YES 7.86 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ LR

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

is transformed to
eltsFM_GE0 key elt rest = 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 FiniteMap
  ((eltsFM_GE :: (Ord c, Ord a) => FiniteMap (a,c) b  ->  (a,c)  ->  [b]) :: (Ord c, Ord a) => FiniteMap (a,c) b  ->  (a,c)  ->  [b])

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

  eltsFM_GE :: Ord b => FiniteMap b a  ->  b  ->  [a]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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



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

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

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

  eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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



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

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

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

  eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

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

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

  eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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

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

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

is transformed to
compare x y = compare3 x y

compare0 x y True = GT

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

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

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

absReal0 x True = `negate` x

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

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

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

  eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

are unpacked to the following functions on top level
reduce2D vyw vyx = gcd vyw vyx

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

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

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

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

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

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



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

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

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

  eltsFM_GE :: Ord b => FiniteMap b a  ->  b  ->  [a]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

  foldFM :: (a  ->  b  ->  c  ->  c)  ->  c  ->  FiniteMap a b  ->  c
foldFM k z EmptyFM = z
foldFM k z (Branch key elt 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 Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

  eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b]
eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm

  
eltsFM_GE0 key elt rest = elt : rest

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Haskell To QDPs


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

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

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

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

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



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

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

new_primPlusNat(Succ(vyy13100), Succ(vyy401000)) → new_primPlusNat(vyy13100, vyy401000)

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

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



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

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

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

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

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



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

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

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

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

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



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

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

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

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

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



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

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

new_ltEs1(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), eh, app(app(ty_@2, fc), fd)) → new_ltEs1(vyy2130011, vyy1511, fc, fd)
new_ltEs1(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(ty_[], df), dg) → new_lt(vyy2130010, vyy1510, df)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), bce, app(ty_Maybe, bcg), bbd) → new_lt0(vyy2130011, vyy1511, bcg)
new_compare21(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, ge, app(app(ty_@2, app(app(ty_Either, ec), ed)), dg)) → new_lt2(vyy2130010, vyy1510, ec, ed)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, bce), bbc), app(app(ty_@2, bea), beb))) → new_ltEs1(vyy2130012, vyy1512, bea, beb)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), bce, app(ty_[], bcf), bbd) → new_lt(vyy2130011, vyy1511, bcf)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), bce, app(app(ty_Either, bdb), bdc), bbd) → new_lt2(vyy2130011, vyy1511, bdb, bdc)
new_ltEs2(Left(vyy2130010), Left(vyy1510), app(app(ty_Either, hc), hd), gg) → new_ltEs2(vyy2130010, vyy1510, hc, hd)
new_compare21(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, ge, app(app(ty_@2, eh), app(app(app(ty_@3, fh), ga), gb))) → new_ltEs3(vyy2130011, vyy1511, fh, ga, gb)
new_ltEs0(Just(vyy2130010), Just(vyy1510), app(ty_Maybe, ce)) → new_ltEs0(vyy2130010, vyy1510, ce)
new_compare21(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, ge, app(app(ty_@2, app(app(ty_@2, ea), eb)), dg)) → new_lt1(vyy2130010, vyy1510, ea, eb)
new_compare21(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, ge, app(app(ty_@2, app(app(app(ty_@3, ee), ef), eg)), dg)) → new_lt3(vyy2130010, vyy1510, ee, ef, eg)
new_compare3(vyy213000, vyy150, bfa, bfb) → new_compare22(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, bfa, bfb), bfa, bfb)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, bce), bbc), app(ty_[], bdg))) → new_ltEs(vyy2130012, vyy1512, bdg)
new_compare21(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, ge, app(ty_Maybe, app(app(app(ty_@3, dc), dd), de))) → new_ltEs3(vyy2130010, vyy1510, dc, dd, de)
new_primCompAux(vyy2130000, vyy1500, vyy178, app(ty_[], bb)) → new_compare(vyy2130000, vyy1500, bb)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, app(app(ty_Either, bbh), bca)), bbc), bbd)) → new_lt2(vyy2130010, vyy1510, bbh, bca)
new_compare21(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, ge, app(app(ty_Either, hh), app(ty_[], baa))) → new_ltEs(vyy2130010, vyy1510, baa)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), bce, app(app(ty_@2, bch), bda), bbd) → new_lt1(vyy2130011, vyy1511, bch, bda)
new_ltEs2(Right(vyy2130010), Right(vyy1510), hh, app(ty_Maybe, bab)) → new_ltEs0(vyy2130010, vyy1510, bab)
new_compare21(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, ge, app(ty_Maybe, app(ty_Maybe, ce))) → new_ltEs0(vyy2130010, vyy1510, ce)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, bce), bbc), app(app(app(ty_@3, bee), bef), beg))) → new_ltEs3(vyy2130012, vyy1512, bee, bef, beg)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(app(ty_Either, bbh), bca), bbc, bbd) → new_lt2(vyy2130010, vyy1510, bbh, bca)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, bce), app(ty_Maybe, bcg)), bbd)) → new_lt0(vyy2130011, vyy1511, bcg)
new_compare21(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, ge, app(app(ty_Either, hh), app(ty_Maybe, bab))) → new_ltEs0(vyy2130010, vyy1510, bab)
new_compare21(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, ge, app(ty_Maybe, app(ty_[], cd))) → new_ltEs(vyy2130010, vyy1510, cd)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(app(ty_@2, bbf), bbg), bbc, bbd) → new_lt1(vyy2130010, vyy1510, bbf, bbg)
new_ltEs0(Just(vyy2130010), Just(vyy1510), app(ty_[], cd)) → new_ltEs(vyy2130010, vyy1510, cd)
new_ltEs1(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(ty_Maybe, dh), dg) → new_lt0(vyy2130010, vyy1510, dh)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), bce, bbc, app(app(ty_@2, bea), beb)) → new_ltEs1(vyy2130012, vyy1512, bea, beb)
new_primCompAux(vyy2130000, vyy1500, vyy178, app(ty_Maybe, bc)) → new_compare1(vyy2130000, vyy1500, bc)
new_primCompAux(vyy2130000, vyy1500, vyy178, app(app(ty_Either, bf), bg)) → new_compare3(vyy2130000, vyy1500, bf, bg)
new_compare21(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, app(app(ty_@2, gc), gd), beh) → new_compare21(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, gc, gd), gc, gd)
new_ltEs1(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), eh, app(ty_[], fa)) → new_ltEs(vyy2130011, vyy1511, fa)
new_compare21(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, ge, app(app(ty_@2, eh), app(app(ty_Either, ff), fg))) → new_ltEs2(vyy2130011, vyy1511, ff, fg)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), bce, app(app(app(ty_@3, bdd), bde), bdf), bbd) → new_lt3(vyy2130011, vyy1511, bdd, bde, bdf)
new_ltEs0(Just(vyy2130010), Just(vyy1510), app(app(ty_@2, cf), cg)) → new_ltEs1(vyy2130010, vyy1510, cf, cg)
new_ltEs0(Just(vyy2130010), Just(vyy1510), app(app(ty_Either, da), db)) → new_ltEs2(vyy2130010, vyy1510, da, db)
new_ltEs1(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(app(ty_Either, ec), ed), dg) → new_lt2(vyy2130010, vyy1510, ec, ed)
new_ltEs(vyy213001, vyy151, h) → new_compare(vyy213001, vyy151, h)
new_ltEs1(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), eh, app(app(app(ty_@3, fh), ga), gb)) → new_ltEs3(vyy2130011, vyy1511, fh, ga, gb)
new_lt0(vyy213000, vyy150, cc) → new_compare20(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, cc), cc)
new_compare21(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, ge, app(app(ty_Either, app(app(ty_@2, ha), hb)), gg)) → new_ltEs1(vyy2130010, vyy1510, ha, hb)
new_compare4(vyy213000, vyy150, bfc, bfd, bfe) → new_compare23(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bfc, bfd, bfe), bfc, bfd, bfe)
new_ltEs2(Right(vyy2130010), Right(vyy1510), hh, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs3(vyy2130010, vyy1510, bag, bah, bba)
new_compare23(vyy213000, vyy150, False, bfc, bfd, bfe) → new_ltEs3(vyy213000, vyy150, bfc, bfd, bfe)
new_compare21(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, ge, app(app(ty_@2, eh), app(app(ty_@2, fc), fd))) → new_ltEs1(vyy2130011, vyy1511, fc, fd)
new_ltEs0(Just(vyy2130010), Just(vyy1510), app(app(app(ty_@3, dc), dd), de)) → new_ltEs3(vyy2130010, vyy1510, dc, dd, de)
new_lt(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), ba) → new_primCompAux(vyy2130000, vyy1500, new_compare0(vyy2130001, vyy1501, ba), ba)
new_compare21(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, ge, app(ty_[], h)) → new_compare(vyy213001, vyy151, h)
new_compare21(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, ge, app(app(ty_Either, app(app(app(ty_@3, he), hf), hg)), gg)) → new_ltEs3(vyy2130010, vyy1510, he, hf, hg)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, app(ty_Maybe, bbe)), bbc), bbd)) → new_lt0(vyy2130010, vyy1510, bbe)
new_ltEs2(Left(vyy2130010), Left(vyy1510), app(app(app(ty_@3, he), hf), hg), gg) → new_ltEs3(vyy2130010, vyy1510, he, hf, hg)
new_lt3(vyy213000, vyy150, bfc, bfd, bfe) → new_compare23(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bfc, bfd, bfe), bfc, bfd, bfe)
new_ltEs1(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), eh, app(ty_Maybe, fb)) → new_ltEs0(vyy2130011, vyy1511, fb)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(ty_[], bbb), bbc, bbd) → new_lt(vyy2130010, vyy1510, bbb)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, bce), app(app(ty_@2, bch), bda)), bbd)) → new_lt1(vyy2130011, vyy1511, bch, bda)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), bce, bbc, app(ty_[], bdg)) → new_ltEs(vyy2130012, vyy1512, bdg)
new_compare21(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, ge, app(app(ty_Either, hh), app(app(ty_Either, bae), baf))) → new_ltEs2(vyy2130010, vyy1510, bae, baf)
new_compare21(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, ge, app(app(ty_@2, eh), app(ty_Maybe, fb))) → new_ltEs0(vyy2130011, vyy1511, fb)
new_compare2(vyy213000, vyy150, gc, gd) → new_compare21(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, gc, gd), gc, gd)
new_ltEs2(Right(vyy2130010), Right(vyy1510), hh, app(app(ty_@2, bac), bad)) → new_ltEs1(vyy2130010, vyy1510, bac, bad)
new_ltEs2(Right(vyy2130010), Right(vyy1510), hh, app(ty_[], baa)) → new_ltEs(vyy2130010, vyy1510, baa)
new_ltEs1(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(app(app(ty_@3, ee), ef), eg), dg) → new_lt3(vyy2130010, vyy1510, ee, ef, eg)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, app(app(ty_@2, bbf), bbg)), bbc), bbd)) → new_lt1(vyy2130010, vyy1510, bbf, bbg)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), bce, bbc, app(ty_Maybe, bdh)) → new_ltEs0(vyy2130012, vyy1512, bdh)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, bce), app(ty_[], bcf)), bbd)) → new_lt(vyy2130011, vyy1511, bcf)
new_lt(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), ba) → new_compare(vyy2130001, vyy1501, ba)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, bce), app(app(ty_Either, bdb), bdc)), bbd)) → new_lt2(vyy2130011, vyy1511, bdb, bdc)
new_compare21(@2(:(vyy2130000, vyy2130001), vyy213001), @2(:(vyy1500, vyy1501), vyy151), False, app(ty_[], ba), beh) → new_compare(vyy2130001, vyy1501, ba)
new_compare21(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, ge, app(app(ty_Either, app(ty_Maybe, gh)), gg)) → new_ltEs0(vyy2130010, vyy1510, gh)
new_compare21(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, ge, app(app(ty_Either, hh), app(app(ty_@2, bac), bad))) → new_ltEs1(vyy2130010, vyy1510, bac, bad)
new_compare21(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, ge, app(ty_Maybe, app(app(ty_Either, da), db))) → new_ltEs2(vyy2130010, vyy1510, da, db)
new_compare21(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, ge, app(app(ty_@2, app(ty_[], df)), dg)) → new_lt(vyy2130010, vyy1510, df)
new_compare21(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, app(app(ty_Either, bfa), bfb), beh) → new_compare22(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, bfa, bfb), bfa, bfb)
new_compare21(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, ge, app(app(ty_Either, app(ty_[], gf)), gg)) → new_ltEs(vyy2130010, vyy1510, gf)
new_compare21(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, app(ty_Maybe, cc), beh) → new_compare20(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, cc), cc)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, bce), bbc), app(ty_Maybe, bdh))) → new_ltEs0(vyy2130012, vyy1512, bdh)
new_ltEs2(Right(vyy2130010), Right(vyy1510), hh, app(app(ty_Either, bae), baf)) → new_ltEs2(vyy2130010, vyy1510, bae, baf)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, app(app(app(ty_@3, bcb), bcc), bcd)), bbc), bbd)) → new_lt3(vyy2130010, vyy1510, bcb, bcc, bcd)
new_ltEs1(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(app(ty_@2, ea), eb), dg) → new_lt1(vyy2130010, vyy1510, ea, eb)
new_compare21(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, ge, app(app(ty_Either, hh), app(app(app(ty_@3, bag), bah), bba))) → new_ltEs3(vyy2130010, vyy1510, bag, bah, bba)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), bce, bbc, app(app(app(ty_@3, bee), bef), beg)) → new_ltEs3(vyy2130012, vyy1512, bee, bef, beg)
new_ltEs2(Left(vyy2130010), Left(vyy1510), app(ty_Maybe, gh), gg) → new_ltEs0(vyy2130010, vyy1510, gh)
new_primCompAux(vyy2130000, vyy1500, vyy178, app(app(ty_@2, bd), be)) → new_compare2(vyy2130000, vyy1500, bd, be)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, bce), bbc), app(app(ty_Either, bec), bed))) → new_ltEs2(vyy2130012, vyy1512, bec, bed)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(app(app(ty_@3, bcb), bcc), bcd), bbc, bbd) → new_lt3(vyy2130010, vyy1510, bcb, bcc, bcd)
new_compare(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), ba) → new_compare(vyy2130001, vyy1501, ba)
new_compare(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), ba) → new_primCompAux(vyy2130000, vyy1500, new_compare0(vyy2130001, vyy1501, ba), ba)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, bce), app(app(app(ty_@3, bdd), bde), bdf)), bbd)) → new_lt3(vyy2130011, vyy1511, bdd, bde, bdf)
new_compare21(@2(:(vyy2130000, vyy2130001), vyy213001), @2(:(vyy1500, vyy1501), vyy151), False, app(ty_[], ba), beh) → new_primCompAux(vyy2130000, vyy1500, new_compare0(vyy2130001, vyy1501, ba), ba)
new_compare21(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, ge, app(app(ty_@2, app(ty_Maybe, dh)), dg)) → new_lt0(vyy2130010, vyy1510, dh)
new_compare1(vyy213000, vyy150, cc) → new_compare20(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, cc), cc)
new_lt1(vyy213000, vyy150, gc, gd) → new_compare21(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, gc, gd), gc, gd)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), bce, bbc, app(app(ty_Either, bec), bed)) → new_ltEs2(vyy2130012, vyy1512, bec, bed)
new_ltEs2(Left(vyy2130010), Left(vyy1510), app(ty_[], gf), gg) → new_ltEs(vyy2130010, vyy1510, gf)
new_ltEs2(Left(vyy2130010), Left(vyy1510), app(app(ty_@2, ha), hb), gg) → new_ltEs1(vyy2130010, vyy1510, ha, hb)
new_lt2(vyy213000, vyy150, bfa, bfb) → new_compare22(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, bfa, bfb), bfa, bfb)
new_compare21(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, ge, app(app(app(ty_@3, app(ty_[], bbb)), bbc), bbd)) → new_lt(vyy2130010, vyy1510, bbb)
new_compare22(vyy213000, vyy150, False, bfa, bfb) → new_ltEs2(vyy213000, vyy150, bfa, bfb)
new_compare20(vyy213000, vyy150, False, cc) → new_ltEs0(vyy213000, vyy150, cc)
new_compare21(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, ge, app(ty_Maybe, app(app(ty_@2, cf), cg))) → new_ltEs1(vyy2130010, vyy1510, cf, cg)
new_primCompAux(vyy2130000, vyy1500, vyy178, app(app(app(ty_@3, bh), ca), cb)) → new_compare4(vyy2130000, vyy1500, bh, ca, cb)
new_compare21(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, app(app(app(ty_@3, bfc), bfd), bfe), beh) → new_compare23(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bfc, bfd, bfe), bfc, bfd, bfe)
new_ltEs3(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(ty_Maybe, bbe), bbc, bbd) → new_lt0(vyy2130010, vyy1510, bbe)
new_compare21(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, ge, app(app(ty_Either, app(app(ty_Either, hc), hd)), gg)) → new_ltEs2(vyy2130010, vyy1510, hc, hd)
new_ltEs1(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), eh, app(app(ty_Either, ff), fg)) → new_ltEs2(vyy2130011, vyy1511, ff, fg)
new_compare21(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, ge, app(app(ty_@2, eh), app(ty_[], fa))) → new_ltEs(vyy2130011, vyy1511, fa)

