730, vyy1731, vyy1732, vyy1733, vyy1734, new_gtEs0(vyy1730, vyy13, h, ba), h, ba, bb)
new_ltEs13(LT, EQ) → True
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, beg) → new_esEs11(vyy3000, vyy400)
new_compare18(vyy970, vyy980, ty_Ordering) → new_compare6(vyy970, vyy980)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs17(vyy3000, vyy400)
new_compare17(vyy970, vyy980, True, cc, cd, ce) → LT
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_ltEs6(vyy972, vyy982, ty_Bool) → new_ltEs9(vyy972, vyy982)
new_lt11(vyy970, vyy980) → new_esEs8(new_compare27(vyy970, vyy980), LT)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, app(ty_Maybe, cgd)) → new_ltEs8(vyy9700, vyy9800, cgd)
new_esEs26(vyy970, vyy980, app(ty_Maybe, cbc)) → new_esEs4(vyy970, vyy980, cbc)
new_compare15(vyy970, vyy980, False, cb) → GT
new_ltEs19(vyy971, vyy981, ty_Bool) → new_ltEs9(vyy971, vyy981)
new_esEs22(vyy3000, vyy400, app(ty_[], ha)) → new_esEs14(vyy3000, vyy400, ha)
new_esEs28(vyy3001, vyy401, app(app(app(ty_@3, dbh), dca), dcb)) → new_esEs5(vyy3001, vyy401, dbh, dca, dcb)
new_esEs22(vyy3000, vyy400, app(ty_Ratio, gh)) → new_esEs18(vyy3000, vyy400, gh)
new_esEs17(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_lt17(vyy970, vyy980) → new_esEs8(new_compare9(vyy970, vyy980), LT)
new_pePe(False, vyy169) → vyy169
new_esEs14([], [], bhe) → True
new_esEs25(vyy3000, vyy400, app(app(ty_@2, bhh), caa)) → new_esEs7(vyy3000, vyy400, bhh, caa)
new_esEs15(False, True) → False
new_esEs15(True, False) → False
new_esEs27(vyy3000, vyy400, ty_@0) → new_esEs16(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), app(ty_[], cfa), cg) → new_ltEs7(vyy9700, vyy9800, cfa)
new_esEs13(vyy971, vyy981, app(ty_Maybe, dc)) → new_esEs4(vyy971, vyy981, dc)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Ordering, cg) → new_ltEs13(vyy9700, vyy9800)
new_esEs26(vyy970, vyy980, ty_Int) → new_esEs11(vyy970, vyy980)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Int) → new_ltEs16(vyy9700, vyy9800)
new_esEs14(:(vyy3000, vyy3001), :(vyy400, vyy401), bhe) → new_asAs(new_esEs25(vyy3000, vyy400, bhe), new_esEs14(vyy3001, vyy401, bhe))
new_esEs22(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Float, cg) → new_ltEs11(vyy9700, vyy9800)
new_ltEs13(EQ, GT) → True
new_esEs22(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare18(vyy970, vyy980, app(ty_Maybe, cdh)) → new_compare19(vyy970, vyy980, cdh)
new_esEs20(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_lt5(vyy971, vyy981, ty_Double) → new_lt19(vyy971, vyy981)
new_primCmpInt(Neg(Succ(vyy9700)), Neg(vyy980)) → new_primCmpNat1(vyy980, vyy9700)
new_esEs12(vyy970, vyy980, ty_Float) → new_esEs10(vyy970, vyy980)
new_esEs12(vyy970, vyy980, ty_Char) → new_esEs9(vyy970, vyy980)
new_esEs19(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_lt4(vyy970, vyy980, ty_@0) → new_lt10(vyy970, vyy980)
new_ltEs8(Nothing, Just(vyy980), bdd) → True
new_esEs6(Right(vyy3000), Left(vyy400), bgb, beg) → False
new_esEs6(Left(vyy3000), Right(vyy400), bgb, beg) → False
new_esEs8(LT, LT) → True
new_ltEs11(vyy97, vyy98) → new_not(new_esEs8(new_compare27(vyy97, vyy98), GT))
new_compare25(vyy970, vyy980, True, cc, cd, ce) → EQ
new_esEs23(vyy3001, vyy401, ty_Double) → new_esEs19(vyy3001, vyy401)
new_esEs25(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), app(ty_Ratio, cgb), cg) → new_ltEs4(vyy9700, vyy9800, cgb)
new_esEs28(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_ltEs8(Just(vyy970), Just(vyy980), app(ty_[], bde)) → new_ltEs7(vyy970, vyy980, bde)
new_compare0([], [], cdf) → EQ
new_esEs23(vyy3001, vyy401, ty_@0) → new_esEs16(vyy3001, vyy401)
new_pePe(True, vyy169) → True
new_primEqNat0(Zero, Zero) → True
new_esEs20(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, app(app(ty_Either, he), hf)) → new_esEs6(vyy3001, vyy401, he, hf)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_@0) → new_esEs16(vyy3000, vyy400)
new_esEs28(vyy3001, vyy401, ty_@0) → new_esEs16(vyy3001, vyy401)
new_ltEs6(vyy972, vyy982, ty_@0) → new_ltEs10(vyy972, vyy982)
new_esEs26(vyy970, vyy980, ty_@0) → new_esEs16(vyy970, vyy980)
new_esEs22(vyy3000, vyy400, app(app(ty_@2, ge), gf)) → new_esEs7(vyy3000, vyy400, ge, gf)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, app(app(ty_Either, bgc), bgd)) → new_esEs6(vyy3000, vyy400, bgc, bgd)
new_esEs26(vyy970, vyy980, ty_Bool) → new_esEs15(vyy970, vyy980)
new_foldFM_GE12(vyy84, vyy13, vyy170, vyy171, vyy172, EmptyFM, vyy174, True, h, ba, bb) → new_foldFM_GE30(vyy170, vyy171, new_foldFM_GE5(vyy84, vyy13, vyy174, h, ba, bb), vyy13, h, ba, bb)
new_compare110(vyy970, vyy980, False, cf, cg) → GT
new_esEs12(vyy970, vyy980, app(app(ty_@2, bd), be)) → new_esEs7(vyy970, vyy980, bd, be)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_esEs28(vyy3001, vyy401, app(app(ty_Either, dba), dbb)) → new_esEs6(vyy3001, vyy401, dba, dbb)
new_compare28(vyy970, vyy980, cf, cg) → new_compare210(vyy970, vyy980, new_esEs6(vyy970, vyy980, cf, cg), cf, cg)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs9(vyy3000, vyy400)
new_ltEs6(vyy972, vyy982, ty_Integer) → new_ltEs17(vyy972, vyy982)