The TRS R consists of the following rules:

new_esEs25(vyy3000, vyy400, app(ty_[], cah)) → new_esEs14(vyy3000, vyy400, cah)
new_compare16(vyy2130000, vyy1500, ty_Ordering) → new_compare29(vyy2130000, vyy1500)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, dcg)) → new_esEs4(vyy3000, vyy400, dcg)
new_compare16(vyy2130000, vyy1500, ty_Float) → new_compare9(vyy2130000, vyy1500)
new_lt4(vyy2130010, vyy1510, ty_Integer) → new_lt16(vyy2130010, vyy1510)
new_ltEs19(vyy2130011, vyy1511, ty_Integer) → new_ltEs16(vyy2130011, vyy1511)
new_lt21(vyy213000, vyy150, ty_Float) → new_lt13(vyy213000, vyy150)
new_esEs25(vyy3000, vyy400, ty_Ordering) → new_esEs17(vyy3000, vyy400)
new_lt21(vyy213000, vyy150, ty_Bool) → new_lt9(vyy213000, vyy150)
new_ltEs5(vyy2130012, vyy1512, ty_Bool) → new_ltEs9(vyy2130012, vyy1512)
new_esEs13(False, True) → False
new_esEs13(True, False) → False
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_compare10(vyy159, vyy160, vyy161, vyy162, False, vyy164, cef, ceg) → new_compare111(vyy159, vyy160, vyy161, vyy162, vyy164, cef, ceg)
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Ordering) → new_ltEs14(vyy2130010, vyy1510)
new_lt4(vyy2130010, vyy1510, ty_Ordering) → new_lt14(vyy2130010, vyy1510)
new_lt4(vyy2130010, vyy1510, app(ty_[], bbb)) → new_lt10(vyy2130010, vyy1510, bbb)
new_ltEs20(vyy213001, vyy151, app(ty_[], h)) → new_ltEs10(vyy213001, vyy151, h)
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Bool, gg) → new_ltEs9(vyy2130010, vyy1510)
new_ltEs14(GT, GT) → True
new_lt21(vyy213000, vyy150, ty_Ordering) → new_lt14(vyy213000, vyy150)
new_esEs24(vyy3001, vyy401, app(ty_Maybe, bhe)) → new_esEs4(vyy3001, vyy401, bhe)
new_esEs4(Nothing, Just(vyy400), dce) → False
new_esEs4(Just(vyy3000), Nothing, dce) → False
new_esEs28(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_ltEs5(vyy2130012, vyy1512, ty_Float) → new_ltEs13(vyy2130012, vyy1512)
new_esEs21(vyy213000, vyy150, ty_Ordering) → new_esEs17(vyy213000, vyy150)
new_lt10(vyy213000, vyy150, ba) → new_esEs17(new_compare0(vyy213000, vyy150, ba), LT)
new_ltEs19(vyy2130011, vyy1511, app(ty_Maybe, fb)) → new_ltEs11(vyy2130011, vyy1511, fb)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs12(vyy3000, vyy400)
new_lt20(vyy2130010, vyy1510, ty_@0) → new_lt6(vyy2130010, vyy1510)
new_primMulNat0(Zero, Zero) → Zero
new_esEs29(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, ccf), ccg), cch), cca) → new_esEs7(vyy3000, vyy400, ccf, ccg, cch)
new_lt6(vyy213000, vyy150) → new_esEs17(new_compare17(vyy213000, vyy150), LT)
new_esEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cgc, cgd, cge) → new_asAs(new_esEs29(vyy3000, vyy400, cgc), new_asAs(new_esEs28(vyy3001, vyy401, cgd), new_esEs27(vyy3002, vyy402, cge)))
new_esEs25(vyy3000, vyy400, app(app(ty_Either, cbf), cbg)) → new_esEs6(vyy3000, vyy400, cbf, cbg)
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, ty_Int) → new_ltEs12(vyy2130010, vyy1510)
new_ltEs15(vyy213001, vyy151) → new_not(new_esEs17(new_compare8(vyy213001, vyy151), GT))
new_esEs20(vyy2130010, vyy1510, app(ty_Maybe, dh)) → new_esEs4(vyy2130010, vyy1510, dh)
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, app(ty_Ratio, bgg)) → new_ltEs7(vyy2130010, vyy1510, bgg)
new_compare7(vyy213000, vyy150) → new_compare27(vyy213000, vyy150, new_esEs13(vyy213000, vyy150))
new_ltEs18(Left(vyy2130010), Left(vyy1510), app(ty_[], gf), gg) → new_ltEs10(vyy2130010, vyy1510, gf)
new_esEs8(vyy2130011, vyy1511, app(ty_[], bcf)) → new_esEs14(vyy2130011, vyy1511, bcf)
new_esEs28(vyy3001, vyy401, ty_Int) → new_esEs15(vyy3001, vyy401)
new_ltEs9(True, False) → False
new_ltEs11(Just(vyy2130010), Just(vyy1510), app(app(app(ty_@3, dc), dd), de)) → new_ltEs4(vyy2130010, vyy1510, dc, dd, de)
new_ltEs12(vyy213001, vyy151) → new_not(new_esEs17(new_compare12(vyy213001, vyy151), GT))
new_esEs24(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_esEs21(vyy213000, vyy150, ty_Integer) → new_esEs19(vyy213000, vyy150)
new_ltEs18(Left(vyy2130010), Left(vyy1510), app(app(app(ty_@3, he), hf), hg), gg) → new_ltEs4(vyy2130010, vyy1510, he, hf, hg)
new_esEs20(vyy2130010, vyy1510, ty_Ordering) → new_esEs17(vyy2130010, vyy1510)
new_lt21(vyy213000, vyy150, app(ty_Maybe, cc)) → new_lt11(vyy213000, vyy150, cc)
new_ltEs11(Just(vyy2130010), Just(vyy1510), app(ty_Ratio, dcd)) → new_ltEs7(vyy2130010, vyy1510, dcd)
new_compare16(vyy2130000, vyy1500, app(app(ty_@2, bd), be)) → new_compare5(vyy2130000, vyy1500, bd, be)
new_esEs21(vyy213000, vyy150, ty_Int) → new_esEs15(vyy213000, vyy150)
new_esEs21(vyy213000, vyy150, ty_Double) → new_esEs18(vyy213000, vyy150)
new_ltEs20(vyy213001, vyy151, app(app(ty_@2, eh), dg)) → new_ltEs17(vyy213001, vyy151, eh, dg)
new_ltEs18(Left(vyy2130010), Left(vyy1510), app(app(ty_Either, hc), hd), gg) → new_ltEs18(vyy2130010, vyy1510, hc, hd)
new_lt5(vyy2130011, vyy1511, ty_Int) → new_lt12(vyy2130011, vyy1511)
new_esEs24(vyy3001, vyy401, app(app(ty_@2, bhg), bhh)) → new_esEs5(vyy3001, vyy401, bhg, bhh)
new_esEs21(vyy213000, vyy150, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs7(vyy213000, vyy150, bfc, bfd, bfe)
new_lt20(vyy2130010, vyy1510, ty_Integer) → new_lt16(vyy2130010, vyy1510)
new_esEs6(Right(vyy3000), Right(vyy400), cdc, app(ty_Ratio, cdd)) → new_esEs11(vyy3000, vyy400, cdd)
new_ltEs18(Right(vyy2130010), Left(vyy1510), hh, gg) → False
new_compare5(vyy213000, vyy150, gc, gd) → new_compare25(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, gc, gd), gc, gd)
new_ltEs20(vyy213001, vyy151, ty_Integer) → new_ltEs16(vyy213001, vyy151)
new_esEs21(vyy213000, vyy150, app(app(ty_Either, bfa), bfb)) → new_esEs6(vyy213000, vyy150, bfa, bfb)
new_compare28(vyy213000, vyy150, False, bfa, bfb) → new_compare113(vyy213000, vyy150, new_ltEs18(vyy213000, vyy150, bfa, bfb), bfa, bfb)
new_esEs29(vyy3000, vyy400, app(app(app(ty_@3, dbg), dbh), dca)) → new_esEs7(vyy3000, vyy400, dbg, dbh, dca)
new_ltEs20(vyy213001, vyy151, app(ty_Maybe, bgd)) → new_ltEs11(vyy213001, vyy151, bgd)
new_esEs8(vyy2130011, vyy1511, app(app(ty_Either, bdb), bdc)) → new_esEs6(vyy2130011, vyy1511, bdb, bdc)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, cfb)) → new_esEs4(vyy3000, vyy400, cfb)
new_lt14(vyy213000, vyy150) → new_esEs17(new_compare29(vyy213000, vyy150), LT)
new_ltEs19(vyy2130011, vyy1511, ty_Bool) → new_ltEs9(vyy2130011, vyy1511)
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs4(vyy2130010, vyy1510, bag, bah, bba)
new_compare24(vyy213000, vyy150, False, cc) → new_compare14(vyy213000, vyy150, new_ltEs11(vyy213000, vyy150, cc), cc)
new_esEs25(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_ltEs20(vyy213001, vyy151, app(ty_Ratio, bgc)) → new_ltEs7(vyy213001, vyy151, bgc)
new_esEs8(vyy2130011, vyy1511, ty_Bool) → new_esEs13(vyy2130011, vyy1511)
new_pePe(False, vyy177) → vyy177
new_esEs14([], [], ceh) → True
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Float) → new_ltEs13(vyy2130010, vyy1510)
new_lt21(vyy213000, vyy150, ty_Char) → new_lt8(vyy213000, vyy150)
new_lt5(vyy2130011, vyy1511, app(ty_Ratio, bfg)) → new_lt7(vyy2130011, vyy1511, bfg)
new_ltEs11(Just(vyy2130010), Just(vyy1510), app(app(ty_Either, da), db)) → new_ltEs18(vyy2130010, vyy1510, da, db)
new_esEs15(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, ty_Integer) → new_ltEs16(vyy2130010, vyy1510)
new_esEs8(vyy2130011, vyy1511, ty_Float) → new_esEs16(vyy2130011, vyy1511)
new_esEs29(vyy3000, vyy400, app(ty_[], dbd)) → new_esEs14(vyy3000, vyy400, dbd)
new_lt9(vyy213000, vyy150) → new_esEs17(new_compare7(vyy213000, vyy150), LT)
new_ltEs14(GT, EQ) → False
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs12(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_lt18(vyy213000, vyy150, bfa, bfb) → new_esEs17(new_compare13(vyy213000, vyy150, bfa, bfb), LT)
new_ltEs11(Just(vyy2130010), Just(vyy1510), app(ty_[], cd)) → new_ltEs10(vyy2130010, vyy1510, cd)
new_lt20(vyy2130010, vyy1510, app(app(ty_@2, ea), eb)) → new_lt17(vyy2130010, vyy1510, ea, eb)
new_compare11(vyy213000, vyy150, False, bfc, bfd, bfe) → GT
new_esEs20(vyy2130010, vyy1510, ty_Char) → new_esEs12(vyy2130010, vyy1510)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, cca) → new_esEs10(vyy3000, vyy400)
new_lt4(vyy2130010, vyy1510, app(ty_Ratio, bff)) → new_lt7(vyy2130010, vyy1510, bff)
new_esEs8(vyy2130011, vyy1511, ty_Integer) → new_esEs19(vyy2130011, vyy1511)
new_esEs9(vyy2130010, vyy1510, ty_Double) → new_esEs18(vyy2130010, vyy1510)
new_ltEs5(vyy2130012, vyy1512, ty_Int) → new_ltEs12(vyy2130012, vyy1512)
new_esEs20(vyy2130010, vyy1510, app(app(ty_@2, ea), eb)) → new_esEs5(vyy2130010, vyy1510, ea, eb)
new_primCmpNat0(Zero, Succ(vyy15000)) → LT
new_esEs27(vyy3002, vyy402, app(app(app(ty_@3, chc), chd), che)) → new_esEs7(vyy3002, vyy402, chc, chd, che)
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, app(app(ty_@2, bac), bad)) → new_ltEs17(vyy2130010, vyy1510, bac, bad)
new_esEs17(LT, LT) → True
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Bool) → new_ltEs9(vyy2130010, vyy1510)
new_esEs27(vyy3002, vyy402, ty_@0) → new_esEs10(vyy3002, vyy402)
new_esEs6(Right(vyy3000), Left(vyy400), cdc, cca) → False
new_esEs6(Left(vyy3000), Right(vyy400), cdc, cca) → False
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs18(vyy3000, vyy400)
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, app(app(ty_Either, bae), baf)) → new_ltEs18(vyy2130010, vyy1510, bae, baf)
new_lt21(vyy213000, vyy150, app(app(app(ty_@3, bfc), bfd), bfe)) → new_lt19(vyy213000, vyy150, bfc, bfd, bfe)
new_lt21(vyy213000, vyy150, app(app(ty_@2, gc), gd)) → new_lt17(vyy213000, vyy150, gc, gd)
new_lt5(vyy2130011, vyy1511, app(app(app(ty_@3, bdd), bde), bdf)) → new_lt19(vyy2130011, vyy1511, bdd, bde, bdf)
new_ltEs19(vyy2130011, vyy1511, app(app(app(ty_@3, fh), ga), gb)) → new_ltEs4(vyy2130011, vyy1511, fh, ga, gb)
new_esEs29(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, ty_Ordering) → new_ltEs14(vyy2130010, vyy1510)
new_compare0([], [], ba) → EQ
new_pePe(True, vyy177) → True
new_ltEs8(vyy213001, vyy151) → new_not(new_esEs17(new_compare19(vyy213001, vyy151), GT))
new_primEqNat0(Zero, Zero) → True
new_ltEs18(Left(vyy2130010), Left(vyy1510), app(ty_Maybe, gh), gg) → new_ltEs11(vyy2130010, vyy1510, gh)
new_ltEs11(Nothing, Just(vyy1510), bgd) → True
new_ltEs11(Just(vyy2130010), Just(vyy1510), app(ty_Maybe, ce)) → new_ltEs11(vyy2130010, vyy1510, ce)
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_@0) → new_ltEs6(vyy2130010, vyy1510)
new_compare17(@0, @0) → EQ
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat1(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs20(vyy2130010, vyy1510, ty_Bool) → new_esEs13(vyy2130010, vyy1510)
new_esEs6(Right(vyy3000), Right(vyy400), cdc, app(app(ty_Either, ced), cee)) → new_esEs6(vyy3000, vyy400, ced, cee)
new_esEs27(vyy3002, vyy402, ty_Char) → new_esEs12(vyy3002, vyy402)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs15(vyy3000, vyy400)
new_esEs9(vyy2130010, vyy1510, app(ty_Ratio, bff)) → new_esEs11(vyy2130010, vyy1510, bff)
new_lt5(vyy2130011, vyy1511, ty_Char) → new_lt8(vyy2130011, vyy1511)
new_ltEs14(EQ, LT) → False
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_ltEs5(vyy2130012, vyy1512, app(ty_Ratio, bfh)) → new_ltEs7(vyy2130012, vyy1512, bfh)
new_esEs28(vyy3001, vyy401, app(app(ty_Either, dah), dba)) → new_esEs6(vyy3001, vyy401, dah, dba)
new_esEs9(vyy2130010, vyy1510, app(app(app(ty_@3, bcb), bcc), bcd)) → new_esEs7(vyy2130010, vyy1510, bcb, bcc, bcd)
new_esEs24(vyy3001, vyy401, ty_Char) → new_esEs12(vyy3001, vyy401)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, cca) → new_esEs12(vyy3000, vyy400)
new_lt20(vyy2130010, vyy1510, app(ty_Maybe, dh)) → new_lt11(vyy2130010, vyy1510, dh)
new_esEs25(vyy3000, vyy400, ty_@0) → new_esEs10(vyy3000, vyy400)
new_ltEs20(vyy213001, vyy151, ty_@0) → new_ltEs6(vyy213001, vyy151)
new_lt21(vyy213000, vyy150, ty_Double) → new_lt15(vyy213000, vyy150)
new_esEs25(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_lt20(vyy2130010, vyy1510, ty_Ordering) → new_lt14(vyy2130010, vyy1510)
new_esEs20(vyy2130010, vyy1510, app(app(app(ty_@3, ee), ef), eg)) → new_esEs7(vyy2130010, vyy1510, ee, ef, eg)
new_compare16(vyy2130000, vyy1500, app(ty_[], bb)) → new_compare0(vyy2130000, vyy1500, bb)
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Int, gg) → new_ltEs12(vyy2130010, vyy1510)
new_lt20(vyy2130010, vyy1510, ty_Bool) → new_lt9(vyy2130010, vyy1510)
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Integer) → new_ltEs16(vyy2130010, vyy1510)
new_lt4(vyy2130010, vyy1510, app(app(app(ty_@3, bcb), bcc), bcd)) → new_lt19(vyy2130010, vyy1510, bcb, bcc, bcd)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, cca) → new_esEs15(vyy3000, vyy400)
new_esEs28(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_esEs8(vyy2130011, vyy1511, ty_Char) → new_esEs12(vyy2130011, vyy1511)
new_ltEs20(vyy213001, vyy151, app(app(app(ty_@3, bce), bbc), bbd)) → new_ltEs4(vyy213001, vyy151, bce, bbc, bbd)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs24(vyy3001, vyy401, app(ty_Ratio, bhd)) → new_esEs11(vyy3001, vyy401, bhd)
new_esEs8(vyy2130011, vyy1511, app(app(ty_@2, bch), bda)) → new_esEs5(vyy2130011, vyy1511, bch, bda)
new_ltEs19(vyy2130011, vyy1511, app(app(ty_@2, fc), fd)) → new_ltEs17(vyy2130011, vyy1511, fc, fd)
new_esEs29(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), cdc, app(app(app(ty_@3, cea), ceb), cec)) → new_esEs7(vyy3000, vyy400, cea, ceb, cec)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs15(vyy3000, vyy400)
new_compare113(vyy213000, vyy150, True, bfa, bfb) → LT
new_esEs27(vyy3002, vyy402, ty_Bool) → new_esEs13(vyy3002, vyy402)
new_lt16(vyy213000, vyy150) → new_esEs17(new_compare15(vyy213000, vyy150), LT)
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs15(vyy3001, vyy401)
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Float, gg) → new_ltEs13(vyy2130010, vyy1510)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs7(vyy3000, vyy400, cff, cfg, cfh)
new_esEs21(vyy213000, vyy150, ty_Char) → new_esEs12(vyy213000, vyy150)
new_esEs28(vyy3001, vyy401, app(ty_Maybe, daa)) → new_esEs4(vyy3001, vyy401, daa)
new_esEs20(vyy2130010, vyy1510, ty_Int) → new_esEs15(vyy2130010, vyy1510)
new_esEs14([], :(vyy400, vyy401), ceh) → False
new_esEs14(:(vyy3000, vyy3001), [], ceh) → False
new_compare30(vyy213000, vyy150, bfc, bfd, bfe) → new_compare26(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bfc, bfd, bfe), bfc, bfd, bfe)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], ccc), cca) → new_esEs14(vyy3000, vyy400, ccc)
new_esEs9(vyy2130010, vyy1510, app(ty_[], bbb)) → new_esEs14(vyy2130010, vyy1510, bbb)
new_compare111(vyy159, vyy160, vyy161, vyy162, True, cef, ceg) → LT
new_lt15(vyy213000, vyy150) → new_esEs17(new_compare8(vyy213000, vyy150), LT)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs16(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs17(EQ, EQ) → True
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Double, gg) → new_ltEs15(vyy2130010, vyy1510)
new_compare11(vyy213000, vyy150, True, bfc, bfd, bfe) → LT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, cca) → new_esEs17(vyy3000, vyy400)
new_esEs8(vyy2130011, vyy1511, ty_Double) → new_esEs18(vyy2130011, vyy1511)
new_esEs26(vyy3000, vyy400, app(ty_[], cfc)) → new_esEs14(vyy3000, vyy400, cfc)
new_esEs28(vyy3001, vyy401, ty_Ordering) → new_esEs17(vyy3001, vyy401)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primCompAux0(vyy183, GT) → GT
new_ltEs18(Left(vyy2130010), Right(vyy1510), hh, gg) → True
new_primPlusNat1(Zero, vyy40100) → Succ(vyy40100)
new_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_esEs20(vyy2130010, vyy1510, ty_@0) → new_esEs10(vyy2130010, vyy1510)
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, ty_Double) → new_ltEs15(vyy2130010, vyy1510)
new_esEs28(vyy3001, vyy401, app(ty_[], dab)) → new_esEs14(vyy3001, vyy401, dab)
new_ltEs6(vyy213001, vyy151) → new_not(new_esEs17(new_compare17(vyy213001, vyy151), GT))
new_compare10(vyy159, vyy160, vyy161, vyy162, True, vyy164, cef, ceg) → new_compare111(vyy159, vyy160, vyy161, vyy162, True, cef, ceg)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_lt20(vyy2130010, vyy1510, ty_Char) → new_lt8(vyy2130010, vyy1510)
new_ltEs20(vyy213001, vyy151, ty_Double) → new_ltEs15(vyy213001, vyy151)
new_ltEs20(vyy213001, vyy151, app(app(ty_Either, hh), gg)) → new_ltEs18(vyy213001, vyy151, hh, gg)
new_esEs5(@2(vyy3000, vyy3001), @2(vyy400, vyy401), bhb, bhc) → new_asAs(new_esEs25(vyy3000, vyy400, bhb), new_esEs24(vyy3001, vyy401, bhc))
new_ltEs16(vyy213001, vyy151) → new_not(new_esEs17(new_compare15(vyy213001, vyy151), GT))
new_primCmpNat0(Succ(vyy21300000), Succ(vyy15000)) → new_primCmpNat0(vyy21300000, vyy15000)
new_compare112(vyy213000, vyy150, True) → LT
new_esEs25(vyy3000, vyy400, app(ty_Maybe, cag)) → new_esEs4(vyy3000, vyy400, cag)
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, ty_Bool) → new_ltEs9(vyy2130010, vyy1510)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, dda), ddb)) → new_esEs5(vyy3000, vyy400, dda, ddb)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, ddf), ddg)) → new_esEs6(vyy3000, vyy400, ddf, ddg)
new_esEs17(GT, LT) → False
new_esEs17(LT, GT) → False
new_compare14(vyy213000, vyy150, False, cc) → GT
new_esEs6(Right(vyy3000), Right(vyy400), cdc, app(ty_Maybe, cde)) → new_esEs4(vyy3000, vyy400, cde)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_compare8(Double(vyy2130000, vyy2130001), Double(vyy1500, vyy1501)) → new_compare12(new_sr(vyy2130000, vyy1500), new_sr(vyy2130001, vyy1501))
new_esEs17(GT, EQ) → False
new_esEs17(EQ, GT) → False
new_compare26(vyy213000, vyy150, False, bfc, bfd, bfe) → new_compare11(vyy213000, vyy150, new_ltEs4(vyy213000, vyy150, bfc, bfd, bfe), bfc, bfd, bfe)
new_esEs21(vyy213000, vyy150, app(ty_[], ba)) → new_esEs14(vyy213000, vyy150, ba)
new_esEs9(vyy2130010, vyy1510, ty_Float) → new_esEs16(vyy2130010, vyy1510)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, cca) → new_esEs16(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), cdc, app(app(ty_@2, cdg), cdh)) → new_esEs5(vyy3000, vyy400, cdg, cdh)
new_compare113(vyy213000, vyy150, False, bfa, bfb) → GT
new_lt4(vyy2130010, vyy1510, app(app(ty_@2, bbf), bbg)) → new_lt17(vyy2130010, vyy1510, bbf, bbg)
new_esEs9(vyy2130010, vyy1510, app(app(ty_Either, bbh), bca)) → new_esEs6(vyy2130010, vyy1510, bbh, bca)
new_lt4(vyy2130010, vyy1510, app(ty_Maybe, bbe)) → new_lt11(vyy2130010, vyy1510, bbe)
new_primCmpInt(Neg(Succ(vyy21300000)), Neg(vyy1500)) → new_primCmpNat0(vyy1500, Succ(vyy21300000))
new_compare16(vyy2130000, vyy1500, app(ty_Maybe, bc)) → new_compare6(vyy2130000, vyy1500, bc)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, dcf)) → new_esEs11(vyy3000, vyy400, dcf)
new_esEs6(Right(vyy3000), Right(vyy400), cdc, ty_@0) → new_esEs10(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), cdc, ty_Char) → new_esEs12(vyy3000, vyy400)
new_ltEs18(Left(vyy2130010), Left(vyy1510), app(app(ty_@2, ha), hb), gg) → new_ltEs17(vyy2130010, vyy1510, ha, hb)
new_ltEs20(vyy213001, vyy151, ty_Ordering) → new_ltEs14(vyy213001, vyy151)
new_compare19(Char(vyy2130000), Char(vyy1500)) → new_primCmpNat0(vyy2130000, vyy1500)
new_ltEs5(vyy2130012, vyy1512, app(ty_Maybe, bdh)) → new_ltEs11(vyy2130012, vyy1512, bdh)
new_ltEs7(vyy213001, vyy151, bgc) → new_not(new_esEs17(new_compare18(vyy213001, vyy151, bgc), GT))
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Ordering, gg) → new_ltEs14(vyy2130010, vyy1510)
new_primPlusNat0(Succ(vyy13100), Zero) → Succ(vyy13100)
new_primPlusNat0(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_esEs24(vyy3001, vyy401, ty_@0) → new_esEs10(vyy3001, vyy401)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, ty_@0) → new_ltEs6(vyy2130010, vyy1510)
new_primCmpNat0(Succ(vyy21300000), Zero) → GT
new_esEs29(vyy3000, vyy400, ty_Double) → new_esEs18(vyy3000, vyy400)
new_lt21(vyy213000, vyy150, app(ty_[], ba)) → new_lt10(vyy213000, vyy150, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy15000))) → LT
new_esEs24(vyy3001, vyy401, ty_Double) → new_esEs18(vyy3001, vyy401)
new_esEs6(Right(vyy3000), Right(vyy400), cdc, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_sr0(Integer(vyy15000), Integer(vyy21300010)) → Integer(new_primMulInt(vyy15000, vyy21300010))
new_ltEs5(vyy2130012, vyy1512, ty_Double) → new_ltEs15(vyy2130012, vyy1512)
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Integer, gg) → new_ltEs16(vyy2130010, vyy1510)
new_compare28(vyy213000, vyy150, True, bfa, bfb) → EQ
new_ltEs4(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), bce, bbc, bbd) → new_pePe(new_lt4(vyy2130010, vyy1510, bce), new_asAs(new_esEs9(vyy2130010, vyy1510, bce), new_pePe(new_lt5(vyy2130011, vyy1511, bbc), new_asAs(new_esEs8(vyy2130011, vyy1511, bbc), new_ltEs5(vyy2130012, vyy1512, bbd)))))
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_esEs16(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs15(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare16(vyy2130000, vyy1500, app(ty_Ratio, bha)) → new_compare18(vyy2130000, vyy1500, bha)
new_esEs25(vyy3000, vyy400, app(ty_Ratio, caf)) → new_esEs11(vyy3000, vyy400, caf)
new_compare16(vyy2130000, vyy1500, ty_@0) → new_compare17(vyy2130000, vyy1500)
new_compare13(vyy213000, vyy150, bfa, bfb) → new_compare28(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, bfa, bfb), bfa, bfb)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs18(vyy3000, vyy400)
new_esEs11(:%(vyy3000, vyy3001), :%(vyy400, vyy401), bgh) → new_asAs(new_esEs23(vyy3000, vyy400, bgh), new_esEs22(vyy3001, vyy401, bgh))
new_esEs9(vyy2130010, vyy1510, ty_@0) → new_esEs10(vyy2130010, vyy1510)
new_lt5(vyy2130011, vyy1511, ty_Bool) → new_lt9(vyy2130011, vyy1511)
new_esEs29(vyy3000, vyy400, app(app(ty_@2, dbe), dbf)) → new_esEs5(vyy3000, vyy400, dbe, dbf)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, ccb), cca) → new_esEs4(vyy3000, vyy400, ccb)
new_compare16(vyy2130000, vyy1500, ty_Int) → new_compare12(vyy2130000, vyy1500)
new_esEs25(vyy3000, vyy400, ty_Char) → new_esEs12(vyy3000, vyy400)
new_compare12(vyy213000, vyy150) → new_primCmpInt(vyy213000, vyy150)
new_esEs27(vyy3002, vyy402, app(ty_Ratio, cgf)) → new_esEs11(vyy3002, vyy402, cgf)
new_lt4(vyy2130010, vyy1510, ty_Double) → new_lt15(vyy2130010, vyy1510)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy15000))) → new_primCmpNat0(Zero, Succ(vyy15000))
new_esEs6(Right(vyy3000), Right(vyy400), cdc, ty_Double) → new_esEs18(vyy3000, vyy400)
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Char, gg) → new_ltEs8(vyy2130010, vyy1510)
new_lt4(vyy2130010, vyy1510, app(app(ty_Either, bbh), bca)) → new_lt18(vyy2130010, vyy1510, bbh, bca)
new_compare18(:%(vyy2130000, vyy2130001), :%(vyy1500, vyy1501), ty_Int) → new_compare12(new_sr(vyy2130000, vyy1501), new_sr(vyy1500, vyy2130001))
new_esEs8(vyy2130011, vyy1511, ty_@0) → new_esEs10(vyy2130011, vyy1511)
new_primCompAux1(vyy2130000, vyy1500, vyy178, ba) → new_primCompAux0(vyy178, new_compare16(vyy2130000, vyy1500, ba))
new_lt4(vyy2130010, vyy1510, ty_Float) → new_lt13(vyy2130010, vyy1510)
new_esEs8(vyy2130011, vyy1511, ty_Int) → new_esEs15(vyy2130011, vyy1511)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, cfd), cfe)) → new_esEs5(vyy3000, vyy400, cfd, cfe)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_primCompAux0(vyy183, LT) → LT
new_esEs21(vyy213000, vyy150, app(app(ty_@2, gc), gd)) → new_esEs5(vyy213000, vyy150, gc, gd)
new_ltEs19(vyy2130011, vyy1511, ty_Char) → new_ltEs8(vyy2130011, vyy1511)
new_esEs12(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_not(False) → True
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, cda), cdb), cca) → new_esEs6(vyy3000, vyy400, cda, cdb)
new_compare27(vyy213000, vyy150, False) → new_compare110(vyy213000, vyy150, new_ltEs9(vyy213000, vyy150))
new_compare24(vyy213000, vyy150, True, cc) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), cdc, ty_Ordering) → new_esEs17(vyy3000, vyy400)
new_primCmpInt(Pos(Succ(vyy21300000)), Pos(vyy1500)) → new_primCmpNat0(Succ(vyy21300000), vyy1500)
new_esEs9(vyy2130010, vyy1510, ty_Bool) → new_esEs13(vyy2130010, vyy1510)
new_compare9(Float(vyy2130000, vyy2130001), Float(vyy1500, vyy1501)) → new_compare12(new_sr(vyy2130000, vyy1500), new_sr(vyy2130001, vyy1501))
new_ltEs19(vyy2130011, vyy1511, app(ty_[], fa)) → new_ltEs10(vyy2130011, vyy1511, fa)
new_esEs24(vyy3001, vyy401, app(app(ty_Either, cad), cae)) → new_esEs6(vyy3001, vyy401, cad, cae)
new_esEs19(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_ltEs14(LT, LT) → True
new_lt20(vyy2130010, vyy1510, app(ty_[], df)) → new_lt10(vyy2130010, vyy1510, df)
new_esEs24(vyy3001, vyy401, app(ty_[], bhf)) → new_esEs14(vyy3001, vyy401, bhf)
new_esEs28(vyy3001, vyy401, app(app(ty_@2, dac), dad)) → new_esEs5(vyy3001, vyy401, dac, dad)
new_compare0(:(vyy2130000, vyy2130001), [], ba) → GT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, cca) → new_esEs13(vyy3000, vyy400)
new_esEs29(vyy3000, vyy400, ty_Int) → new_esEs15(vyy3000, vyy400)
new_esEs27(vyy3002, vyy402, app(app(ty_Either, chf), chg)) → new_esEs6(vyy3002, vyy402, chf, chg)
new_compare16(vyy2130000, vyy1500, ty_Integer) → new_compare15(vyy2130000, vyy1500)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs15(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs15(vyy3001, vyy401)
new_ltEs19(vyy2130011, vyy1511, app(app(ty_Either, ff), fg)) → new_ltEs18(vyy2130011, vyy1511, ff, fg)
new_esEs20(vyy2130010, vyy1510, app(ty_Ratio, bga)) → new_esEs11(vyy2130010, vyy1510, bga)
new_primCmpInt(Pos(Succ(vyy21300000)), Neg(vyy1500)) → GT
new_esEs8(vyy2130011, vyy1511, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs7(vyy2130011, vyy1511, bdd, bde, bdf)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, cca) → new_esEs18(vyy3000, vyy400)
new_compare16(vyy2130000, vyy1500, ty_Char) → new_compare19(vyy2130000, vyy1500)
new_lt4(vyy2130010, vyy1510, ty_@0) → new_lt6(vyy2130010, vyy1510)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, cca) → new_esEs19(vyy3000, vyy400)
new_esEs9(vyy2130010, vyy1510, ty_Char) → new_esEs12(vyy2130010, vyy1510)
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Double) → new_ltEs15(vyy2130010, vyy1510)
new_ltEs19(vyy2130011, vyy1511, ty_Float) → new_ltEs13(vyy2130011, vyy1511)
new_lt20(vyy2130010, vyy1510, ty_Double) → new_lt15(vyy2130010, vyy1510)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs10(vyy3000, vyy400)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_lt21(vyy213000, vyy150, ty_Int) → new_lt12(vyy213000, vyy150)
new_compare16(vyy2130000, vyy1500, ty_Bool) → new_compare7(vyy2130000, vyy1500)
new_ltEs5(vyy2130012, vyy1512, ty_Ordering) → new_ltEs14(vyy2130012, vyy1512)
new_esEs6(Right(vyy3000), Right(vyy400), cdc, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, app(ty_[], baa)) → new_ltEs10(vyy2130010, vyy1510, baa)
new_esEs28(vyy3001, vyy401, app(app(app(ty_@3, dae), daf), dag)) → new_esEs7(vyy3001, vyy401, dae, daf, dag)
new_compare18(:%(vyy2130000, vyy2130001), :%(vyy1500, vyy1501), ty_Integer) → new_compare15(new_sr0(vyy2130000, vyy1501), new_sr0(vyy1500, vyy2130001))
new_compare16(vyy2130000, vyy1500, ty_Double) → new_compare8(vyy2130000, vyy1500)
new_ltEs20(vyy213001, vyy151, ty_Bool) → new_ltEs9(vyy213001, vyy151)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, ccd), cce), cca) → new_esEs5(vyy3000, vyy400, ccd, cce)
new_ltEs9(True, True) → True
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Char) → new_ltEs8(vyy2130010, vyy1510)
new_ltEs11(Just(vyy2130010), Just(vyy1510), app(app(ty_@2, cf), cg)) → new_ltEs17(vyy2130010, vyy1510, cf, cg)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs5(vyy2130012, vyy1512, app(app(ty_@2, bea), beb)) → new_ltEs17(vyy2130012, vyy1512, bea, beb)
new_compare110(vyy213000, vyy150, True) → LT
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Int) → new_ltEs12(vyy2130010, vyy1510)
new_ltEs17(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), eh, dg) → new_pePe(new_lt20(vyy2130010, vyy1510, eh), new_asAs(new_esEs20(vyy2130010, vyy1510, eh), new_ltEs19(vyy2130011, vyy1511, dg)))
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_esEs21(vyy213000, vyy150, ty_@0) → new_esEs10(vyy213000, vyy150)
new_ltEs19(vyy2130011, vyy1511, ty_Int) → new_ltEs12(vyy2130011, vyy1511)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs19(vyy2130011, vyy1511, ty_@0) → new_ltEs6(vyy2130011, vyy1511)
new_lt20(vyy2130010, vyy1510, app(app(ty_Either, ec), ed)) → new_lt18(vyy2130010, vyy1510, ec, ed)
new_compare25(vyy21300, vyy15, True, ge, beh) → EQ
new_lt21(vyy213000, vyy150, ty_Integer) → new_lt16(vyy213000, vyy150)
new_compare110(vyy213000, vyy150, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs9(False, False) → True
new_esEs4(Nothing, Nothing, dce) → True
new_ltEs10(vyy213001, vyy151, h) → new_not(new_esEs17(new_compare0(vyy213001, vyy151, h), GT))
new_esEs8(vyy2130011, vyy1511, ty_Ordering) → new_esEs17(vyy2130011, vyy1511)
new_esEs20(vyy2130010, vyy1510, app(app(ty_Either, ec), ed)) → new_esEs6(vyy2130010, vyy1510, ec, ed)
new_esEs27(vyy3002, vyy402, app(app(ty_@2, cha), chb)) → new_esEs5(vyy3002, vyy402, cha, chb)
new_compare210(vyy213000, vyy150, True) → EQ
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, app(ty_Maybe, bab)) → new_ltEs11(vyy2130010, vyy1510, bab)
new_lt5(vyy2130011, vyy1511, ty_Integer) → new_lt16(vyy2130011, vyy1511)
new_esEs29(vyy3000, vyy400, app(app(ty_Either, dcb), dcc)) → new_esEs6(vyy3000, vyy400, dcb, dcc)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs27(vyy3002, vyy402, app(ty_Maybe, cgg)) → new_esEs4(vyy3002, vyy402, cgg)
new_primPlusNat1(Succ(vyy1310), vyy40100) → Succ(Succ(new_primPlusNat0(vyy1310, vyy40100)))
new_lt20(vyy2130010, vyy1510, ty_Int) → new_lt12(vyy2130010, vyy1510)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy15000))) → new_primCmpNat0(Succ(vyy15000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy15000))) → GT
new_esEs6(Right(vyy3000), Right(vyy400), cdc, app(ty_[], cdf)) → new_esEs14(vyy3000, vyy400, cdf)
new_lt4(vyy2130010, vyy1510, ty_Char) → new_lt8(vyy2130010, vyy1510)
new_ltEs20(vyy213001, vyy151, ty_Char) → new_ltEs8(vyy213001, vyy151)
new_compare0(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), ba) → new_primCompAux1(vyy2130000, vyy1500, new_compare0(vyy2130001, vyy1501, ba), ba)
new_ltEs20(vyy213001, vyy151, ty_Int) → new_ltEs12(vyy213001, vyy151)
new_ltEs20(vyy213001, vyy151, ty_Float) → new_ltEs13(vyy213001, vyy151)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], dch)) → new_esEs14(vyy3000, vyy400, dch)
new_compare25(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, ge, beh) → new_compare10(vyy213000, vyy213001, vyy150, vyy151, new_lt21(vyy213000, vyy150, ge), new_asAs(new_esEs21(vyy213000, vyy150, ge), new_ltEs20(vyy213001, vyy151, beh)), ge, beh)
new_compare210(vyy213000, vyy150, False) → new_compare112(vyy213000, vyy150, new_ltEs14(vyy213000, vyy150))
new_ltEs19(vyy2130011, vyy1511, ty_Ordering) → new_ltEs14(vyy2130011, vyy1511)
new_esEs21(vyy213000, vyy150, app(ty_Maybe, cc)) → new_esEs4(vyy213000, vyy150, cc)
new_lt13(vyy213000, vyy150) → new_esEs17(new_compare9(vyy213000, vyy150), LT)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, cbh), cca) → new_esEs11(vyy3000, vyy400, cbh)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs19(vyy3000, vyy400)
new_ltEs5(vyy2130012, vyy1512, ty_Integer) → new_ltEs16(vyy2130012, vyy1512)
new_esEs27(vyy3002, vyy402, ty_Double) → new_esEs18(vyy3002, vyy402)
new_esEs9(vyy2130010, vyy1510, app(app(ty_@2, bbf), bbg)) → new_esEs5(vyy2130010, vyy1510, bbf, bbg)
new_esEs10(@0, @0) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs24(vyy3001, vyy401, app(app(app(ty_@3, caa), cab), cac)) → new_esEs7(vyy3001, vyy401, caa, cab, cac)
new_esEs9(vyy2130010, vyy1510, ty_Ordering) → new_esEs17(vyy2130010, vyy1510)
new_esEs28(vyy3001, vyy401, ty_@0) → new_esEs10(vyy3001, vyy401)
new_lt19(vyy213000, vyy150, bfc, bfd, bfe) → new_esEs17(new_compare30(vyy213000, vyy150, bfc, bfd, bfe), LT)
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, ty_Float) → new_ltEs13(vyy2130010, vyy1510)
new_asAs(False, vyy111) → False
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_lt4(vyy2130010, vyy1510, ty_Int) → new_lt12(vyy2130010, vyy1510)
new_ltEs13(vyy213001, vyy151) → new_not(new_esEs17(new_compare9(vyy213001, vyy151), GT))
new_esEs29(vyy3000, vyy400, ty_Char) → new_esEs12(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs9(vyy2130010, vyy1510, app(ty_Maybe, bbe)) → new_esEs4(vyy2130010, vyy1510, bbe)
new_esEs21(vyy213000, vyy150, ty_Bool) → new_esEs13(vyy213000, vyy150)
new_compare29(vyy213000, vyy150) → new_compare210(vyy213000, vyy150, new_esEs17(vyy213000, vyy150))
new_lt17(vyy213000, vyy150, gc, gd) → new_esEs17(new_compare5(vyy213000, vyy150, gc, gd), LT)
new_lt5(vyy2130011, vyy1511, ty_Float) → new_lt13(vyy2130011, vyy1511)
new_esEs20(vyy2130010, vyy1510, ty_Float) → new_esEs16(vyy2130010, vyy1510)
new_ltEs14(GT, LT) → False
new_ltEs5(vyy2130012, vyy1512, ty_@0) → new_ltEs6(vyy2130012, vyy1512)
new_esEs28(vyy3001, vyy401, ty_Double) → new_esEs18(vyy3001, vyy401)
new_esEs13(False, False) → True
new_esEs18(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs15(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare14(vyy213000, vyy150, True, cc) → LT
new_esEs8(vyy2130011, vyy1511, app(ty_Ratio, bfg)) → new_esEs11(vyy2130011, vyy1511, bfg)
new_lt5(vyy2130011, vyy1511, app(app(ty_Either, bdb), bdc)) → new_lt18(vyy2130011, vyy1511, bdb, bdc)
new_esEs27(vyy3002, vyy402, ty_Integer) → new_esEs19(vyy3002, vyy402)
new_lt20(vyy2130010, vyy1510, ty_Float) → new_lt13(vyy2130010, vyy1510)
new_lt5(vyy2130011, vyy1511, app(ty_[], bcf)) → new_lt10(vyy2130011, vyy1511, bcf)
new_compare111(vyy159, vyy160, vyy161, vyy162, False, cef, ceg) → GT
new_ltEs9(False, True) → True
new_esEs9(vyy2130010, vyy1510, ty_Integer) → new_esEs19(vyy2130010, vyy1510)
new_compare27(vyy213000, vyy150, True) → EQ
new_esEs17(EQ, LT) → False
new_esEs17(LT, EQ) → False
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs20(vyy2130010, vyy1510, ty_Integer) → new_esEs19(vyy2130010, vyy1510)
new_lt7(vyy213000, vyy150, bge) → new_esEs17(new_compare18(vyy213000, vyy150, bge), LT)
new_ltEs5(vyy2130012, vyy1512, app(ty_[], bdg)) → new_ltEs10(vyy2130012, vyy1512, bdg)
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs10(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, app(app(app(ty_@3, cbc), cbd), cbe)) → new_esEs7(vyy3000, vyy400, cbc, cbd, cbe)
new_compare16(vyy2130000, vyy1500, app(app(ty_Either, bf), bg)) → new_compare13(vyy2130000, vyy1500, bf, bg)
new_esEs24(vyy3001, vyy401, ty_Ordering) → new_esEs17(vyy3001, vyy401)
new_esEs27(vyy3002, vyy402, ty_Int) → new_esEs15(vyy3002, vyy402)
new_esEs8(vyy2130011, vyy1511, app(ty_Maybe, bcg)) → new_esEs4(vyy2130011, vyy1511, bcg)
new_ltEs14(LT, GT) → True
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs17(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, app(app(ty_@2, cba), cbb)) → new_esEs5(vyy3000, vyy400, cba, cbb)
new_compare6(vyy213000, vyy150, cc) → new_compare24(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, cc), cc)
new_ltEs14(LT, EQ) → True
new_esEs25(vyy3000, vyy400, ty_Double) → new_esEs18(vyy3000, vyy400)
new_lt5(vyy2130011, vyy1511, ty_@0) → new_lt6(vyy2130011, vyy1511)
new_esEs27(vyy3002, vyy402, ty_Ordering) → new_esEs17(vyy3002, vyy402)
new_ltEs18(Left(vyy2130010), Left(vyy1510), app(ty_Ratio, bgf), gg) → new_ltEs7(vyy2130010, vyy1510, bgf)
new_esEs28(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_compare112(vyy213000, vyy150, False) → GT
new_lt21(vyy213000, vyy150, app(ty_Ratio, bge)) → new_lt7(vyy213000, vyy150, bge)
new_esEs29(vyy3000, vyy400, ty_Ordering) → new_esEs17(vyy3000, vyy400)
new_lt4(vyy2130010, vyy1510, ty_Bool) → new_lt9(vyy2130010, vyy1510)
new_lt5(vyy2130011, vyy1511, ty_Ordering) → new_lt14(vyy2130011, vyy1511)
new_lt21(vyy213000, vyy150, app(app(ty_Either, bfa), bfb)) → new_lt18(vyy213000, vyy150, bfa, bfb)
new_ltEs19(vyy2130011, vyy1511, ty_Double) → new_ltEs15(vyy2130011, vyy1511)
new_esEs28(vyy3001, vyy401, app(ty_Ratio, chh)) → new_esEs11(vyy3001, vyy401, chh)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, cfa)) → new_esEs11(vyy3000, vyy400, cfa)
new_compare16(vyy2130000, vyy1500, app(app(app(ty_@3, bh), ca), cb)) → new_compare30(vyy2130000, vyy1500, bh, ca, cb)
new_lt21(vyy213000, vyy150, ty_@0) → new_lt6(vyy213000, vyy150)
new_compare26(vyy213000, vyy150, True, bfc, bfd, bfe) → EQ
new_primPlusNat0(Succ(vyy13100), Succ(vyy401000)) → Succ(Succ(new_primPlusNat0(vyy13100, vyy401000)))
new_esEs29(vyy3000, vyy400, ty_@0) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, cga), cgb)) → new_esEs6(vyy3000, vyy400, cga, cgb)
new_compare15(Integer(vyy2130000), Integer(vyy1500)) → new_primCmpInt(vyy2130000, vyy1500)
new_compare0([], :(vyy1500, vyy1501), ba) → LT
new_esEs27(vyy3002, vyy402, app(ty_[], cgh)) → new_esEs14(vyy3002, vyy402, cgh)
new_lt20(vyy2130010, vyy1510, app(app(app(ty_@3, ee), ef), eg)) → new_lt19(vyy2130010, vyy1510, ee, ef, eg)
new_esEs14(:(vyy3000, vyy3001), :(vyy400, vyy401), ceh) → new_asAs(new_esEs26(vyy3000, vyy400, ceh), new_esEs14(vyy3001, vyy401, ceh))
new_ltEs14(EQ, EQ) → True
new_esEs24(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_asAs(True, vyy111) → vyy111
new_lt11(vyy213000, vyy150, cc) → new_esEs17(new_compare6(vyy213000, vyy150, cc), LT)
new_ltEs19(vyy2130011, vyy1511, app(ty_Ratio, bgb)) → new_ltEs7(vyy2130011, vyy1511, bgb)
new_esEs27(vyy3002, vyy402, ty_Float) → new_esEs16(vyy3002, vyy402)
new_ltEs11(Nothing, Nothing, bgd) → True
new_esEs13(True, True) → True
new_esEs17(GT, GT) → True
new_esEs29(vyy3000, vyy400, app(ty_Ratio, dbb)) → new_esEs11(vyy3000, vyy400, dbb)
new_esEs6(Right(vyy3000), Right(vyy400), cdc, ty_Float) → new_esEs16(vyy3000, vyy400)
new_lt8(vyy213000, vyy150) → new_esEs17(new_compare19(vyy213000, vyy150), LT)
new_ltEs5(vyy2130012, vyy1512, ty_Char) → new_ltEs8(vyy2130012, vyy1512)
new_lt5(vyy2130011, vyy1511, app(app(ty_@2, bch), bda)) → new_lt17(vyy2130011, vyy1511, bch, bda)
new_esEs9(vyy2130010, vyy1510, ty_Int) → new_esEs15(vyy2130010, vyy1510)
new_esEs20(vyy2130010, vyy1510, app(ty_[], df)) → new_esEs14(vyy2130010, vyy1510, df)
new_lt12(vyy213000, vyy150) → new_esEs17(new_compare12(vyy213000, vyy150), LT)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ddc), ddd), dde)) → new_esEs7(vyy3000, vyy400, ddc, ddd, dde)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs17(vyy3000, vyy400)
new_lt5(vyy2130011, vyy1511, ty_Double) → new_lt15(vyy2130011, vyy1511)
new_esEs29(vyy3000, vyy400, app(ty_Maybe, dbc)) → new_esEs4(vyy3000, vyy400, dbc)
new_lt5(vyy2130011, vyy1511, app(ty_Maybe, bcg)) → new_lt11(vyy2130011, vyy1511, bcg)
new_lt20(vyy2130010, vyy1510, app(ty_Ratio, bga)) → new_lt7(vyy2130010, vyy1510, bga)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs15(vyy3000, vyy400)
new_esEs21(vyy213000, vyy150, app(ty_Ratio, bge)) → new_esEs11(vyy213000, vyy150, bge)
new_ltEs5(vyy2130012, vyy1512, app(app(ty_Either, bec), bed)) → new_ltEs18(vyy2130012, vyy1512, bec, bed)
new_esEs21(vyy213000, vyy150, ty_Float) → new_esEs16(vyy213000, vyy150)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_primCompAux0(vyy183, EQ) → vyy183
new_ltEs5(vyy2130012, vyy1512, app(app(app(ty_@3, bee), bef), beg)) → new_ltEs4(vyy2130012, vyy1512, bee, bef, beg)
new_ltEs18(Right(vyy2130010), Right(vyy1510), hh, ty_Char) → new_ltEs8(vyy2130010, vyy1510)
new_esEs28(vyy3001, vyy401, ty_Char) → new_esEs12(vyy3001, vyy401)
new_ltEs11(Just(vyy2130010), Nothing, bgd) → False
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_@0, gg) → new_ltEs6(vyy2130010, vyy1510)
new_primCmpInt(Neg(Succ(vyy21300000)), Pos(vyy1500)) → LT
new_esEs6(Right(vyy3000), Right(vyy400), cdc, ty_Int) → new_esEs15(vyy3000, vyy400)
new_esEs20(vyy2130010, vyy1510, ty_Double) → new_esEs18(vyy2130010, vyy1510)
new_not(True) → False