new_esEs24(vyy3002, vyy402, app(app(ty_@2, bba), bbb)) → new_esEs7(vyy3002, vyy402, bba, bbb)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy9800))) → new_primCmpNat0(vyy9800, Zero)
new_esEs26(vyy970, vyy980, ty_Ordering) → new_esEs8(vyy970, vyy980)
new_esEs8(GT, GT) → True
new_esEs9(Char(vyy3000), Char(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy1480), vyy40100) → Succ(Succ(new_primPlusNat1(vyy1480, vyy40100)))
new_primCmpInt(Pos(Zero), Pos(Succ(vyy9800))) → new_primCmpNat1(Zero, vyy9800)
new_gtEs0(vyy1730, vyy13, h, ba) → new_not(new_esEs8(new_compare210(vyy1730, Left(vyy13), new_esEs6(vyy1730, Left(vyy13), h, ba), h, ba), LT))
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_lt20(vyy970, vyy980, ty_Bool) → new_lt9(vyy970, vyy980)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, bcg)) → new_esEs18(vyy3000, vyy400, bcg)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, app(app(app(ty_@3, cge), cgf), cgg)) → new_ltEs5(vyy9700, vyy9800, cge, cgf, cgg)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs15(True, True) → True
new_esEs23(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_ltEs12(Left(vyy9700), Left(vyy9800), app(ty_Maybe, cfb), cg) → new_ltEs8(vyy9700, vyy9800, cfb)
new_primPlusNat1(Succ(vyy14800), Zero) → Succ(vyy14800)
new_primPlusNat1(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_compare27(Float(vyy970, vyy971), Float(vyy980, vyy981)) → new_compare8(new_sr(vyy970, vyy980), new_sr(vyy971, vyy981))
new_compare13(vyy970, vyy980, False) → GT
new_ltEs12(Left(vyy9700), Left(vyy9800), app(app(app(ty_@3, cfc), cfd), cfe), cg) → new_ltEs5(vyy9700, vyy9800, cfc, cfd, cfe)
new_esEs28(vyy3001, vyy401, app(ty_Maybe, dbe)) → new_esEs4(vyy3001, vyy401, dbe)
new_compare18(vyy970, vyy980, ty_Float) → new_compare27(vyy970, vyy980)
new_ltEs13(LT, GT) → True
new_compare16(vyy970, vyy980, True) → LT
new_esEs14([], :(vyy400, vyy401), bhe) → False
new_esEs14(:(vyy3000, vyy3001), [], bhe) → False
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], bff), beg) → new_esEs14(vyy3000, vyy400, bff)
new_primCmpNat1(Zero, vyy9700) → LT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), fh, ga, gb) → new_asAs(new_esEs22(vyy3000, vyy400, fh), new_asAs(new_esEs23(vyy3001, vyy401, ga), new_esEs24(vyy3002, vyy402, gb)))
new_ltEs8(Just(vyy970), Just(vyy980), ty_Char) → new_ltEs14(vyy970, vyy980)
new_lt4(vyy970, vyy980, app(app(ty_@2, bd), be)) → new_lt15(vyy970, vyy980, bd, be)
new_esEs26(vyy970, vyy980, app(ty_[], cbb)) → new_esEs14(vyy970, vyy980, cbb)
new_lt5(vyy971, vyy981, ty_Int) → new_lt16(vyy971, vyy981)
new_compare8(vyy97, vyy98) → new_primCmpInt(vyy97, vyy98)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primCompAux0(vyy174, GT) → GT
new_esEs18(:%(vyy3000, vyy3001), :%(vyy400, vyy401), fg) → new_asAs(new_esEs20(vyy3000, vyy400, fg), new_esEs21(vyy3001, vyy401, fg))
new_esEs8(EQ, EQ) → True
new_ltEs8(Just(vyy970), Just(vyy980), ty_Double) → new_ltEs18(vyy970, vyy980)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, app(ty_[], cgc)) → new_ltEs7(vyy9700, vyy9800, cgc)
new_lt20(vyy970, vyy980, ty_@0) → new_lt10(vyy970, vyy980)
new_lt5(vyy971, vyy981, app(app(app(ty_@3, dd), de), df)) → new_lt8(vyy971, vyy981, dd, de, df)
new_lt20(vyy970, vyy980, ty_Ordering) → new_lt13(vyy970, vyy980)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs23(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Int, cg) → new_ltEs16(vyy9700, vyy9800)
new_esEs28(vyy3001, vyy401, app(ty_[], dbg)) → new_esEs14(vyy3001, vyy401, dbg)
new_esEs22(vyy3000, vyy400, app(app(app(ty_@3, hb), hc), hd)) → new_esEs5(vyy3000, vyy400, hb, hc, hd)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Char, cg) → new_ltEs14(vyy9700, vyy9800)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_compare18(vyy970, vyy980, ty_Int) → new_compare8(vyy970, vyy980)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, bfe), beg) → new_esEs18(vyy3000, vyy400, bfe)
new_esEs28(vyy3001, vyy401, app(app(ty_@2, dbc), dbd)) → new_esEs7(vyy3001, vyy401, dbc, dbd)
new_ltEs19(vyy971, vyy981, app(ty_Ratio, cde)) → new_ltEs4(vyy971, vyy981, cde)
new_esEs23(vyy3001, vyy401, ty_Float) → new_esEs10(vyy3001, vyy401)
new_esEs22(vyy3000, vyy400, app(ty_Maybe, gg)) → new_esEs4(vyy3000, vyy400, gg)
new_esEs25(vyy3000, vyy400, app(ty_Maybe, cab)) → new_esEs4(vyy3000, vyy400, cab)
new_esEs26(vyy970, vyy980, ty_Integer) → new_esEs17(vyy970, vyy980)
new_ltEs13(GT, LT) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs12(vyy970, vyy980, app(app(app(ty_@3, cc), cd), ce)) → new_esEs5(vyy970, vyy980, cc, cd, ce)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs15(vyy3000, vyy400)
new_compare10(vyy970, vyy980, False, bd, be) → GT
new_ltEs19(vyy971, vyy981, ty_Integer) → new_ltEs17(vyy971, vyy981)
new_ltEs13(EQ, EQ) → True
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, bcb), bcc)) → new_esEs6(vyy3000, vyy400, bcb, bcc)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bfg), bfh), bga), beg) → new_esEs5(vyy3000, vyy400, bfg, bfh, bga)
new_esEs22(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs7(@2(vyy3000, vyy3001), @2(vyy400, vyy401), che, chf) → new_asAs(new_esEs27(vyy3000, vyy400, che), new_esEs28(vyy3001, vyy401, chf))