The set Q consists of the following terms:

new_ltEs18(Left(x0), Left(x1), ty_@0, x2)
new_lt21(x0, x1, ty_Char)
new_esEs17(LT, GT)
new_esEs17(GT, LT)
new_ltEs11(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, True)
new_esEs26(x0, x1, ty_Ordering)
new_asAs(True, x0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_ltEs11(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs18(Left(x0), Left(x1), ty_Float, x2)
new_ltEs5(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs18(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs14([], :(x0, x1), x2)
new_esEs20(x0, x1, ty_Integer)
new_esEs17(LT, LT)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs11(Just(x0), Just(x1), ty_Char)
new_compare16(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs9(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt16(x0, x1)
new_ltEs15(x0, x1)
new_ltEs18(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs11(Nothing, Just(x0), x1)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_ltEs13(x0, x1)
new_esEs25(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs4(Just(x0), Nothing, x1)
new_compare0([], :(x0, x1), x2)
new_esEs25(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_compare210(x0, x1, False)
new_ltEs18(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Bool)
new_compare210(x0, x1, True)
new_lt20(x0, x1, ty_Int)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_lt21(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, app(ty_[], x2))
new_esEs17(EQ, GT)
new_esEs17(GT, EQ)
new_compare113(x0, x1, True, x2, x3)
new_lt21(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_lt4(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Bool)
new_compare13(x0, x1, x2, x3)
new_lt5(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Integer)
new_lt4(x0, x1, ty_Ordering)
new_lt21(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_compare16(x0, x1, ty_Integer)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_compare24(x0, x1, True, x2)
new_esEs27(x0, x1, ty_Int)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_compare17(@0, @0)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Float)
new_compare28(x0, x1, False, x2, x3)
new_lt21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Double)
new_ltEs11(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_sr(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs8(x0, x1, ty_Ordering)
new_compare29(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs17(GT, GT)
new_ltEs11(Just(x0), Just(x1), ty_Ordering)
new_compare27(x0, x1, False)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_compare16(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Double)
new_compare16(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_Double)
new_esEs9(x0, x1, ty_@0)
new_primCompAux0(x0, LT)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt4(x0, x1, ty_Bool)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Ordering)
new_ltEs5(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Integer)
new_compare16(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Int)
new_compare11(x0, x1, False, x2, x3, x4)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt19(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare25(x0, x1, True, x2, x3)
new_ltEs9(False, False)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs26(x0, x1, ty_Float)
new_esEs13(False, False)
new_primMulNat0(Zero, Zero)
new_ltEs18(Right(x0), Left(x1), x2, x3)
new_ltEs18(Left(x0), Right(x1), x2, x3)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs19(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Int)
new_compare16(x0, x1, ty_Float)
new_ltEs18(Right(x0), Right(x1), x2, ty_Integer)
new_primPlusNat1(Zero, x0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt5(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_ltEs18(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs11(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Char)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Char)
new_ltEs11(Just(x0), Just(x1), ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_ltEs18(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare5(x0, x1, x2, x3)
new_lt13(x0, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_lt21(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt14(x0, x1)
new_pePe(True, x0)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare7(x0, x1)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare6(x0, x1, x2)
new_esEs14(:(x0, x1), [], x2)
new_esEs29(x0, x1, ty_Char)
new_ltEs18(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, ty_@0)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Char)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, ty_@0)
new_ltEs18(Left(x0), Left(x1), ty_Int, x2)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_@0)
new_compare0([], [], x0)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_compare112(x0, x1, True)
new_esEs27(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_primPlusNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs18(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, ty_Char)
new_ltEs14(LT, LT)
new_ltEs18(Left(x0), Left(x1), ty_Double, x2)
new_lt20(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Float)
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1)
new_esEs27(x0, x1, ty_Ordering)
new_compare16(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2, x3)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_primCompAux0(x0, EQ)
new_compare24(x0, x1, False, x2)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs9(False, True)
new_ltEs9(True, False)
new_lt5(x0, x1, ty_Ordering)
new_esEs15(x0, x1)
new_ltEs9(True, True)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_ltEs18(Left(x0), Left(x1), ty_Char, x2)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs10(@0, @0)
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare10(x0, x1, x2, x3, True, x4, x5, x6)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs5(x0, x1, ty_Double)
new_lt17(x0, x1, x2, x3)
new_ltEs11(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, x2)
new_compare14(x0, x1, True, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare26(x0, x1, True, x2, x3, x4)
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_ltEs8(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(:%(x0, x1), :%(x2, x3), x4)
new_asAs(False, x0)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Bool)
new_lt4(x0, x1, ty_Double)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_compare12(x0, x1)
new_compare16(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Char)
new_esEs4(Nothing, Nothing, x0)
new_ltEs11(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Double)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs21(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Int)
new_compare112(x0, x1, False)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Succ(x0), x1)
new_ltEs20(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs18(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt5(x0, x1, app(ty_[], x2))
new_ltEs11(Just(x0), Just(x1), app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Double)
new_ltEs16(x0, x1)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Char)
new_compare8(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_compare19(Char(x0), Char(x1))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Right(x0), Right(x1), x2, ty_Float)
new_esEs29(x0, x1, ty_Double)
new_lt12(x0, x1)
new_compare110(x0, x1, False)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Float)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, ty_Float)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_lt21(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Integer)
new_esEs9(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_primCmpNat0(Zero, Zero)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, ty_@0)
new_compare25(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_ltEs18(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_Double)
new_ltEs18(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs25(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(Right(x0), Right(x1), x2, ty_@0)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs20(x0, x1, ty_Bool)
new_compare15(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare16(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs18(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs10(x0, x1, x2)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare27(x0, x1, True)
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_esEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_@0)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_compare26(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, ty_Float)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_ltEs20(x0, x1, ty_Int)
new_esEs13(False, True)
new_esEs13(True, False)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs11(Just(x0), Just(x1), ty_Float)
new_compare16(x0, x1, ty_Ordering)
new_compare16(x0, x1, ty_@0)
new_compare16(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_ltEs14(GT, GT)
new_not(True)
new_lt7(x0, x1, x2)
new_ltEs11(Just(x0), Nothing, x1)
new_esEs24(x0, x1, ty_Float)
new_esEs16(Float(x0, x1), Float(x2, x3))
new_esEs13(True, True)
new_compare16(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_@0)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_ltEs7(x0, x1, x2)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs11(Nothing, Nothing, x0)
new_esEs14([], [], x0)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_compare9(Float(x0, x1), Float(x2, x3))
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs24(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_lt8(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_compare113(x0, x1, False, x2, x3)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare11(x0, x1, True, x2, x3, x4)
new_compare30(x0, x1, x2, x3, x4)
new_ltEs18(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(x0, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare14(x0, x1, False, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs5(x0, x1, ty_@0)
new_ltEs18(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt11(x0, x1, x2)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_lt15(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, ty_@0)
new_primCompAux0(x0, GT)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs4(Nothing, Just(x0), x1)
new_esEs21(x0, x1, app(ty_[], x2))
new_primPlusNat0(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs18(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs11(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Zero)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_lt4(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Double)
new_esEs9(x0, x1, ty_Ordering)
new_pePe(False, x0)
new_ltEs11(Just(x0), Just(x1), ty_@0)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs19(Integer(x0), Integer(x1))
new_ltEs5(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs17(EQ, EQ)
new_esEs9(x0, x1, ty_Float)
new_lt5(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, True, x2, x3)
new_esEs17(EQ, LT)
new_esEs17(LT, EQ)
new_esEs8(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Bool)
new_ltEs18(Left(x0), Left(x1), ty_Integer, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs11(Just(x0), Just(x1), ty_Integer)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs12(Char(x0), Char(x1))
new_esEs25(x0, x1, ty_Float)
new_compare10(x0, x1, x2, x3, False, x4, x5, x6)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt4(x0, x1, app(ty_Ratio, x2))

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

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



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

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

new_foldFM_GE10(vyy61, vyy15, vyy16, vyy210, vyy211, vyy212, EmptyFM, vyy214, False, h, ba, bb) → new_foldFM_GE(vyy61, vyy15, vyy16, vyy214, h, ba, bb)
new_foldFM_GE10(vyy61, vyy15, vyy16, vyy210, vyy211, vyy212, Branch(vyy2130, vyy2131, vyy2132, vyy2133, vyy2134), vyy214, False, h, ba, bb) → new_foldFM_GE1(new_eltsFM_GE0(vyy210, vyy211, new_foldFM_GE0(vyy61, vyy15, vyy16, vyy214, h, ba, bb), h, ba, bb), vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, h, ba, bb)
new_foldFM_GE1(vyy113, vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, h, ba, bb) → new_foldFM_GE10(vyy113, vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, new_esEs17(new_compare25(vyy2130, @2(vyy15, vyy16), new_esEs5(vyy2130, @2(vyy15, vyy16), ba, bb), ba, bb), LT), h, ba, bb)
new_foldFM_GE10(vyy61, vyy15, vyy16, vyy210, vyy211, vyy212, Branch(vyy2130, vyy2131, vyy2132, vyy2133, vyy2134), vyy214, False, h, ba, bb) → new_foldFM_GE(vyy61, vyy15, vyy16, vyy214, h, ba, bb)
new_foldFM_GE10(vyy61, vyy15, vyy16, vyy210, vyy211, vyy212, vyy213, Branch(vyy2140, vyy2141, vyy2142, vyy2143, vyy2144), True, h, ba, bb) → new_foldFM_GE1(vyy61, vyy15, vyy16, vyy2140, vyy2141, vyy2142, vyy2143, vyy2144, h, ba, bb)
new_foldFM_GE(vyy61, vyy15, vyy16, Branch(vyy2140, vyy2141, vyy2142, vyy2143, vyy2144), h, ba, bb) → new_foldFM_GE1(vyy61, vyy15, vyy16, vyy2140, vyy2141, vyy2142, vyy2143, vyy2144, h, ba, bb)

The TRS R consists of the following rules:

new_esEs25(vyy3000, vyy400, app(ty_[], cch)) → new_esEs14(vyy3000, vyy400, cch)
new_compare16(vyy2130000, vyy1500, ty_Ordering) → new_compare29(vyy2130000, vyy1500)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, ddb)) → new_esEs4(vyy3000, vyy400, ddb)
new_compare16(vyy2130000, vyy1500, ty_Float) → new_compare9(vyy2130000, vyy1500)
new_lt4(vyy2130010, vyy1510, ty_Integer) → new_lt16(vyy2130010, vyy1510)
new_ltEs19(vyy2130011, vyy1511, ty_Integer) → new_ltEs16(vyy2130011, vyy1511)
new_lt21(vyy213000, vyy150, ty_Float) → new_lt13(vyy213000, vyy150)
new_esEs25(vyy3000, vyy400, ty_Ordering) → new_esEs17(vyy3000, vyy400)
new_lt21(vyy213000, vyy150, ty_Bool) → new_lt9(vyy213000, vyy150)
new_ltEs5(vyy2130012, vyy1512, ty_Bool) → new_ltEs9(vyy2130012, vyy1512)
new_esEs13(False, True) → False
new_esEs13(True, False) → False
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_compare10(vyy159, vyy160, vyy161, vyy162, False, vyy164, cdh, cea) → new_compare111(vyy159, vyy160, vyy161, vyy162, vyy164, cdh, cea)
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Ordering) → new_ltEs14(vyy2130010, vyy1510)
new_lt4(vyy2130010, vyy1510, ty_Ordering) → new_lt14(vyy2130010, vyy1510)
new_lt4(vyy2130010, vyy1510, app(ty_[], bg)) → new_lt10(vyy2130010, vyy1510, bg)
new_ltEs20(vyy213001, vyy151, app(ty_[], bbb)) → new_ltEs10(vyy213001, vyy151, bbb)
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Bool, bbe) → new_ltEs9(vyy2130010, vyy1510)
new_foldFM_GE11(vyy61, vyy15, vyy16, vyy210, vyy211, vyy212, vyy213, vyy214, True, h, ba, bb) → new_foldFM_GE0(vyy61, vyy15, vyy16, vyy214, h, ba, bb)
new_ltEs14(GT, GT) → True
new_lt21(vyy213000, vyy150, ty_Ordering) → new_lt14(vyy213000, vyy150)
new_esEs24(vyy3001, vyy401, app(ty_Maybe, cbe)) → new_esEs4(vyy3001, vyy401, cbe)
new_esEs4(Nothing, Just(vyy400), dch) → False
new_esEs4(Just(vyy3000), Nothing, dch) → False
new_esEs28(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_ltEs5(vyy2130012, vyy1512, ty_Float) → new_ltEs13(vyy2130012, vyy1512)
new_esEs21(vyy213000, vyy150, ty_Ordering) → new_esEs17(vyy213000, vyy150)
new_lt10(vyy213000, vyy150, bbg) → new_esEs17(new_compare0(vyy213000, vyy150, bbg), LT)
new_ltEs19(vyy2130011, vyy1511, app(ty_Maybe, hg)) → new_ltEs11(vyy2130011, vyy1511, hg)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs12(vyy3000, vyy400)
new_lt20(vyy2130010, vyy1510, ty_@0) → new_lt6(vyy2130010, vyy1510)
new_primMulNat0(Zero, Zero) → Zero
new_esEs29(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bhb), bhc), bhd), bge) → new_esEs7(vyy3000, vyy400, bhb, bhc, bhd)
new_lt6(vyy213000, vyy150) → new_esEs17(new_compare17(vyy213000, vyy150), LT)
new_esEs7(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), cfe, cff, cfg) → new_asAs(new_esEs29(vyy3000, vyy400, cfe), new_asAs(new_esEs28(vyy3001, vyy401, cff), new_esEs27(vyy3002, vyy402, cfg)))
new_esEs25(vyy3000, vyy400, app(app(ty_Either, cdf), cdg)) → new_esEs6(vyy3000, vyy400, cdf, cdg)
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, ty_Int) → new_ltEs12(vyy2130010, vyy1510)
new_ltEs15(vyy213001, vyy151) → new_not(new_esEs17(new_compare8(vyy213001, vyy151), GT))
new_esEs20(vyy2130010, vyy1510, app(ty_Maybe, ge)) → new_esEs4(vyy2130010, vyy1510, ge)
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, app(ty_Ratio, bdg)) → new_ltEs7(vyy2130010, vyy1510, bdg)
new_compare7(vyy213000, vyy150) → new_compare27(vyy213000, vyy150, new_esEs13(vyy213000, vyy150))
new_ltEs18(Left(vyy2130010), Left(vyy1510), app(ty_[], bcf), bbe) → new_ltEs10(vyy2130010, vyy1510, bcf)
new_esEs8(vyy2130011, vyy1511, app(ty_[], db)) → new_esEs14(vyy2130011, vyy1511, db)
new_esEs28(vyy3001, vyy401, ty_Int) → new_esEs15(vyy3001, vyy401)
new_ltEs9(True, False) → False
new_ltEs11(Just(vyy2130010), Just(vyy1510), app(app(app(ty_@3, dce), dcf), dcg)) → new_ltEs4(vyy2130010, vyy1510, dce, dcf, dcg)
new_ltEs12(vyy213001, vyy151) → new_not(new_esEs17(new_compare12(vyy213001, vyy151), GT))
new_esEs24(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_esEs21(vyy213000, vyy150, ty_Integer) → new_esEs19(vyy213000, vyy150)
new_ltEs18(Left(vyy2130010), Left(vyy1510), app(app(app(ty_@3, bdd), bde), bdf), bbe) → new_ltEs4(vyy2130010, vyy1510, bdd, bde, bdf)
new_esEs20(vyy2130010, vyy1510, ty_Ordering) → new_esEs17(vyy2130010, vyy1510)
new_lt21(vyy213000, vyy150, app(ty_Maybe, fh)) → new_lt11(vyy213000, vyy150, fh)
new_ltEs11(Just(vyy2130010), Just(vyy1510), app(ty_Ratio, dbf)) → new_ltEs7(vyy2130010, vyy1510, dbf)
new_compare16(vyy2130000, vyy1500, app(app(ty_@2, bfe), bff)) → new_compare5(vyy2130000, vyy1500, bfe, bff)
new_esEs21(vyy213000, vyy150, ty_Int) → new_esEs15(vyy213000, vyy150)
new_esEs21(vyy213000, vyy150, ty_Double) → new_esEs18(vyy213000, vyy150)
new_ltEs20(vyy213001, vyy151, app(app(ty_@2, ga), gb)) → new_ltEs17(vyy213001, vyy151, ga, gb)
new_ltEs18(Left(vyy2130010), Left(vyy1510), app(app(ty_Either, bdb), bdc), bbe) → new_ltEs18(vyy2130010, vyy1510, bdb, bdc)
new_lt5(vyy2130011, vyy1511, ty_Int) → new_lt12(vyy2130011, vyy1511)
new_esEs24(vyy3001, vyy401, app(app(ty_@2, cbg), cbh)) → new_esEs5(vyy3001, vyy401, cbg, cbh)
new_esEs21(vyy213000, vyy150, app(app(app(ty_@3, bcb), bcc), bcd)) → new_esEs7(vyy213000, vyy150, bcb, bcc, bcd)
new_lt20(vyy2130010, vyy1510, ty_Integer) → new_lt16(vyy2130010, vyy1510)
new_esEs6(Right(vyy3000), Right(vyy400), bhg, app(ty_Ratio, bhh)) → new_esEs11(vyy3000, vyy400, bhh)
new_ltEs18(Right(vyy2130010), Left(vyy1510), bbd, bbe) → False
new_compare5(vyy213000, vyy150, ff, fg) → new_compare25(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, ff, fg), ff, fg)
new_ltEs20(vyy213001, vyy151, ty_Integer) → new_ltEs16(vyy213001, vyy151)
new_esEs21(vyy213000, vyy150, app(app(ty_Either, bbh), bca)) → new_esEs6(vyy213000, vyy150, bbh, bca)
new_compare28(vyy213000, vyy150, False, bbh, bca) → new_compare113(vyy213000, vyy150, new_ltEs18(vyy213000, vyy150, bbh, bca), bbh, bca)
new_esEs29(vyy3000, vyy400, app(app(app(ty_@3, dba), dbb), dbc)) → new_esEs7(vyy3000, vyy400, dba, dbb, dbc)
new_ltEs20(vyy213001, vyy151, app(ty_Maybe, bbc)) → new_ltEs11(vyy213001, vyy151, bbc)
new_esEs8(vyy2130011, vyy1511, app(app(ty_Either, df), dg)) → new_esEs6(vyy2130011, vyy1511, df, dg)
new_esEs26(vyy3000, vyy400, app(ty_Maybe, ced)) → new_esEs4(vyy3000, vyy400, ced)
new_lt14(vyy213000, vyy150) → new_esEs17(new_compare29(vyy213000, vyy150), LT)
new_ltEs19(vyy2130011, vyy1511, ty_Bool) → new_ltEs9(vyy2130011, vyy1511)
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, app(app(app(ty_@3, bef), beg), beh)) → new_ltEs4(vyy2130010, vyy1510, bef, beg, beh)
new_compare24(vyy213000, vyy150, False, fh) → new_compare14(vyy213000, vyy150, new_ltEs11(vyy213000, vyy150, fh), fh)
new_esEs25(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_ltEs20(vyy213001, vyy151, app(ty_Ratio, bba)) → new_ltEs7(vyy213001, vyy151, bba)
new_esEs8(vyy2130011, vyy1511, ty_Bool) → new_esEs13(vyy2130011, vyy1511)
new_pePe(False, vyy177) → vyy177
new_esEs14([], [], ceb) → True
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Float) → new_ltEs13(vyy2130010, vyy1510)
new_lt21(vyy213000, vyy150, ty_Char) → new_lt8(vyy213000, vyy150)
new_lt5(vyy2130011, vyy1511, app(ty_Ratio, da)) → new_lt7(vyy2130011, vyy1511, da)
new_ltEs11(Just(vyy2130010), Just(vyy1510), app(app(ty_Either, dcc), dcd)) → new_ltEs18(vyy2130010, vyy1510, dcc, dcd)
new_esEs15(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, ty_Integer) → new_ltEs16(vyy2130010, vyy1510)
new_esEs8(vyy2130011, vyy1511, ty_Float) → new_esEs16(vyy2130011, vyy1511)
new_esEs29(vyy3000, vyy400, app(ty_[], daf)) → new_esEs14(vyy3000, vyy400, daf)
new_lt9(vyy213000, vyy150) → new_esEs17(new_compare7(vyy213000, vyy150), LT)
new_foldFM_GE11(vyy61, vyy15, vyy16, vyy210, vyy211, vyy212, EmptyFM, vyy214, False, h, ba, bb) → new_eltsFM_GE0(vyy210, vyy211, new_foldFM_GE0(vyy61, vyy15, vyy16, vyy214, h, ba, bb), h, ba, bb)
new_ltEs14(GT, EQ) → False
new_esEs26(vyy3000, vyy400, ty_Char) → new_esEs12(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_lt18(vyy213000, vyy150, bbh, bca) → new_esEs17(new_compare13(vyy213000, vyy150, bbh, bca), LT)
new_ltEs11(Just(vyy2130010), Just(vyy1510), app(ty_[], dbg)) → new_ltEs10(vyy2130010, vyy1510, dbg)
new_lt20(vyy2130010, vyy1510, app(app(ty_@2, gf), gg)) → new_lt17(vyy2130010, vyy1510, gf, gg)
new_compare11(vyy213000, vyy150, False, bcb, bcc, bcd) → GT
new_esEs20(vyy2130010, vyy1510, ty_Char) → new_esEs12(vyy2130010, vyy1510)
new_esEs6(Left(vyy3000), Left(vyy400), ty_@0, bge) → new_esEs10(vyy3000, vyy400)
new_lt4(vyy2130010, vyy1510, app(ty_Ratio, bf)) → new_lt7(vyy2130010, vyy1510, bf)
new_esEs8(vyy2130011, vyy1511, ty_Integer) → new_esEs19(vyy2130011, vyy1511)
new_esEs9(vyy2130010, vyy1510, ty_Double) → new_esEs18(vyy2130010, vyy1510)
new_ltEs5(vyy2130012, vyy1512, ty_Int) → new_ltEs12(vyy2130012, vyy1512)
new_esEs20(vyy2130010, vyy1510, app(app(ty_@2, gf), gg)) → new_esEs5(vyy2130010, vyy1510, gf, gg)
new_primCmpNat0(Zero, Succ(vyy15000)) → LT
new_esEs27(vyy3002, vyy402, app(app(app(ty_@3, cge), cgf), cgg)) → new_esEs7(vyy3002, vyy402, cge, cgf, cgg)
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, app(app(ty_@2, beb), bec)) → new_ltEs17(vyy2130010, vyy1510, beb, bec)
new_esEs17(LT, LT) → True
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Bool) → new_ltEs9(vyy2130010, vyy1510)
new_esEs27(vyy3002, vyy402, ty_@0) → new_esEs10(vyy3002, vyy402)
new_esEs6(Right(vyy3000), Left(vyy400), bhg, bge) → False
new_esEs6(Left(vyy3000), Right(vyy400), bhg, bge) → False
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs18(vyy3000, vyy400)
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, app(app(ty_Either, bed), bee)) → new_ltEs18(vyy2130010, vyy1510, bed, bee)
new_lt21(vyy213000, vyy150, app(app(app(ty_@3, bcb), bcc), bcd)) → new_lt19(vyy213000, vyy150, bcb, bcc, bcd)
new_lt21(vyy213000, vyy150, app(app(ty_@2, ff), fg)) → new_lt17(vyy213000, vyy150, ff, fg)
new_foldFM_GE0(vyy61, vyy15, vyy16, EmptyFM, h, ba, bb) → vyy61
new_lt5(vyy2130011, vyy1511, app(app(app(ty_@3, dh), ea), eb)) → new_lt19(vyy2130011, vyy1511, dh, ea, eb)
new_ltEs19(vyy2130011, vyy1511, app(app(app(ty_@3, bad), bae), baf)) → new_ltEs4(vyy2130011, vyy1511, bad, bae, baf)
new_esEs29(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, ty_Ordering) → new_ltEs14(vyy2130010, vyy1510)
new_compare0([], [], bbg) → EQ
new_pePe(True, vyy177) → True
new_ltEs8(vyy213001, vyy151) → new_not(new_esEs17(new_compare19(vyy213001, vyy151), GT))
new_primEqNat0(Zero, Zero) → True
new_ltEs18(Left(vyy2130010), Left(vyy1510), app(ty_Maybe, bcg), bbe) → new_ltEs11(vyy2130010, vyy1510, bcg)
new_ltEs11(Nothing, Just(vyy1510), bbc) → True
new_ltEs11(Just(vyy2130010), Just(vyy1510), app(ty_Maybe, dbh)) → new_ltEs11(vyy2130010, vyy1510, dbh)
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_@0) → new_ltEs6(vyy2130010, vyy1510)
new_compare17(@0, @0) → EQ
new_primMulNat0(Succ(vyy300100), Succ(vyy40100)) → new_primPlusNat1(new_primMulNat0(vyy300100, Succ(vyy40100)), vyy40100)
new_esEs20(vyy2130010, vyy1510, ty_Bool) → new_esEs13(vyy2130010, vyy1510)
new_esEs6(Right(vyy3000), Right(vyy400), bhg, app(app(ty_Either, cah), cba)) → new_esEs6(vyy3000, vyy400, cah, cba)
new_esEs27(vyy3002, vyy402, ty_Char) → new_esEs12(vyy3002, vyy402)
new_esEs25(vyy3000, vyy400, ty_Int) → new_esEs15(vyy3000, vyy400)
new_esEs9(vyy2130010, vyy1510, app(ty_Ratio, bf)) → new_esEs11(vyy2130010, vyy1510, bf)
new_lt5(vyy2130011, vyy1511, ty_Char) → new_lt8(vyy2130011, vyy1511)
new_sr(vyy3001, vyy401) → new_primMulInt(vyy3001, vyy401)
new_ltEs14(EQ, LT) → False
new_ltEs5(vyy2130012, vyy1512, app(ty_Ratio, ec)) → new_ltEs7(vyy2130012, vyy1512, ec)
new_esEs28(vyy3001, vyy401, app(app(ty_Either, dab), dac)) → new_esEs6(vyy3001, vyy401, dab, dac)
new_esEs9(vyy2130010, vyy1510, app(app(app(ty_@3, ce), cf), cg)) → new_esEs7(vyy2130010, vyy1510, ce, cf, cg)
new_esEs24(vyy3001, vyy401, ty_Char) → new_esEs12(vyy3001, vyy401)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Char, bge) → new_esEs12(vyy3000, vyy400)
new_lt20(vyy2130010, vyy1510, app(ty_Maybe, ge)) → new_lt11(vyy2130010, vyy1510, ge)
new_esEs25(vyy3000, vyy400, ty_@0) → new_esEs10(vyy3000, vyy400)
new_ltEs20(vyy213001, vyy151, ty_@0) → new_ltEs6(vyy213001, vyy151)
new_lt21(vyy213000, vyy150, ty_Double) → new_lt15(vyy213000, vyy150)
new_esEs25(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_lt20(vyy2130010, vyy1510, ty_Ordering) → new_lt14(vyy2130010, vyy1510)
new_esEs20(vyy2130010, vyy1510, app(app(app(ty_@3, hb), hc), hd)) → new_esEs7(vyy2130010, vyy1510, hb, hc, hd)
new_compare16(vyy2130000, vyy1500, app(ty_[], bfc)) → new_compare0(vyy2130000, vyy1500, bfc)
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Int, bbe) → new_ltEs12(vyy2130010, vyy1510)
new_lt20(vyy2130010, vyy1510, ty_Bool) → new_lt9(vyy2130010, vyy1510)
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Integer) → new_ltEs16(vyy2130010, vyy1510)
new_lt4(vyy2130010, vyy1510, app(app(app(ty_@3, ce), cf), cg)) → new_lt19(vyy2130010, vyy1510, ce, cf, cg)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Int, bge) → new_esEs15(vyy3000, vyy400)
new_esEs28(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_esEs8(vyy2130011, vyy1511, ty_Char) → new_esEs12(vyy2130011, vyy1511)
new_ltEs20(vyy213001, vyy151, app(app(app(ty_@3, bc), bd), be)) → new_ltEs4(vyy213001, vyy151, bc, bd, be)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs24(vyy3001, vyy401, app(ty_Ratio, cbd)) → new_esEs11(vyy3001, vyy401, cbd)
new_esEs8(vyy2130011, vyy1511, app(app(ty_@2, dd), de)) → new_esEs5(vyy2130011, vyy1511, dd, de)
new_ltEs19(vyy2130011, vyy1511, app(app(ty_@2, hh), baa)) → new_ltEs17(vyy2130011, vyy1511, hh, baa)
new_foldFM_GE11(vyy61, vyy15, vyy16, vyy210, vyy211, vyy212, Branch(vyy2130, vyy2131, vyy2132, vyy2133, vyy2134), vyy214, False, h, ba, bb) → new_foldFM_GE12(new_eltsFM_GE0(vyy210, vyy211, new_foldFM_GE0(vyy61, vyy15, vyy16, vyy214, h, ba, bb), h, ba, bb), vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, h, ba, bb)