new_esEs6(Right(vyy3000), Right(vyy400), bgb, app(ty_Maybe, bgg)) → new_esEs4(vyy3000, vyy400, bgg)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, beg) → new_esEs16(vyy3000, vyy400)
new_primEqNat0(Succ(vyy300000), Succ(vyy40000)) → new_primEqNat0(vyy300000, vyy40000)
new_esEs24(vyy3002, vyy402, ty_@0) → new_esEs16(vyy3002, vyy402)
new_esEs27(vyy3000, vyy400, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_esEs27(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, beg) → new_esEs9(vyy3000, vyy400)
new_esEs24(vyy3002, vyy402, app(ty_Ratio, bbd)) → new_esEs18(vyy3002, vyy402, bbd)
new_esEs13(vyy971, vyy981, app(app(app(ty_@3, dd), de), df)) → new_esEs5(vyy971, vyy981, dd, de, df)
new_lt13(vyy970, vyy980) → new_esEs8(new_compare6(vyy970, vyy980), LT)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs5(vyy3000, vyy400, bda, bdb, bdc)
new_ltEs8(Just(vyy970), Just(vyy980), app(app(ty_Either, beb), bec)) → new_ltEs12(vyy970, vyy980, beb, bec)
new_lt5(vyy971, vyy981, ty_Float) → new_lt11(vyy971, vyy981)
new_lt20(vyy970, vyy980, ty_Integer) → new_lt17(vyy970, vyy980)
new_esEs28(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_compare212(vyy970, vyy980, True, cb) → EQ
new_ltEs6(vyy972, vyy982, app(ty_Ratio, ff)) → new_ltEs4(vyy972, vyy982, ff)
new_esEs24(vyy3002, vyy402, ty_Ordering) → new_esEs8(vyy3002, vyy402)
new_ltEs8(Just(vyy970), Nothing, bdd) → False
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Char) → new_ltEs14(vyy9700, vyy9800)
new_esEs23(vyy3001, vyy401, ty_Bool) → new_esEs15(vyy3001, vyy401)
new_esEs27(vyy3000, vyy400, app(app(app(ty_@3, daf), dag), dah)) → new_esEs5(vyy3000, vyy400, daf, dag, dah)
new_compare5(:%(vyy970, vyy971), :%(vyy980, vyy981), ty_Integer) → new_compare9(new_sr0(vyy970, vyy981), new_sr0(vyy980, vyy971))
new_esEs12(vyy970, vyy980, app(ty_Ratio, da)) → new_esEs18(vyy970, vyy980, da)
new_esEs10(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs11(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare17(vyy970, vyy980, False, cc, cd, ce) → GT
new_esEs21(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_esEs28(vyy3001, vyy401, ty_Ordering) → new_esEs8(vyy3001, vyy401)
new_esEs25(vyy3000, vyy400, ty_Char) → new_esEs9(vyy3000, vyy400)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_ltEs16(vyy97, vyy98) → new_not(new_esEs8(new_compare8(vyy97, vyy98), GT))
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_@0, cg) → new_ltEs10(vyy9700, vyy9800)
new_ltEs6(vyy972, vyy982, ty_Ordering) → new_ltEs13(vyy972, vyy982)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy9800))) → LT
new_sr0(Integer(vyy9800), Integer(vyy9710)) → Integer(new_primMulInt(vyy9800, vyy9710))
new_lt15(vyy970, vyy980, bd, be) → new_esEs8(new_compare29(vyy970, vyy980, bd, be), LT)
new_compare13(vyy970, vyy980, True) → LT
new_lt4(vyy970, vyy980, app(ty_Maybe, cb)) → new_lt7(vyy970, vyy980, cb)
new_primPlusNat1(Succ(vyy14800), Succ(vyy401000)) → Succ(Succ(new_primPlusNat1(vyy14800, vyy401000)))
new_lt6(vyy970, vyy980, ca) → new_esEs8(new_compare0(vyy970, vyy980, ca), LT)
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_ltEs12(Left(vyy9700), Right(vyy9800), cf, cg) → True
new_compare213(vyy970, vyy980, False, bd, be) → new_compare10(vyy970, vyy980, new_ltEs15(vyy970, vyy980, bd, be), bd, be)
new_esEs13(vyy971, vyy981, ty_Bool) → new_esEs15(vyy971, vyy981)
new_compare211(vyy970, vyy980, False) → new_compare13(vyy970, vyy980, new_ltEs9(vyy970, vyy980))
new_lt5(vyy971, vyy981, app(ty_Ratio, ec)) → new_lt18(vyy971, vyy981, ec)
new_esEs13(vyy971, vyy981, ty_@0) → new_esEs16(vyy971, vyy981)
new_compare18(vyy970, vyy980, ty_Double) → new_compare7(vyy970, vyy980)
new_lt5(vyy971, vyy981, ty_Bool) → new_lt9(vyy971, vyy981)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, bfd), beg) → new_esEs4(vyy3000, vyy400, bfd)
new_ltEs6(vyy972, vyy982, app(ty_Maybe, ee)) → new_ltEs8(vyy972, vyy982, ee)
new_primCmpNat2(Zero, Succ(vyy98000)) → LT
new_lt7(vyy970, vyy980, cb) → new_esEs8(new_compare19(vyy970, vyy980, cb), LT)
new_compare18(vyy970, vyy980, ty_Bool) → new_compare12(vyy970, vyy980)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_lt5(vyy971, vyy981, app(app(ty_@2, ea), eb)) → new_lt15(vyy971, vyy981, ea, eb)
new_lt8(vyy970, vyy980, cc, cd, ce) → new_esEs8(new_compare14(vyy970, vyy980, cc, cd, ce), LT)
new_foldFM_GE12(vyy84, vyy13, vyy170, vyy171, vyy172, vyy173, vyy174, False, h, ba, bb) → new_foldFM_GE5(vyy84, vyy13, vyy174, h, ba, bb)
new_compare24(vyy970, vyy980, True) → EQ
new_esEs27(vyy3000, vyy400, app(app(ty_@2, daa), dab)) → new_esEs7(vyy3000, vyy400, daa, dab)
new_lt5(vyy971, vyy981, ty_Char) → new_lt14(vyy971, vyy981)
new_ltEs19(vyy971, vyy981, ty_Double) → new_ltEs18(vyy971, vyy981)
new_ltEs13(GT, EQ) → False
new_ltEs13(EQ, LT) → False
new_esEs22(vyy3000, vyy400, ty_@0) → new_esEs16(vyy3000, vyy400)
new_esEs27(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_lt19(vyy970, vyy980) → new_esEs8(new_compare7(vyy970, vyy980), LT)
new_primCompAux0(vyy174, LT) → LT
new_ltEs4(vyy97, vyy98, bc) → new_not(new_esEs8(new_compare5(vyy97, vyy98, bc), GT))
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, bfb), bfc), beg) → new_esEs7(vyy3000, vyy400, bfb, bfc)
new_esEs12(vyy970, vyy980, ty_Integer) → new_esEs17(vyy970, vyy980)
new_esEs11(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_not(False) → True
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, beh), bfa), beg) → new_esEs6(vyy3000, vyy400, beh, bfa)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, beg) → new_esEs15(vyy3000, vyy400)
new_compare210(vyy970, vyy980, True, cf, cg) → EQ
new_primPlusNat0(Zero, vyy40100) → Succ(vyy40100)
new_ltEs19(vyy971, vyy981, app(app(ty_Either, cda), cdb)) → new_ltEs12(vyy971, vyy981, cda, cdb)
new_esEs24(vyy3002, vyy402, app(app(ty_Either, bag), bah)) → new_esEs6(vyy3002, vyy402, bag, bah)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, app(app(ty_Either, cgh), cha)) → new_ltEs12(vyy9700, vyy9800, cgh, cha)
new_esEs26(vyy970, vyy980, app(ty_Ratio, ccc)) → new_esEs18(vyy970, vyy980, ccc)
new_ltEs12(Right(vyy9700), Left(vyy9800), cf, cg) → False
new_esEs28(vyy3001, vyy401, ty_Char) → new_esEs9(vyy3001, vyy401)
new_esEs25(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs24(vyy3002, vyy402, app(ty_[], bbe)) → new_esEs14(vyy3002, vyy402, bbe)
new_compare0(:(vyy970, vyy971), [], cdf) → GT
new_ltEs6(vyy972, vyy982, ty_Double) → new_ltEs18(vyy972, vyy982)
new_esEs27(vyy3000, vyy400, app(app(ty_Either, chg), chh)) → new_esEs6(vyy3000, vyy400, chg, chh)
new_esEs13(vyy971, vyy981, ty_Char) → new_esEs9(vyy971, vyy981)
new_esEs27(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_lt4(vyy970, vyy980, ty_Double) → new_lt19(vyy970, vyy980)
new_compare18(vyy970, vyy980, app(ty_[], cdg)) → new_compare0(vyy970, vyy980, cdg)
new_primCmpInt(Pos(Succ(vyy9700)), Neg(vyy980)) → GT
new_esEs13(vyy971, vyy981, app(app(ty_Either, dg), dh)) → new_esEs6(vyy971, vyy981, dg, dh)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_compare5(:%(vyy970, vyy971), :%(vyy980, vyy981), ty_Int) → new_compare8(new_sr(vyy970, vyy981), new_sr(vyy980, vyy971))
new_ltEs6(vyy972, vyy982, ty_Char) → new_ltEs14(vyy972, vyy982)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Ordering) → new_ltEs13(vyy970, vyy980)
new_ltEs9(True, True) → True
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Double) → new_esEs19(vyy3000, vyy400)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs19(vyy971, vyy981, app(ty_Maybe, cce)) → new_ltEs8(vyy971, vyy981, cce)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs24(vyy3002, vyy402, ty_Bool) → new_esEs15(vyy3002, vyy402)
new_compare12(vyy970, vyy980) → new_compare211(vyy970, vyy980, new_esEs15(vyy970, vyy980))
new_primEqNat0(Zero, Succ(vyy40000)) → False
new_primEqNat0(Succ(vyy300000), Zero) → False
new_esEs26(vyy970, vyy980, app(app(ty_@2, cca), ccb)) → new_esEs7(vyy970, vyy980, cca, ccb)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs9(False, False) → True
new_esEs23(vyy3001, vyy401, app(ty_Ratio, bab)) → new_esEs18(vyy3001, vyy401, bab)
new_ltEs10(vyy97, vyy98) → new_not(new_esEs8(new_compare26(vyy97, vyy98), GT))
new_esEs4(Nothing, Nothing, bca) → True
new_esEs12(vyy970, vyy980, ty_Double) → new_esEs19(vyy970, vyy980)
new_primCmpInt(Pos(Succ(vyy9700)), Pos(vyy980)) → new_primCmpNat0(vyy9700, vyy980)
new_primCmpNat2(Succ(vyy97000), Succ(vyy98000)) → new_primCmpNat2(vyy97000, vyy98000)
new_esEs13(vyy971, vyy981, app(app(ty_@2, ea), eb)) → new_esEs7(vyy971, vyy981, ea, eb)
new_ltEs12(Left(vyy9700), Left(vyy9800), app(app(ty_Either, cff), cfg), cg) → new_ltEs12(vyy9700, vyy9800, cff, cfg)
new_primCmpNat0(vyy9700, Zero) → GT
new_esEs23(vyy3001, vyy401, ty_Int) → new_esEs11(vyy3001, vyy401)
new_lt20(vyy970, vyy980, ty_Char) → new_lt14(vyy970, vyy980)
new_esEs27(vyy3000, vyy400, app(ty_Maybe, dac)) → new_esEs4(vyy3000, vyy400, dac)
new_lt4(vyy970, vyy980, app(ty_Ratio, da)) → new_lt18(vyy970, vyy980, da)
new_compare6(vyy970, vyy980) → new_compare24(vyy970, vyy980, new_esEs8(vyy970, vyy980))
new_lt4(vyy970, vyy980, app(ty_[], ca)) → new_lt6(vyy970, vyy980, ca)
new_esEs23(vyy3001, vyy401, app(ty_[], bac)) → new_esEs14(vyy3001, vyy401, bac)
new_esEs24(vyy3002, vyy402, ty_Double) → new_esEs19(vyy3002, vyy402)
new_lt12(vyy970, vyy980, cf, cg) → new_esEs8(new_compare28(vyy970, vyy980, cf, cg), LT)
new_esEs12(vyy970, vyy980, ty_@0) → new_esEs16(vyy970, vyy980)
new_ltEs15(@2(vyy970, vyy971), @2(vyy980, vyy981), cah, cba) → new_pePe(new_lt20(vyy970, vyy980, cah), new_asAs(new_esEs26(vyy970, vyy980, cah), new_ltEs19(vyy971, vyy981, cba)))
new_primCmpInt(Pos(Zero), Neg(Succ(vyy9800))) → GT
new_lt20(vyy970, vyy980, app(app(ty_@2, cca), ccb)) → new_lt15(vyy970, vyy980, cca, ccb)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, app(ty_[], bha)) → new_esEs14(vyy3000, vyy400, bha)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, beg) → new_esEs8(vyy3000, vyy400)
new_lt9(vyy970, vyy980) → new_esEs8(new_compare12(vyy970, vyy980), LT)
new_compare0(:(vyy970, vyy971), :(vyy980, vyy981), cdf) → new_primCompAux1(vyy970, vyy980, new_compare0(vyy971, vyy981, cdf), cdf)