new_esEs29(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bhg, app(app(app(ty_@3, cae), caf), cag)) → new_esEs7(vyy3000, vyy400, cae, caf, cag)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs15(vyy3000, vyy400)
new_compare113(vyy213000, vyy150, True, bbh, bca) → LT
new_esEs27(vyy3002, vyy402, ty_Bool) → new_esEs13(vyy3002, vyy402)
new_lt16(vyy213000, vyy150) → new_esEs17(new_compare15(vyy213000, vyy150), LT)
new_esEs22(vyy3001, vyy401, ty_Int) → new_esEs15(vyy3001, vyy401)
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Float, bbe) → new_ltEs13(vyy2130010, vyy1510)
new_esEs26(vyy3000, vyy400, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs7(vyy3000, vyy400, ceh, cfa, cfb)
new_esEs21(vyy213000, vyy150, ty_Char) → new_esEs12(vyy213000, vyy150)
new_esEs28(vyy3001, vyy401, app(ty_Maybe, chc)) → new_esEs4(vyy3001, vyy401, chc)
new_esEs20(vyy2130010, vyy1510, ty_Int) → new_esEs15(vyy2130010, vyy1510)
new_esEs14([], :(vyy400, vyy401), ceb) → False
new_esEs14(:(vyy3000, vyy3001), [], ceb) → False
new_compare30(vyy213000, vyy150, bcb, bcc, bcd) → new_compare26(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bcb, bcc, bcd), bcb, bcc, bcd)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_[], bgg), bge) → new_esEs14(vyy3000, vyy400, bgg)
new_esEs9(vyy2130010, vyy1510, app(ty_[], bg)) → new_esEs14(vyy2130010, vyy1510, bg)
new_compare111(vyy159, vyy160, vyy161, vyy162, True, cdh, cea) → LT
new_lt15(vyy213000, vyy150) → new_esEs17(new_compare8(vyy213000, vyy150), LT)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs16(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs17(EQ, EQ) → True
new_esEs26(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Double, bbe) → new_ltEs15(vyy2130010, vyy1510)
new_compare11(vyy213000, vyy150, True, bcb, bcc, bcd) → LT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Ordering, bge) → new_esEs17(vyy3000, vyy400)
new_esEs8(vyy2130011, vyy1511, ty_Double) → new_esEs18(vyy2130011, vyy1511)
new_esEs26(vyy3000, vyy400, app(ty_[], cee)) → new_esEs14(vyy3000, vyy400, cee)
new_esEs28(vyy3001, vyy401, ty_Ordering) → new_esEs17(vyy3001, vyy401)
new_foldFM_GE12(vyy113, vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, h, ba, bb) → new_foldFM_GE11(vyy113, vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, new_esEs17(new_compare25(vyy2130, @2(vyy15, vyy16), new_esEs5(vyy2130, @2(vyy15, vyy16), ba, bb), ba, bb), LT), h, ba, bb)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primCompAux0(vyy183, GT) → GT
new_ltEs18(Left(vyy2130010), Right(vyy1510), bbd, bbe) → True
new_primPlusNat1(Zero, vyy40100) → Succ(vyy40100)
new_esEs22(vyy3001, vyy401, ty_Integer) → new_esEs19(vyy3001, vyy401)
new_esEs20(vyy2130010, vyy1510, ty_@0) → new_esEs10(vyy2130010, vyy1510)
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, ty_Double) → new_ltEs15(vyy2130010, vyy1510)
new_esEs28(vyy3001, vyy401, app(ty_[], chd)) → new_esEs14(vyy3001, vyy401, chd)
new_ltEs6(vyy213001, vyy151) → new_not(new_esEs17(new_compare17(vyy213001, vyy151), GT))
new_compare10(vyy159, vyy160, vyy161, vyy162, True, vyy164, cdh, cea) → new_compare111(vyy159, vyy160, vyy161, vyy162, True, cdh, cea)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_lt20(vyy2130010, vyy1510, ty_Char) → new_lt8(vyy2130010, vyy1510)
new_ltEs20(vyy213001, vyy151, ty_Double) → new_ltEs15(vyy213001, vyy151)
new_ltEs20(vyy213001, vyy151, app(app(ty_Either, bbd), bbe)) → new_ltEs18(vyy213001, vyy151, bbd, bbe)
new_esEs5(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cbb, cbc) → new_asAs(new_esEs25(vyy3000, vyy400, cbb), new_esEs24(vyy3001, vyy401, cbc))
new_ltEs16(vyy213001, vyy151) → new_not(new_esEs17(new_compare15(vyy213001, vyy151), GT))
new_primCmpNat0(Succ(vyy21300000), Succ(vyy15000)) → new_primCmpNat0(vyy21300000, vyy15000)
new_compare112(vyy213000, vyy150, True) → LT
new_esEs25(vyy3000, vyy400, app(ty_Maybe, ccg)) → new_esEs4(vyy3000, vyy400, ccg)
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, ty_Bool) → new_ltEs9(vyy2130010, vyy1510)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, ddd), dde)) → new_esEs5(vyy3000, vyy400, ddd, dde)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, dea), deb)) → new_esEs6(vyy3000, vyy400, dea, deb)
new_esEs17(GT, LT) → False
new_esEs17(LT, GT) → False
new_compare14(vyy213000, vyy150, False, fh) → GT
new_esEs6(Right(vyy3000), Right(vyy400), bhg, app(ty_Maybe, caa)) → new_esEs4(vyy3000, vyy400, caa)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_compare8(Double(vyy2130000, vyy2130001), Double(vyy1500, vyy1501)) → new_compare12(new_sr(vyy2130000, vyy1500), new_sr(vyy2130001, vyy1501))
new_esEs17(GT, EQ) → False
new_esEs17(EQ, GT) → False
new_compare26(vyy213000, vyy150, False, bcb, bcc, bcd) → new_compare11(vyy213000, vyy150, new_ltEs4(vyy213000, vyy150, bcb, bcc, bcd), bcb, bcc, bcd)
new_esEs21(vyy213000, vyy150, app(ty_[], bbg)) → new_esEs14(vyy213000, vyy150, bbg)
new_esEs9(vyy2130010, vyy1510, ty_Float) → new_esEs16(vyy2130010, vyy1510)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Float, bge) → new_esEs16(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bhg, app(app(ty_@2, cac), cad)) → new_esEs5(vyy3000, vyy400, cac, cad)
new_compare113(vyy213000, vyy150, False, bbh, bca) → GT
new_lt4(vyy2130010, vyy1510, app(app(ty_@2, ca), cb)) → new_lt17(vyy2130010, vyy1510, ca, cb)
new_esEs9(vyy2130010, vyy1510, app(app(ty_Either, cc), cd)) → new_esEs6(vyy2130010, vyy1510, cc, cd)
new_lt4(vyy2130010, vyy1510, app(ty_Maybe, bh)) → new_lt11(vyy2130010, vyy1510, bh)
new_primCmpInt(Neg(Succ(vyy21300000)), Neg(vyy1500)) → new_primCmpNat0(vyy1500, Succ(vyy21300000))
new_compare16(vyy2130000, vyy1500, app(ty_Maybe, bfd)) → new_compare6(vyy2130000, vyy1500, bfd)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, dda)) → new_esEs11(vyy3000, vyy400, dda)
new_esEs6(Right(vyy3000), Right(vyy400), bhg, ty_@0) → new_esEs10(vyy3000, vyy400)
new_esEs6(Right(vyy3000), Right(vyy400), bhg, ty_Char) → new_esEs12(vyy3000, vyy400)
new_ltEs18(Left(vyy2130010), Left(vyy1510), app(app(ty_@2, bch), bda), bbe) → new_ltEs17(vyy2130010, vyy1510, bch, bda)
new_ltEs20(vyy213001, vyy151, ty_Ordering) → new_ltEs14(vyy213001, vyy151)
new_compare19(Char(vyy2130000), Char(vyy1500)) → new_primCmpNat0(vyy2130000, vyy1500)
new_ltEs5(vyy2130012, vyy1512, app(ty_Maybe, ee)) → new_ltEs11(vyy2130012, vyy1512, ee)
new_ltEs7(vyy213001, vyy151, bba) → new_not(new_esEs17(new_compare18(vyy213001, vyy151, bba), GT))
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Ordering, bbe) → new_ltEs14(vyy2130010, vyy1510)
new_primPlusNat0(Zero, Succ(vyy401000)) → Succ(vyy401000)
new_primPlusNat0(Succ(vyy13100), Zero) → Succ(vyy13100)
new_foldFM_GE0(vyy61, vyy15, vyy16, Branch(vyy2140, vyy2141, vyy2142, vyy2143, vyy2144), h, ba, bb) → new_foldFM_GE12(vyy61, vyy15, vyy16, vyy2140, vyy2141, vyy2142, vyy2143, vyy2144, h, ba, bb)
new_esEs24(vyy3001, vyy401, ty_@0) → new_esEs10(vyy3001, vyy401)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, ty_@0) → new_ltEs6(vyy2130010, vyy1510)
new_primCmpNat0(Succ(vyy21300000), Zero) → GT
new_esEs29(vyy3000, vyy400, ty_Double) → new_esEs18(vyy3000, vyy400)
new_lt21(vyy213000, vyy150, app(ty_[], bbg)) → new_lt10(vyy213000, vyy150, bbg)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy15000))) → LT
new_esEs24(vyy3001, vyy401, ty_Double) → new_esEs18(vyy3001, vyy401)
new_esEs6(Right(vyy3000), Right(vyy400), bhg, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_sr0(Integer(vyy15000), Integer(vyy21300010)) → Integer(new_primMulInt(vyy15000, vyy21300010))
new_ltEs5(vyy2130012, vyy1512, ty_Double) → new_ltEs15(vyy2130012, vyy1512)
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Integer, bbe) → new_ltEs16(vyy2130010, vyy1510)
new_compare28(vyy213000, vyy150, True, bbh, bca) → EQ
new_ltEs4(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), bc, bd, be) → new_pePe(new_lt4(vyy2130010, vyy1510, bc), new_asAs(new_esEs9(vyy2130010, vyy1510, bc), new_pePe(new_lt5(vyy2130011, vyy1511, bd), new_asAs(new_esEs8(vyy2130011, vyy1511, bd), new_ltEs5(vyy2130012, vyy1512, be)))))
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_esEs16(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs15(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare16(vyy2130000, vyy1500, app(ty_Ratio, bfb)) → new_compare18(vyy2130000, vyy1500, bfb)
new_esEs25(vyy3000, vyy400, app(ty_Ratio, ccf)) → new_esEs11(vyy3000, vyy400, ccf)
new_compare16(vyy2130000, vyy1500, ty_@0) → new_compare17(vyy2130000, vyy1500)
new_compare13(vyy213000, vyy150, bbh, bca) → new_compare28(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, bbh, bca), bbh, bca)
new_esEs26(vyy3000, vyy400, ty_Double) → new_esEs18(vyy3000, vyy400)
new_esEs11(:%(vyy3000, vyy3001), :%(vyy400, vyy401), bfa) → new_asAs(new_esEs23(vyy3000, vyy400, bfa), new_esEs22(vyy3001, vyy401, bfa))
new_esEs9(vyy2130010, vyy1510, ty_@0) → new_esEs10(vyy2130010, vyy1510)
new_lt5(vyy2130011, vyy1511, ty_Bool) → new_lt9(vyy2130011, vyy1511)
new_esEs29(vyy3000, vyy400, app(app(ty_@2, dag), dah)) → new_esEs5(vyy3000, vyy400, dag, dah)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Maybe, bgf), bge) → new_esEs4(vyy3000, vyy400, bgf)
new_compare16(vyy2130000, vyy1500, ty_Int) → new_compare12(vyy2130000, vyy1500)
new_esEs25(vyy3000, vyy400, ty_Char) → new_esEs12(vyy3000, vyy400)
new_compare12(vyy213000, vyy150) → new_primCmpInt(vyy213000, vyy150)
new_esEs27(vyy3002, vyy402, app(ty_Ratio, cfh)) → new_esEs11(vyy3002, vyy402, cfh)
new_lt4(vyy2130010, vyy1510, ty_Double) → new_lt15(vyy2130010, vyy1510)
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy15000))) → new_primCmpNat0(Zero, Succ(vyy15000))
new_esEs6(Right(vyy3000), Right(vyy400), bhg, ty_Double) → new_esEs18(vyy3000, vyy400)
new_eltsFM_GE0(vyy210, vyy211, vyy112, h, ba, bb) → :(vyy211, vyy112)
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_Char, bbe) → new_ltEs8(vyy2130010, vyy1510)
new_lt4(vyy2130010, vyy1510, app(app(ty_Either, cc), cd)) → new_lt18(vyy2130010, vyy1510, cc, cd)
new_compare18(:%(vyy2130000, vyy2130001), :%(vyy1500, vyy1501), ty_Int) → new_compare12(new_sr(vyy2130000, vyy1501), new_sr(vyy1500, vyy2130001))
new_esEs8(vyy2130011, vyy1511, ty_@0) → new_esEs10(vyy2130011, vyy1511)
new_primCompAux1(vyy2130000, vyy1500, vyy178, bbg) → new_primCompAux0(vyy178, new_compare16(vyy2130000, vyy1500, bbg))
new_lt4(vyy2130010, vyy1510, ty_Float) → new_lt13(vyy2130010, vyy1510)
new_esEs8(vyy2130011, vyy1511, ty_Int) → new_esEs15(vyy2130011, vyy1511)
new_esEs26(vyy3000, vyy400, app(app(ty_@2, cef), ceg)) → new_esEs5(vyy3000, vyy400, cef, ceg)
new_esEs26(vyy3000, vyy400, ty_Float) → new_esEs16(vyy3000, vyy400)
new_primCompAux0(vyy183, LT) → LT
new_esEs21(vyy213000, vyy150, app(app(ty_@2, ff), fg)) → new_esEs5(vyy213000, vyy150, ff, fg)
new_ltEs19(vyy2130011, vyy1511, ty_Char) → new_ltEs8(vyy2130011, vyy1511)
new_esEs12(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_not(False) → True
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_Either, bhe), bhf), bge) → new_esEs6(vyy3000, vyy400, bhe, bhf)
new_compare27(vyy213000, vyy150, False) → new_compare110(vyy213000, vyy150, new_ltEs9(vyy213000, vyy150))
new_compare24(vyy213000, vyy150, True, fh) → EQ
new_esEs6(Right(vyy3000), Right(vyy400), bhg, ty_Ordering) → new_esEs17(vyy3000, vyy400)
new_primCmpInt(Pos(Succ(vyy21300000)), Pos(vyy1500)) → new_primCmpNat0(Succ(vyy21300000), vyy1500)
new_esEs9(vyy2130010, vyy1510, ty_Bool) → new_esEs13(vyy2130010, vyy1510)
new_compare9(Float(vyy2130000, vyy2130001), Float(vyy1500, vyy1501)) → new_compare12(new_sr(vyy2130000, vyy1500), new_sr(vyy2130001, vyy1501))
new_ltEs19(vyy2130011, vyy1511, app(ty_[], hf)) → new_ltEs10(vyy2130011, vyy1511, hf)
new_esEs24(vyy3001, vyy401, app(app(ty_Either, ccd), cce)) → new_esEs6(vyy3001, vyy401, ccd, cce)
new_esEs19(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_lt20(vyy2130010, vyy1510, app(ty_[], gd)) → new_lt10(vyy2130010, vyy1510, gd)
new_ltEs14(LT, LT) → True
new_esEs24(vyy3001, vyy401, app(ty_[], cbf)) → new_esEs14(vyy3001, vyy401, cbf)
new_esEs28(vyy3001, vyy401, app(app(ty_@2, che), chf)) → new_esEs5(vyy3001, vyy401, che, chf)
new_compare0(:(vyy2130000, vyy2130001), [], bbg) → GT
new_esEs6(Left(vyy3000), Left(vyy400), ty_Bool, bge) → new_esEs13(vyy3000, vyy400)
new_esEs29(vyy3000, vyy400, ty_Int) → new_esEs15(vyy3000, vyy400)
new_esEs27(vyy3002, vyy402, app(app(ty_Either, cgh), cha)) → new_esEs6(vyy3002, vyy402, cgh, cha)
new_compare16(vyy2130000, vyy1500, ty_Integer) → new_compare15(vyy2130000, vyy1500)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs15(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs15(vyy3001, vyy401)
new_ltEs19(vyy2130011, vyy1511, app(app(ty_Either, bab), bac)) → new_ltEs18(vyy2130011, vyy1511, bab, bac)
new_esEs20(vyy2130010, vyy1510, app(ty_Ratio, gc)) → new_esEs11(vyy2130010, vyy1510, gc)
new_primCmpInt(Pos(Succ(vyy21300000)), Neg(vyy1500)) → GT
new_esEs8(vyy2130011, vyy1511, app(app(app(ty_@3, dh), ea), eb)) → new_esEs7(vyy2130011, vyy1511, dh, ea, eb)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Double, bge) → new_esEs18(vyy3000, vyy400)
new_compare16(vyy2130000, vyy1500, ty_Char) → new_compare19(vyy2130000, vyy1500)
new_lt4(vyy2130010, vyy1510, ty_@0) → new_lt6(vyy2130010, vyy1510)
new_esEs6(Left(vyy3000), Left(vyy400), ty_Integer, bge) → new_esEs19(vyy3000, vyy400)
new_esEs9(vyy2130010, vyy1510, ty_Char) → new_esEs12(vyy2130010, vyy1510)
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Double) → new_ltEs15(vyy2130010, vyy1510)
new_ltEs19(vyy2130011, vyy1511, ty_Float) → new_ltEs13(vyy2130011, vyy1511)
new_lt20(vyy2130010, vyy1510, ty_Double) → new_lt15(vyy2130010, vyy1510)
new_esEs26(vyy3000, vyy400, ty_@0) → new_esEs10(vyy3000, vyy400)