new_ltEs19(vyy971, vyy981, app(ty_[], ccd)) → new_ltEs7(vyy971, vyy981, ccd)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], bch)) → new_esEs14(vyy3000, vyy400, bch)
new_ltEs19(vyy971, vyy981, ty_Char) → new_ltEs14(vyy971, vyy981)
new_esEs24(vyy3002, vyy402, ty_Int) → new_esEs11(vyy3002, vyy402)
new_esEs13(vyy971, vyy981, app(ty_Ratio, ec)) → new_esEs18(vyy971, vyy981, ec)
new_lt5(vyy971, vyy981, app(ty_Maybe, dc)) → new_lt7(vyy971, vyy981, dc)
new_ltEs17(vyy97, vyy98) → new_not(new_esEs8(new_compare9(vyy97, vyy98), GT))
new_lt4(vyy970, vyy980, ty_Ordering) → new_lt13(vyy970, vyy980)
new_esEs21(vyy3001, vyy401, ty_Integer) → new_esEs17(vyy3001, vyy401)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Bool) → new_ltEs9(vyy970, vyy980)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Int) → new_esEs11(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Integer, cg) → new_ltEs17(vyy9700, vyy9800)
new_compare18(vyy970, vyy980, app(app(ty_Either, ced), cee)) → new_compare28(vyy970, vyy980, ced, cee)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare18(vyy970, vyy980, app(app(ty_@2, cef), ceg)) → new_compare29(vyy970, vyy980, cef, ceg)
new_ltEs18(vyy97, vyy98) → new_not(new_esEs8(new_compare7(vyy97, vyy98), GT))
new_esEs12(vyy970, vyy980, app(app(ty_Either, cf), cg)) → new_esEs6(vyy970, vyy980, cf, cg)
new_ltEs8(Just(vyy970), Just(vyy980), app(ty_Maybe, bdf)) → new_ltEs8(vyy970, vyy980, bdf)
new_lt20(vyy970, vyy980, app(ty_Maybe, cbc)) → new_lt7(vyy970, vyy980, cbc)
new_ltEs13(GT, GT) → True
new_esEs12(vyy970, vyy980, app(ty_Maybe, cb)) → new_esEs4(vyy970, vyy980, cb)
new_compare9(Integer(vyy970), Integer(vyy980)) → new_primCmpInt(vyy970, vyy980)
new_asAs(False, vyy137) → False
new_lt4(vyy970, vyy980, ty_Integer) → new_lt17(vyy970, vyy980)
new_lt20(vyy970, vyy980, ty_Double) → new_lt19(vyy970, vyy980)
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Bool) → new_ltEs9(vyy9700, vyy9800)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, app(ty_Ratio, chd)) → new_ltEs4(vyy9700, vyy9800, chd)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_compare14(vyy970, vyy980, cc, cd, ce) → new_compare25(vyy970, vyy980, new_esEs5(vyy970, vyy980, cc, cd, ce), cc, cd, ce)
new_esEs25(vyy3000, vyy400, ty_@0) → new_esEs16(vyy3000, vyy400)
new_lt5(vyy971, vyy981, ty_@0) → new_lt10(vyy971, vyy981)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, app(ty_Ratio, bgh)) → new_esEs18(vyy3000, vyy400, bgh)
new_esEs24(vyy3002, vyy402, ty_Float) → new_esEs10(vyy3002, vyy402)
new_esEs23(vyy3001, vyy401, app(app(ty_@2, hg), hh)) → new_esEs7(vyy3001, vyy401, hg, hh)
new_ltEs19(vyy971, vyy981, ty_@0) → new_ltEs10(vyy971, vyy981)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Double, cg) → new_ltEs18(vyy9700, vyy9800)
new_primCmpNat1(Succ(vyy9800), vyy9700) → new_primCmpNat2(vyy9800, vyy9700)
new_esEs24(vyy3002, vyy402, ty_Integer) → new_esEs17(vyy3002, vyy402)
new_primCmpNat2(Succ(vyy97000), Zero) → GT
new_foldFM_GE5(vyy84, vyy13, Branch(vyy1740, vyy1741, vyy1742, vyy1743, vyy1744), h, ba, bb) → new_foldFM_GE12(vyy84, vyy13, vyy1740, vyy1741, vyy1742, vyy1743, vyy1744, new_gtEs0(vyy1740, vyy13, h, ba), h, ba, bb)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs19(vyy3000, vyy400)
new_ltEs8(Just(vyy970), Just(vyy980), ty_Int) → new_ltEs16(vyy970, vyy980)
new_compare11(Char(vyy970), Char(vyy980)) → new_primCmpInt(vyy970, vyy980)
new_ltEs9(False, True) → True
new_esEs23(vyy3001, vyy401, ty_Char) → new_esEs9(vyy3001, vyy401)
new_esEs16(@0, @0) → True
new_lt20(vyy970, vyy980, app(ty_Ratio, ccc)) → new_lt18(vyy970, vyy980, ccc)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_@0) → new_ltEs10(vyy9700, vyy9800)
new_ltEs19(vyy971, vyy981, ty_Int) → new_ltEs16(vyy971, vyy981)
new_esEs26(vyy970, vyy980, ty_Double) → new_esEs19(vyy970, vyy980)
new_lt18(vyy970, vyy980, da) → new_esEs8(new_compare5(vyy970, vyy980, da), LT)
new_lt14(vyy970, vyy980) → new_esEs8(new_compare11(vyy970, vyy980), LT)
new_esEs22(vyy3000, vyy400, ty_Bool) → new_esEs15(vyy3000, vyy400)
new_ltEs6(vyy972, vyy982, app(ty_[], ed)) → new_ltEs7(vyy972, vyy982, ed)
new_esEs28(vyy3001, vyy401, ty_Bool) → new_esEs15(vyy3001, vyy401)
new_ltEs19(vyy971, vyy981, app(app(app(ty_@3, ccf), ccg), cch)) → new_ltEs5(vyy971, vyy981, ccf, ccg, cch)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Ordering) → new_ltEs13(vyy9700, vyy9800)
new_compare26(@0, @0) → EQ
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs11(vyy3000, vyy400)
new_ltEs12(Left(vyy9700), Left(vyy9800), ty_Bool, cg) → new_ltEs9(vyy9700, vyy9800)
new_compare29(vyy970, vyy980, bd, be) → new_compare213(vyy970, vyy980, new_esEs7(vyy970, vyy980, bd, be), bd, be)
new_ltEs8(Nothing, Nothing, bdd) → True
new_lt20(vyy970, vyy980, ty_Float) → new_lt11(vyy970, vyy980)
new_ltEs19(vyy971, vyy981, app(app(ty_@2, cdc), cdd)) → new_ltEs15(vyy971, vyy981, cdc, cdd)
new_esEs25(vyy3000, vyy400, app(app(app(ty_@3, cae), caf), cag)) → new_esEs5(vyy3000, vyy400, cae, caf, cag)
new_compare25(vyy970, vyy980, False, cc, cd, ce) → new_compare17(vyy970, vyy980, new_ltEs5(vyy970, vyy980, cc, cd, ce), cc, cd, ce)
new_esEs22(vyy3000, vyy400, app(app(ty_Either, gc), gd)) → new_esEs6(vyy3000, vyy400, gc, gd)
new_lt5(vyy971, vyy981, app(app(ty_Either, dg), dh)) → new_lt12(vyy971, vyy981, dg, dh)
new_esEs22(vyy3000, vyy400, ty_Integer) → new_esEs17(vyy3000, vyy400)
new_lt4(vyy970, vyy980, ty_Bool) → new_lt9(vyy970, vyy980)
new_esEs12(vyy970, vyy980, ty_Int) → new_esEs11(vyy970, vyy980)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, bcd), bce)) → new_esEs7(vyy3000, vyy400, bcd, bce)
new_ltEs8(Just(vyy970), Just(vyy980), app(app(ty_@2, bed), bee)) → new_ltEs15(vyy970, vyy980, bed, bee)
new_esEs26(vyy970, vyy980, ty_Char) → new_esEs9(vyy970, vyy980)
new_ltEs13(LT, LT) → True
new_esEs22(vyy3000, vyy400, ty_Float) → new_esEs10(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)
new_esEs26(vyy970, vyy980, app(app(ty_Either, cbg), cbh)) → new_esEs6(vyy970, vyy980, cbg, cbh)
new_compare213(vyy970, vyy980, True, bd, be) → EQ
new_compare0([], :(vyy980, vyy981), cdf) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_compare15(vyy970, vyy980, True, cb) → LT
new_esEs12(vyy970, vyy980, ty_Ordering) → new_esEs8(vyy970, vyy980)
new_foldFM_GE30(vyy170, vyy171, vyy107, vyy13, h, ba, bb) → new_fmToList_GE0(vyy170, vyy171, vyy107, h, ba, bb)
new_esEs27(vyy3000, vyy400, app(ty_[], dae)) → new_esEs14(vyy3000, vyy400, dae)
new_lt4(vyy970, vyy980, app(app(app(ty_@3, cc), cd), ce)) → new_lt8(vyy970, vyy980, cc, cd, ce)
new_esEs13(vyy971, vyy981, ty_Ordering) → new_esEs8(vyy971, vyy981)
new_esEs12(vyy970, vyy980, app(ty_[], ca)) → new_esEs14(vyy970, vyy980, ca)
new_asAs(True, vyy137) → vyy137
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs11(vyy3000, vyy400)
new_esEs26(vyy970, vyy980, app(app(app(ty_@3, cbd), cbe), cbf)) → new_esEs5(vyy970, vyy980, cbd, cbe, cbf)
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat0(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs28(vyy3001, vyy401, app(ty_Ratio, dbf)) → new_esEs18(vyy3001, vyy401, dbf)
new_compare18(vyy970, vyy980, ty_Integer) → new_compare9(vyy970, vyy980)
new_esEs27(vyy3000, vyy400, ty_Bool) → new_esEs15(vyy3000, vyy400)
new_ltEs12(Right(vyy9700), Right(vyy9800), cf, ty_Float) → new_ltEs11(vyy9700, vyy9800)
new_compare211(vyy970, vyy980, True) → EQ
new_ltEs8(Just(vyy970), Just(vyy980), app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs5(vyy970, vyy980, bdg, bdh, bea)
new_esEs23(vyy3001, vyy401, app(app(app(ty_@3, bad), bae), baf)) → new_esEs5(vyy3001, vyy401, bad, bae, baf)
new_lt4(vyy970, vyy980, app(app(ty_Either, cf), cg)) → new_lt12(vyy970, vyy980, cf, cg)
new_ltEs7(vyy97, vyy98, cdf) → new_not(new_esEs8(new_compare0(vyy97, vyy98, cdf), GT))
new_compare210(vyy970, vyy980, False, cf, cg) → new_compare110(vyy970, vyy980, new_ltEs12(vyy970, vyy980, cf, cg), cf, cg)
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs16(vyy3000, vyy400)
new_foldFM_GE5(vyy84, vyy13, EmptyFM, h, ba, bb) → vyy84
new_compare18(vyy970, vyy980, ty_@0) → new_compare26(vyy970, vyy980)
new_lt5(vyy971, vyy981, app(ty_[], db)) → new_lt6(vyy971, vyy981, db)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), bgb, ty_Ordering) → new_esEs8(vyy3000, vyy400)
new_compare212(vyy970, vyy980, False, cb) → new_compare15(vyy970, vyy980, new_ltEs8(vyy970, vyy980, cb), cb)
new_esEs6(Right(vyy3000), Right(vyy400), bgb, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs5(vyy3000, vyy400, bhb, bhc, bhd)
new_primCompAux0(vyy174, EQ) → vyy174
new_lt10(vyy970, vyy980) → new_esEs8(new_compare26(vyy970, vyy980), LT)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_compare18(vyy970, vyy980, ty_Char) → new_compare11(vyy970, vyy980)
new_esEs27(vyy3000, vyy400, ty_Char) → new_esEs9(vyy3000, vyy400)
new_primCmpInt(Neg(Succ(vyy9700)), Pos(vyy980)) → LT
new_ltEs19(vyy971, vyy981, ty_Ordering) → new_ltEs13(vyy971, vyy981)
new_not(True) → False
new_compare16(vyy970, vyy980, False) → GT
new_esEs15(False, False) → True
new_esEs27(vyy3000, vyy400, ty_Double) → new_esEs19(vyy3000, vyy400)

The set Q consists of the following terms:

new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Float)
new_compare5(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_compare110(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_@0)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, ty_@0)
new_compare6(x0, x1)
new_ltEs12(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_compare213(x0, x1, True, x2, x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_foldFM_GE12(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, True, x11, x12, x13)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_lt6(x0, x1, x2)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs8(Just(x0), Nothing, x1)
new_esEs24(x0, x1, ty_@0)
new_primCmpNat2(Zero, Succ(x0))
new_esEs12(x0, x1, ty_Bool)
new_esEs12(x0, x1, ty_Int)
new_ltEs18(x0, x1)
new_lt20(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs12(Left(x0), Left(x1), ty_Double, x2)
new_esEs13(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs17(x0, x1)
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs15(True, True)
new_ltEs7(x0, x1, x2)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Zero, Succ(x0))
new_compare18(x0, x1, app(ty_Maybe, x2))