new_primMulInt(Pos(vyy30010), Pos(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_lt21(vyy213000, vyy150, ty_Int) → new_lt12(vyy213000, vyy150)
new_compare16(vyy2130000, vyy1500, ty_Bool) → new_compare7(vyy2130000, vyy1500)
new_ltEs5(vyy2130012, vyy1512, ty_Ordering) → new_ltEs14(vyy2130012, vyy1512)
new_esEs6(Right(vyy3000), Right(vyy400), bhg, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, app(ty_[], bdh)) → new_ltEs10(vyy2130010, vyy1510, bdh)
new_esEs28(vyy3001, vyy401, app(app(app(ty_@3, chg), chh), daa)) → new_esEs7(vyy3001, vyy401, chg, chh, daa)
new_compare18(:%(vyy2130000, vyy2130001), :%(vyy1500, vyy1501), ty_Integer) → new_compare15(new_sr0(vyy2130000, vyy1501), new_sr0(vyy1500, vyy2130001))
new_compare16(vyy2130000, vyy1500, ty_Double) → new_compare8(vyy2130000, vyy1500)
new_ltEs20(vyy213001, vyy151, ty_Bool) → new_ltEs9(vyy213001, vyy151)
new_esEs6(Left(vyy3000), Left(vyy400), app(app(ty_@2, bgh), bha), bge) → new_esEs5(vyy3000, vyy400, bgh, bha)
new_ltEs9(True, True) → True
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Char) → new_ltEs8(vyy2130010, vyy1510)
new_ltEs11(Just(vyy2130010), Just(vyy1510), app(app(ty_@2, dca), dcb)) → new_ltEs17(vyy2130010, vyy1510, dca, dcb)
new_primMulInt(Neg(vyy30010), Neg(vyy4010)) → Pos(new_primMulNat0(vyy30010, vyy4010))
new_ltEs5(vyy2130012, vyy1512, app(app(ty_@2, ef), eg)) → new_ltEs17(vyy2130012, vyy1512, ef, eg)
new_compare110(vyy213000, vyy150, True) → LT
new_ltEs11(Just(vyy2130010), Just(vyy1510), ty_Int) → new_ltEs12(vyy2130010, vyy1510)
new_ltEs17(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), ga, gb) → new_pePe(new_lt20(vyy2130010, vyy1510, ga), new_asAs(new_esEs20(vyy2130010, vyy1510, ga), new_ltEs19(vyy2130011, vyy1511, gb)))
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_esEs21(vyy213000, vyy150, ty_@0) → new_esEs10(vyy213000, vyy150)
new_ltEs19(vyy2130011, vyy1511, ty_Int) → new_ltEs12(vyy2130011, vyy1511)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs19(vyy2130011, vyy1511, ty_@0) → new_ltEs6(vyy2130011, vyy1511)
new_lt20(vyy2130010, vyy1510, app(app(ty_Either, gh), ha)) → new_lt18(vyy2130010, vyy1510, gh, ha)
new_compare25(vyy21300, vyy15, True, bag, bah) → EQ
new_lt21(vyy213000, vyy150, ty_Integer) → new_lt16(vyy213000, vyy150)
new_compare110(vyy213000, vyy150, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs9(False, False) → True
new_esEs4(Nothing, Nothing, dch) → True
new_ltEs10(vyy213001, vyy151, bbb) → new_not(new_esEs17(new_compare0(vyy213001, vyy151, bbb), GT))
new_esEs8(vyy2130011, vyy1511, ty_Ordering) → new_esEs17(vyy2130011, vyy1511)
new_esEs20(vyy2130010, vyy1510, app(app(ty_Either, gh), ha)) → new_esEs6(vyy2130010, vyy1510, gh, ha)
new_esEs27(vyy3002, vyy402, app(app(ty_@2, cgc), cgd)) → new_esEs5(vyy3002, vyy402, cgc, cgd)
new_compare210(vyy213000, vyy150, True) → EQ
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, app(ty_Maybe, bea)) → new_ltEs11(vyy2130010, vyy1510, bea)
new_lt5(vyy2130011, vyy1511, ty_Integer) → new_lt16(vyy2130011, vyy1511)
new_esEs29(vyy3000, vyy400, app(app(ty_Either, dbd), dbe)) → new_esEs6(vyy3000, vyy400, dbd, dbe)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs13(vyy3000, vyy400)
new_esEs27(vyy3002, vyy402, app(ty_Maybe, cga)) → new_esEs4(vyy3002, vyy402, cga)
new_primPlusNat1(Succ(vyy1310), vyy40100) → Succ(Succ(new_primPlusNat0(vyy1310, vyy40100)))
new_lt20(vyy2130010, vyy1510, ty_Int) → new_lt12(vyy2130010, vyy1510)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy15000))) → new_primCmpNat0(Succ(vyy15000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy15000))) → GT
new_esEs6(Right(vyy3000), Right(vyy400), bhg, app(ty_[], cab)) → new_esEs14(vyy3000, vyy400, cab)
new_lt4(vyy2130010, vyy1510, ty_Char) → new_lt8(vyy2130010, vyy1510)
new_ltEs20(vyy213001, vyy151, ty_Char) → new_ltEs8(vyy213001, vyy151)
new_compare0(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), bbg) → new_primCompAux1(vyy2130000, vyy1500, new_compare0(vyy2130001, vyy1501, bbg), bbg)
new_ltEs20(vyy213001, vyy151, ty_Int) → new_ltEs12(vyy213001, vyy151)
new_ltEs20(vyy213001, vyy151, ty_Float) → new_ltEs13(vyy213001, vyy151)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], ddc)) → new_esEs14(vyy3000, vyy400, ddc)
new_compare25(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, bag, bah) → new_compare10(vyy213000, vyy213001, vyy150, vyy151, new_lt21(vyy213000, vyy150, bag), new_asAs(new_esEs21(vyy213000, vyy150, bag), new_ltEs20(vyy213001, vyy151, bah)), bag, bah)
new_compare210(vyy213000, vyy150, False) → new_compare112(vyy213000, vyy150, new_ltEs14(vyy213000, vyy150))
new_ltEs19(vyy2130011, vyy1511, ty_Ordering) → new_ltEs14(vyy2130011, vyy1511)
new_esEs21(vyy213000, vyy150, app(ty_Maybe, fh)) → new_esEs4(vyy213000, vyy150, fh)
new_lt13(vyy213000, vyy150) → new_esEs17(new_compare9(vyy213000, vyy150), LT)
new_esEs6(Left(vyy3000), Left(vyy400), app(ty_Ratio, bgd), bge) → new_esEs11(vyy3000, vyy400, bgd)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs19(vyy3000, vyy400)
new_ltEs5(vyy2130012, vyy1512, ty_Integer) → new_ltEs16(vyy2130012, vyy1512)
new_esEs27(vyy3002, vyy402, ty_Double) → new_esEs18(vyy3002, vyy402)
new_esEs9(vyy2130010, vyy1510, app(app(ty_@2, ca), cb)) → new_esEs5(vyy2130010, vyy1510, ca, cb)
new_esEs10(@0, @0) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs24(vyy3001, vyy401, app(app(app(ty_@3, cca), ccb), ccc)) → new_esEs7(vyy3001, vyy401, cca, ccb, ccc)
new_esEs9(vyy2130010, vyy1510, ty_Ordering) → new_esEs17(vyy2130010, vyy1510)
new_esEs28(vyy3001, vyy401, ty_@0) → new_esEs10(vyy3001, vyy401)
new_lt19(vyy213000, vyy150, bcb, bcc, bcd) → new_esEs17(new_compare30(vyy213000, vyy150, bcb, bcc, bcd), LT)
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, ty_Float) → new_ltEs13(vyy2130010, vyy1510)
new_asAs(False, vyy111) → False
new_primMulInt(Neg(vyy30010), Pos(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_primMulInt(Pos(vyy30010), Neg(vyy4010)) → Neg(new_primMulNat0(vyy30010, vyy4010))
new_lt4(vyy2130010, vyy1510, ty_Int) → new_lt12(vyy2130010, vyy1510)
new_ltEs13(vyy213001, vyy151) → new_not(new_esEs17(new_compare9(vyy213001, vyy151), GT))
new_esEs29(vyy3000, vyy400, ty_Char) → new_esEs12(vyy3000, vyy400)
new_primMulNat0(Succ(vyy300100), Zero) → Zero
new_primMulNat0(Zero, Succ(vyy40100)) → Zero
new_esEs9(vyy2130010, vyy1510, app(ty_Maybe, bh)) → new_esEs4(vyy2130010, vyy1510, bh)
new_esEs21(vyy213000, vyy150, ty_Bool) → new_esEs13(vyy213000, vyy150)
new_compare29(vyy213000, vyy150) → new_compare210(vyy213000, vyy150, new_esEs17(vyy213000, vyy150))
new_lt17(vyy213000, vyy150, ff, fg) → new_esEs17(new_compare5(vyy213000, vyy150, ff, fg), LT)
new_lt5(vyy2130011, vyy1511, ty_Float) → new_lt13(vyy2130011, vyy1511)
new_esEs20(vyy2130010, vyy1510, ty_Float) → new_esEs16(vyy2130010, vyy1510)
new_ltEs14(GT, LT) → False
new_ltEs5(vyy2130012, vyy1512, ty_@0) → new_ltEs6(vyy2130012, vyy1512)
new_esEs28(vyy3001, vyy401, ty_Double) → new_esEs18(vyy3001, vyy401)
new_esEs13(False, False) → True
new_esEs18(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs15(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare14(vyy213000, vyy150, True, fh) → LT
new_esEs8(vyy2130011, vyy1511, app(ty_Ratio, da)) → new_esEs11(vyy2130011, vyy1511, da)
new_lt5(vyy2130011, vyy1511, app(app(ty_Either, df), dg)) → new_lt18(vyy2130011, vyy1511, df, dg)
new_esEs27(vyy3002, vyy402, ty_Integer) → new_esEs19(vyy3002, vyy402)
new_lt20(vyy2130010, vyy1510, ty_Float) → new_lt13(vyy2130010, vyy1510)
new_lt5(vyy2130011, vyy1511, app(ty_[], db)) → new_lt10(vyy2130011, vyy1511, db)
new_compare111(vyy159, vyy160, vyy161, vyy162, False, cdh, cea) → GT
new_ltEs9(False, True) → True
new_esEs9(vyy2130010, vyy1510, ty_Integer) → new_esEs19(vyy2130010, vyy1510)
new_compare27(vyy213000, vyy150, True) → EQ
new_esEs17(EQ, LT) → False
new_esEs17(LT, EQ) → False
new_esEs25(vyy3000, vyy400, ty_Integer) → new_esEs19(vyy3000, vyy400)
new_esEs20(vyy2130010, vyy1510, ty_Integer) → new_esEs19(vyy2130010, vyy1510)
new_lt7(vyy213000, vyy150, bbf) → new_esEs17(new_compare18(vyy213000, vyy150, bbf), LT)
new_ltEs5(vyy2130012, vyy1512, app(ty_[], ed)) → new_ltEs10(vyy2130012, vyy1512, ed)
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs10(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, app(app(app(ty_@3, cdc), cdd), cde)) → new_esEs7(vyy3000, vyy400, cdc, cdd, cde)
new_compare16(vyy2130000, vyy1500, app(app(ty_Either, bfg), bfh)) → new_compare13(vyy2130000, vyy1500, bfg, bfh)
new_esEs24(vyy3001, vyy401, ty_Ordering) → new_esEs17(vyy3001, vyy401)
new_esEs27(vyy3002, vyy402, ty_Int) → new_esEs15(vyy3002, vyy402)
new_esEs8(vyy2130011, vyy1511, app(ty_Maybe, dc)) → new_esEs4(vyy2130011, vyy1511, dc)
new_esEs26(vyy3000, vyy400, ty_Ordering) → new_esEs17(vyy3000, vyy400)
new_esEs25(vyy3000, vyy400, app(app(ty_@2, cda), cdb)) → new_esEs5(vyy3000, vyy400, cda, cdb)
new_ltEs14(LT, GT) → True
new_compare6(vyy213000, vyy150, fh) → new_compare24(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, fh), fh)
new_ltEs14(LT, EQ) → True
new_esEs25(vyy3000, vyy400, ty_Double) → new_esEs18(vyy3000, vyy400)
new_lt5(vyy2130011, vyy1511, ty_@0) → new_lt6(vyy2130011, vyy1511)
new_esEs27(vyy3002, vyy402, ty_Ordering) → new_esEs17(vyy3002, vyy402)
new_ltEs18(Left(vyy2130010), Left(vyy1510), app(ty_Ratio, bce), bbe) → new_ltEs7(vyy2130010, vyy1510, bce)
new_esEs28(vyy3001, vyy401, ty_Bool) → new_esEs13(vyy3001, vyy401)
new_compare112(vyy213000, vyy150, False) → GT
new_lt21(vyy213000, vyy150, app(ty_Ratio, bbf)) → new_lt7(vyy213000, vyy150, bbf)
new_esEs29(vyy3000, vyy400, ty_Ordering) → new_esEs17(vyy3000, vyy400)
new_lt4(vyy2130010, vyy1510, ty_Bool) → new_lt9(vyy2130010, vyy1510)
new_lt5(vyy2130011, vyy1511, ty_Ordering) → new_lt14(vyy2130011, vyy1511)
new_lt21(vyy213000, vyy150, app(app(ty_Either, bbh), bca)) → new_lt18(vyy213000, vyy150, bbh, bca)
new_ltEs19(vyy2130011, vyy1511, ty_Double) → new_ltEs15(vyy2130011, vyy1511)
new_esEs28(vyy3001, vyy401, app(ty_Ratio, chb)) → new_esEs11(vyy3001, vyy401, chb)
new_esEs26(vyy3000, vyy400, app(ty_Ratio, cec)) → new_esEs11(vyy3000, vyy400, cec)
new_compare16(vyy2130000, vyy1500, app(app(app(ty_@3, bga), bgb), bgc)) → new_compare30(vyy2130000, vyy1500, bga, bgb, bgc)
new_lt21(vyy213000, vyy150, ty_@0) → new_lt6(vyy213000, vyy150)
new_compare26(vyy213000, vyy150, True, bcb, bcc, bcd) → EQ
new_primPlusNat0(Succ(vyy13100), Succ(vyy401000)) → Succ(Succ(new_primPlusNat0(vyy13100, vyy401000)))
new_esEs29(vyy3000, vyy400, ty_@0) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy3000, vyy400, app(app(ty_Either, cfc), cfd)) → new_esEs6(vyy3000, vyy400, cfc, cfd)
new_compare15(Integer(vyy2130000), Integer(vyy1500)) → new_primCmpInt(vyy2130000, vyy1500)
new_compare0([], :(vyy1500, vyy1501), bbg) → LT
new_esEs27(vyy3002, vyy402, app(ty_[], cgb)) → new_esEs14(vyy3002, vyy402, cgb)
new_lt20(vyy2130010, vyy1510, app(app(app(ty_@3, hb), hc), hd)) → new_lt19(vyy2130010, vyy1510, hb, hc, hd)
new_esEs14(:(vyy3000, vyy3001), :(vyy400, vyy401), ceb) → new_asAs(new_esEs26(vyy3000, vyy400, ceb), new_esEs14(vyy3001, vyy401, ceb))
new_esEs24(vyy3001, vyy401, ty_Float) → new_esEs16(vyy3001, vyy401)
new_ltEs14(EQ, EQ) → True
new_asAs(True, vyy111) → vyy111
new_lt11(vyy213000, vyy150, fh) → new_esEs17(new_compare6(vyy213000, vyy150, fh), LT)
new_ltEs19(vyy2130011, vyy1511, app(ty_Ratio, he)) → new_ltEs7(vyy2130011, vyy1511, he)
new_esEs27(vyy3002, vyy402, ty_Float) → new_esEs16(vyy3002, vyy402)
new_ltEs11(Nothing, Nothing, bbc) → True
new_esEs13(True, True) → True
new_esEs17(GT, GT) → True
new_esEs29(vyy3000, vyy400, app(ty_Ratio, dad)) → new_esEs11(vyy3000, vyy400, dad)
new_esEs6(Right(vyy3000), Right(vyy400), bhg, ty_Float) → new_esEs16(vyy3000, vyy400)
new_lt8(vyy213000, vyy150) → new_esEs17(new_compare19(vyy213000, vyy150), LT)
new_ltEs5(vyy2130012, vyy1512, ty_Char) → new_ltEs8(vyy2130012, vyy1512)
new_lt5(vyy2130011, vyy1511, app(app(ty_@2, dd), de)) → new_lt17(vyy2130011, vyy1511, dd, de)
new_esEs9(vyy2130010, vyy1510, ty_Int) → new_esEs15(vyy2130010, vyy1510)
new_esEs20(vyy2130010, vyy1510, app(ty_[], gd)) → new_esEs14(vyy2130010, vyy1510, gd)
new_lt12(vyy213000, vyy150) → new_esEs17(new_compare12(vyy213000, vyy150), LT)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, ddf), ddg), ddh)) → new_esEs7(vyy3000, vyy400, ddf, ddg, ddh)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs17(vyy3000, vyy400)
new_lt5(vyy2130011, vyy1511, ty_Double) → new_lt15(vyy2130011, vyy1511)
new_esEs29(vyy3000, vyy400, app(ty_Maybe, dae)) → new_esEs4(vyy3000, vyy400, dae)
new_lt5(vyy2130011, vyy1511, app(ty_Maybe, dc)) → new_lt11(vyy2130011, vyy1511, dc)
new_lt20(vyy2130010, vyy1510, app(ty_Ratio, gc)) → new_lt7(vyy2130010, vyy1510, gc)
new_esEs26(vyy3000, vyy400, ty_Int) → new_esEs15(vyy3000, vyy400)
new_esEs21(vyy213000, vyy150, app(ty_Ratio, bbf)) → new_esEs11(vyy213000, vyy150, bbf)
new_ltEs5(vyy2130012, vyy1512, app(app(ty_Either, eh), fa)) → new_ltEs18(vyy2130012, vyy1512, eh, fa)
new_esEs21(vyy213000, vyy150, ty_Float) → new_esEs16(vyy213000, vyy150)
new_esEs26(vyy3000, vyy400, ty_Bool) → new_esEs13(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs14(EQ, GT) → True
new_primCompAux0(vyy183, EQ) → vyy183
new_ltEs5(vyy2130012, vyy1512, app(app(app(ty_@3, fb), fc), fd)) → new_ltEs4(vyy2130012, vyy1512, fb, fc, fd)
new_ltEs18(Right(vyy2130010), Right(vyy1510), bbd, ty_Char) → new_ltEs8(vyy2130010, vyy1510)
new_esEs28(vyy3001, vyy401, ty_Char) → new_esEs12(vyy3001, vyy401)
new_ltEs11(Just(vyy2130010), Nothing, bbc) → False
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs18(Left(vyy2130010), Left(vyy1510), ty_@0, bbe) → new_ltEs6(vyy2130010, vyy1510)
new_primCmpInt(Neg(Succ(vyy21300000)), Pos(vyy1500)) → LT
new_esEs6(Right(vyy3000), Right(vyy400), bhg, ty_Int) → new_esEs15(vyy3000, vyy400)
new_esEs20(vyy2130010, vyy1510, ty_Double) → new_esEs18(vyy2130010, vyy1510)
new_not(True) → False

The set Q consists of the following terms:

new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs17(LT, GT)
new_esEs17(GT, LT)
new_ltEs11(Just(x0), Just(x1), ty_Int)
new_compare110(x0, x1, True)
new_esEs26(x0, x1, ty_Ordering)
new_asAs(True, x0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs5(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs18(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs20(x0, x1, ty_Integer)
new_esEs17(LT, LT)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(Just(x0), Just(x1), ty_Char)
new_compare16(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt16(x0, x1)
new_ltEs15(x0, x1)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_lt7(x0, x1, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs18(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs13(x0, x1)
new_esEs25(x0, x1, ty_Ordering)
new_compare5(x0, x1, x2, x3)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs25(x0, x1, ty_Integer)
new_ltEs18(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare210(x0, x1, False)
new_esEs21(x0, x1, app(ty_[], x2))
new_compare14(x0, x1, True, x2)
new_primMulNat0(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs20(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Bool)
new_compare210(x0, x1, True)
new_lt20(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Ordering)
new_lt21(x0, x1, ty_Integer)
new_esEs14([], :(x0, x1), x2)
new_ltEs18(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs11(Nothing, Just(x0), x1)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs17(EQ, GT)
new_esEs17(GT, EQ)
new_ltEs18(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs11(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_ltEs18(Left(x0), Left(x1), ty_@0, x2)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs18(Double(x0, x1), Double(x2, x3))
new_lt4(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Bool)
new_lt5(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Integer)
new_compare26(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1, ty_Ordering)
new_lt21(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_compare16(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_compare17(@0, @0)
new_lt21(x0, x1, app(ty_[], x2))
new_ltEs18(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs18(Left(x0), Left(x1), ty_Float, x2)
new_ltEs5(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Double)
new_sr(x0, x1)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs8(x0, x1, ty_Ordering)
new_compare29(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs17(GT, GT)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs11(Just(x0), Just(x1), ty_Ordering)
new_compare27(x0, x1, False)
new_compare13(x0, x1, x2, x3)
new_esEs8(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Double)
new_compare16(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Ordering)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_compare14(x0, x1, False, x2)
new_lt5(x0, x1, ty_Double)
new_esEs9(x0, x1, ty_@0)
new_primCompAux0(x0, LT)
new_compare0(:(x0, x1), [], x2)
new_lt4(x0, x1, ty_Bool)
new_ltEs14(EQ, EQ)
new_primEqNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Integer)
new_compare16(x0, x1, ty_Char)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_lt17(x0, x1, x2, x3)
new_ltEs18(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2, x3)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs9(False, False)
new_esEs26(x0, x1, ty_Float)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare11(x0, x1, True, x2, x3, x4)
new_esEs13(False, False)
new_primMulNat0(Zero, Zero)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs19(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Int)
new_compare16(x0, x1, ty_Float)
new_primPlusNat1(Zero, x0)
new_lt5(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(Just(x0), Just(x1), ty_Double)
new_esEs25(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(Just(x0), Just(x1), ty_Bool)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_sr0(Integer(x0), Integer(x1))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare16(x0, x1, app(ty_[], x2))
new_ltEs18(Left(x0), Left(x1), ty_Char, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt14(x0, x1)
new_pePe(True, x0)
new_compare7(x0, x1)
new_compare18(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare26(x0, x1, True, x2, x3, x4)
new_compare30(x0, x1, x2, x3, x4)
new_esEs27(x0, x1, ty_Char)
new_ltEs18(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, ty_@0)
new_compare113(x0, x1, True, x2, x3)
new_esEs14([], [], x0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_Double)
new_ltEs18(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare16(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_@0)
new_compare112(x0, x1, True)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1, ty_Int)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare10(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs18(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_primPlusNat0(Zero, Zero)
new_esEs4(Nothing, Nothing, x0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt20(x0, x1, ty_Char)
new_ltEs14(LT, LT)
new_lt20(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Float)
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs25(x0, x1, app(ty_[], x2))
new_lt9(x0, x1)
new_esEs27(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_compare28(x0, x1, True, x2, x3)
new_primCompAux0(x0, EQ)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs9(False, True)
new_ltEs9(True, False)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt5(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, app(ty_Ratio, x2))
new_ltEs11(Just(x0), Just(x1), app(ty_[], x2))
new_compare16(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_foldFM_GE11(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9, x10)
new_esEs15(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_ltEs9(True, True)
new_esEs20(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_esEs10(@0, @0)
new_esEs28(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_compare10(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(LT, EQ)
new_ltEs14(EQ, LT)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, x2)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs8(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs18(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_asAs(False, x0)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Bool)
new_lt4(x0, x1, ty_Double)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_foldFM_GE0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_lt4(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs28(x0, x1, ty_Float)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, ty_Double)
new_esEs4(Nothing, Just(x0), x1)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs21(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs18(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(x0, x1, ty_Int)
new_compare112(x0, x1, False)
new_compare28(x0, x1, False, x2, x3)
new_ltEs6(x0, x1)
new_ltEs18(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Just(x0), Nothing, x1)
new_primPlusNat1(Succ(x0), x1)
new_ltEs20(x0, x1, ty_Float)
new_ltEs18(Right(x0), Right(x1), x2, app(ty_[], x3))
new_foldFM_GE11(x0, x1, x2, x3, x4, x5, EmptyFM, x6, False, x7, x8, x9)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Double)
new_ltEs16(x0, x1)
new_esEs24(x0, x1, ty_Char)
new_compare8(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_Int)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_compare19(Char(x0), Char(x1))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare16(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Double)
new_lt12(x0, x1)
new_compare110(x0, x1, False)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(Nothing, Nothing, x0)
new_ltEs18(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(Right(x0), Right(x1), x2, ty_Bool)
new_esEs20(x0, x1, ty_Float)
new_lt19(x0, x1, x2, x3, x4)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, ty_Float)
new_ltEs14(EQ, GT)
new_ltEs14(GT, EQ)
new_lt21(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Integer)
new_esEs9(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_@0)
new_primCmpNat0(Zero, Zero)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_foldFM_GE11(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, False, x12, x13, x14)
new_compare16(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, ty_@0)
new_lt10(x0, x1, x2)
new_esEs26(x0, x1, ty_Double)
new_compare6(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Bool)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs7(x0, x1, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare18(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare27(x0, x1, True)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs14(LT, GT)
new_ltEs14(GT, LT)
new_compare24(x0, x1, True, x2)
new_esEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, ty_Int)
new_esEs13(False, True)
new_esEs13(True, False)
new_ltEs18(Right(x0), Right(x1), x2, ty_@0)
new_ltEs11(Just(x0), Just(x1), ty_Float)
new_ltEs10(x0, x1, x2)
new_compare16(x0, x1, ty_Ordering)
new_compare16(x0, x1, ty_@0)
new_compare0([], :(x0, x1), x2)
new_primPlusNat0(Zero, Succ(x0))
new_esEs11(:%(x0, x1), :%(x2, x3), x4)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Succ(x0), Zero)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(GT, GT)
new_compare0([], [], x0)
new_not(True)
new_esEs24(x0, x1, ty_Float)
new_esEs16(Float(x0, x1), Float(x2, x3))
new_esEs13(True, True)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_compare16(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_@0)
new_ltEs18(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, ty_Double)
new_ltEs11(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_compare9(Float(x0, x1), Float(x2, x3))
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs24(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1)
new_compare25(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_esEs29(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_foldFM_GE12(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs18(Right(x0), Right(x1), x2, ty_Float)
new_esEs29(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Char)
new_ltEs11(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, ty_Float)
new_compare113(x0, x1, False, x2, x3)
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_primCompAux1(x0, x1, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs12(x0, x1)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Right(x0), Left(x1), x2, x3)
new_ltEs18(Left(x0), Right(x1), x2, x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs18(Left(x0), Left(x1), ty_Double, x2)
new_ltEs18(Right(x0), Right(x1), x2, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1)
new_esEs14(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_primCompAux0(x0, GT)
new_esEs28(x0, x1, app(ty_[], x2))
new_primPlusNat0(Succ(x0), Zero)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare24(x0, x1, False, x2)
new_primEqNat0(Succ(x0), Zero)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs11(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs18(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_eltsFM_GE0(x0, x1, x2, x3, x4, x5)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, ty_Bool)
new_compare25(x0, x1, True, x2, x3)
new_lt4(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Double)
new_foldFM_GE0(x0, x1, x2, EmptyFM, x3, x4, x5)
new_esEs9(x0, x1, ty_Ordering)
new_ltEs11(Just(x0), Nothing, x1)
new_pePe(False, x0)
new_ltEs11(Just(x0), Just(x1), ty_@0)
new_esEs19(Integer(x0), Integer(x1))
new_ltEs5(x0, x1, ty_Integer)
new_esEs17(EQ, EQ)
new_esEs9(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt5(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs17(EQ, LT)
new_esEs17(LT, EQ)
new_esEs8(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs11(Just(x0), Just(x1), ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs12(Char(x0), Char(x1))
new_esEs25(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Integer)
new_compare11(x0, x1, False, x2, x3, x4)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))

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

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