new_compare7(Double(x0, x1), Double(x2, x3))
new_esEs25(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primMulNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, True)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs24(x0, x1, ty_Char)
new_lt7(x0, x1, x2)
new_esEs28(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_foldFM_GE30(x0, x1, x2, x3, x4, x5, x6)
new_lt4(x0, x1, ty_Float)
new_esEs15(False, False)
new_compare15(x0, x1, False, x2)
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_Ordering)
new_foldFM_GE5(x0, x1, EmptyFM, x2, x3, x4)
new_fmToList_GE0(x0, x1, x2, x3, x4, x5)
new_esEs25(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, x2)
new_ltEs12(Left(x0), Left(x1), ty_Ordering, x2)
new_lt4(x0, x1, ty_Integer)
new_ltEs12(Left(x0), Left(x1), ty_Float, x2)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs12(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, ty_@0)
new_esEs8(LT, LT)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs16(@0, @0)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs26(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(True, x0)
new_compare18(x0, x1, app(app(ty_Either, x2), x3))
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs19(Double(x0, x1), Double(x2, x3))
new_esEs13(x0, x1, ty_Integer)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_foldFM_GE12(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_compare0([], [], x0)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare16(x0, x1, True)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, ty_Char)
new_esEs14([], [], x0)
new_esEs28(x0, x1, ty_Integer)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_ltEs19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, ty_Char)
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_ltEs13(EQ, EQ)
new_ltEs19(x0, x1, ty_Ordering)
new_compare0([], :(x0, x1), x2)
new_esEs26(x0, x1, ty_Float)
new_ltEs9(False, False)
new_ltEs12(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_compare18(x0, x1, ty_Float)
new_primPlusNat1(Zero, Succ(x0))
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs11(x0, x1)
new_ltEs12(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_lt18(x0, x1, x2)
new_ltEs12(Left(x0), Left(x1), ty_@0, x2)
new_esEs22(x0, x1, ty_Bool)
new_lt5(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(x0, x1, ty_Bool)
new_compare18(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs28(x0, x1, ty_Char)
new_esEs14(:(x0, x1), [], x2)
new_ltEs13(LT, EQ)
new_ltEs13(EQ, LT)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_lt5(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_ltEs6(x0, x1, ty_Char)
new_esEs14([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs12(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs6(x0, x1, ty_Ordering)
new_lt5(x0, x1, ty_Int)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_foldFM_GE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_compare18(x0, x1, ty_Bool)
new_esEs13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_ltEs8(Nothing, Nothing, x0)
new_lt9(x0, x1)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, ty_Integer)
new_esEs10(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, ty_Bool)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs12(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_ltEs4(x0, x1, x2)
new_ltEs19(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Char)
new_ltEs12(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare10(x0, x1, True, x2, x3)
new_compare18(x0, x1, app(app(ty_@2, x2), x3))
new_compare211(x0, x1, False)
new_ltEs10(x0, x1)
new_compare18(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_primPlusNat1(Zero, Zero)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Zero, x0)
new_primCmpNat2(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare27(Float(x0, x1), Float(x2, x3))
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_asAs(True, x0)
new_primPlusNat1(Succ(x0), Zero)
new_compare29(x0, x1, x2, x3)
new_ltEs11(x0, x1)
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs24(x0, x1, ty_Double)
new_primCmpNat1(Succ(x0), x1)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Int)
new_compare15(x0, x1, True, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs12(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare18(x0, x1, ty_@0)
new_lt5(x0, x1, ty_Ordering)
new_ltEs9(False, True)
new_ltEs9(True, False)
new_compare9(Integer(x0), Integer(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs9(True, True)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_ltEs13(EQ, GT)
new_esEs28(x0, x1, ty_Int)
new_ltEs13(GT, EQ)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs19(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt4(x0, x1, ty_@0)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs12(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs12(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs23(x0, x1, ty_Bool)
new_primCompAux0(x0, EQ)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs12(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs13(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Ordering)
new_compare16(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, ty_Int)
new_esEs12(x0, x1, app(ty_[], x2))
new_ltEs13(LT, GT)
new_ltEs13(GT, LT)
new_compare213(x0, x1, False, x2, x3)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare212(x0, x1, False, x2)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs15(True, False)
new_esEs15(False, True)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, ty_Bool)
new_compare11(Char(x0), Char(x1))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare210(x0, x1, False, x2, x3)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, ty_Float)
new_ltEs12(Right(x0), Right(x1), x2, ty_Float)
new_esEs12(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs13(x0, x1, ty_Char)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare14(x0, x1, x2, x3, x4)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare18(x0, x1, ty_Double)
new_sr0(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Int)
new_compare210(x0, x1, True, x2, x3)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare24(x0, x1, False)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare8(x0, x1)
new_esEs13(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs13(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs20(x0, x1, ty_Int)
new_primCompAux1(x0, x1, x2, x3)
new_lt8(x0, x1, x2, x3, x4)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs9(Char(x0), Char(x1))
new_lt5(x0, x1, app(ty_[], x2))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_lt16(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs24(x0, x1, ty_Integer)
new_esEs12(x0, x1, ty_Ordering)
new_lt17(x0, x1)
new_ltEs12(Right(x0), Right(x1), x2, ty_Bool)
new_primPlusNat0(Zero, x0)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs23(x0, x1, ty_@0)
new_compare18(x0, x1, ty_Char)
new_foldFM_GE22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs17(Integer(x0), Integer(x1))
new_compare24(x0, x1, True)
new_esEs24(x0, x1, ty_Ordering)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_esEs13(x0, x1, app(ty_Ratio, x2))
new_ltEs13(LT, LT)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Int)
new_compare28(x0, x1, x2, x3)
new_lt5(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Double)
new_compare5(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_compare18(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_foldFM_GE12(x0, x1, x2, x3, x4, EmptyFM, x5, True, x6, x7, x8)
new_esEs26(x0, x1, ty_Ordering)
new_lt11(x0, x1)
new_ltEs12(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Bool)
new_compare17(x0, x1, False, x2, x3, x4)
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs12(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Char)
new_primCmpNat2(Succ(x0), Zero)
new_esEs27(x0, x1, ty_@0)
new_ltEs13(GT, GT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt19(x0, x1)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs27(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_compare10(x0, x1, False, x2, x3)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(False, x0)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_compare212(x0, x1, True, x2)
new_primCmpNat2(Succ(x0), Succ(x1))
new_not(True)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_esEs13(x0, x1, ty_Int)
new_gtEs0(x0, x1, x2, x3)
new_compare18(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs19(x0, x1, ty_Double)
new_esEs13(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Nothing, Just(x0), x1)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare17(x0, x1, True, x2, x3, x4)
new_lt20(x0, x1, app(ty_[], x2))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs14(x0, x1)
new_esEs4(Nothing, Just(x0), x1)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Double)
new_primEqNat0(Succ(x0), Succ(x1))
new_lt15(x0, x1, x2, x3)
new_lt10(x0, x1)
new_ltEs16(x0, x1)
new_esEs27(x0, x1, ty_Double)
new_ltEs12(Right(x0), Right(x1), x2, ty_Double)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Left(x0), Right(x1), x2, x3)
new_ltEs12(Right(x0), Left(x1), x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Just(x0), Nothing, x1)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Bool)
new_lt4(x0, x1, ty_Bool)
new_compare110(x0, x1, True, x2, x3)
new_lt20(x0, x1, ty_Double)
new_esEs13(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare26(@0, @0)
new_primCmpNat0(x0, Zero)
new_compare211(x0, x1, True)
new_primCmpNat0(x0, Succ(x1))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs4(Nothing, Nothing, x0)
new_ltEs12(Right(x0), Right(x1), x2, ty_@0)
new_lt14(x0, x1)
new_ltEs12(Left(x0), Left(x1), ty_Int, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, ty_Double)
new_primEqNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_compare25(x0, x1, False, x2, x3, x4)
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_primCompAux0(x0, GT)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs13(x0, x1, ty_@0)
new_compare12(x0, x1)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, False)
new_primCompAux0(x0, LT)
new_esEs22(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Double)

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: