YES 7.567 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ LR

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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



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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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



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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

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

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

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

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

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

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

  foldFM_GE :: Ord a => (a  ->  c  ->  b  ->  b)  ->  b  ->  a  ->  FiniteMap a c  ->  b
foldFM_GE k z fr EmptyFM = z
foldFM_GE k z fr (Branch key elt 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 b a  ->  Int
sizeFM EmptyFM = 0
sizeFM (Branch vx vy size vz wu) = size


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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

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

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

is transformed to
compare x y = compare3 x y

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

compare0 x y True = GT

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

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

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

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

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

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

  foldFM :: (a  ->  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


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

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

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

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

are unpacked to the following functions on top level
gcd0Gcd'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

gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y)



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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Haskell To QDPs


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

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

new_primCmpNat(Succ(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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primPlusNat(Succ(vyy13100), Succ(vyy400000)) → new_primPlusNat(vyy13100, vyy400000)

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

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



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

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

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

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

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



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

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

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

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

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



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

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

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

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_ltEs3(Left(vyy2130010), Left(vyy1510), app(app(ty_Either, bcb), bcc), bbc) → new_ltEs3(vyy2130010, vyy1510, bcb, bcc)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), gf, app(app(app(ty_@3, hb), hc), hd), fd) → new_lt1(vyy2130011, vyy1511, hb, hc, hd)
new_ltEs(Just(vyy2130010), Just(vyy1510), app(ty_[], bf)) → new_ltEs2(vyy2130010, vyy1510, bf)
new_ltEs0(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(ty_[], da), cb) → new_lt2(vyy2130010, vyy1510, da)
new_ltEs0(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(app(ty_Either, db), dc), cb) → new_lt3(vyy2130010, vyy1510, db, dc)
new_ltEs0(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), dd, app(app(app(ty_@3, dh), ea), eb)) → new_ltEs1(vyy2130011, vyy1511, dh, ea, eb)
new_compare20(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, fa, app(ty_Maybe, app(app(ty_@2, ba), bb))) → new_ltEs0(vyy2130010, vyy1510, ba, bb)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(app(ty_Either, gd), ge), fc, fd) → new_lt3(vyy2130010, vyy1510, gd, ge)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(ty_[], gc), fc, fd) → new_lt2(vyy2130010, vyy1510, gc)
new_ltEs0(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), dd, app(ty_Maybe, de)) → new_ltEs(vyy2130011, vyy1511, de)
new_ltEs2(vyy213001, vyy151, bba) → new_compare1(vyy213001, vyy151, bba)
new_ltEs3(Left(vyy2130010), Left(vyy1510), app(ty_Maybe, bbb), bbc) → new_ltEs(vyy2130010, vyy1510, bbb)
new_compare20(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, fa, app(app(ty_@2, app(app(ty_@2, cc), cd)), cb)) → new_lt0(vyy2130010, vyy1510, cc, cd)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, gf), app(ty_Maybe, gg)), fd)) → new_lt(vyy2130011, vyy1511, gg)
new_compare20(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, fa, app(app(ty_@2, app(app(ty_Either, db), dc)), cb)) → new_lt3(vyy2130010, vyy1510, db, dc)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, gf), app(ty_[], he)), fd)) → new_lt2(vyy2130011, vyy1511, he)
new_ltEs(Just(vyy2130010), Just(vyy1510), app(app(ty_@2, ba), bb)) → new_ltEs0(vyy2130010, vyy1510, ba, bb)
new_compare20(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, fa, app(app(ty_Either, bcd), app(ty_Maybe, bce))) → new_ltEs(vyy2130010, vyy1510, bce)
new_compare20(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, fa, app(app(ty_@2, dd), app(app(ty_Either, ed), ee))) → new_ltEs3(vyy2130011, vyy1511, ed, ee)
new_compare20(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, fa, app(app(ty_@2, dd), app(app(app(ty_@3, dh), ea), eb))) → new_ltEs1(vyy2130011, vyy1511, dh, ea, eb)
new_lt3(vyy213000, vyy150, bec, bed) → new_compare22(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bec, bed), bec, bed)
new_ltEs(Just(vyy2130010), Just(vyy1510), app(app(ty_Either, bg), bh)) → new_ltEs3(vyy2130010, vyy1510, bg, bh)
new_lt0(vyy213000, vyy150, eg, eh) → new_compare20(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, eg, eh), eg, eh)
new_primCompAux(vyy2130000, vyy1500, vyy178, app(app(ty_Either, bfd), bfe)) → new_compare5(vyy2130000, vyy1500, bfd, bfe)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), gf, fc, app(app(ty_@2, baa), bab)) → new_ltEs0(vyy2130012, vyy1512, baa, bab)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, gf), fc), app(app(app(ty_@3, bac), bad), bae))) → new_ltEs1(vyy2130012, vyy1512, bac, bad, bae)
new_ltEs3(Right(vyy2130010), Right(vyy1510), bcd, app(app(ty_Either, bdd), bde)) → new_ltEs3(vyy2130010, vyy1510, bdd, bde)
new_compare20(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, fa, app(app(ty_@2, app(ty_Maybe, ca)), cb)) → new_lt(vyy2130010, vyy1510, ca)
new_compare1(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), beb) → new_compare1(vyy2130001, vyy1501, beb)
new_compare1(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), beb) → new_primCompAux(vyy2130000, vyy1500, new_compare3(vyy2130001, vyy1501, beb), beb)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, app(app(ty_Either, gd), ge)), fc), fd)) → new_lt3(vyy2130010, vyy1510, gd, ge)
new_compare20(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, fa, app(app(ty_Either, bcd), app(ty_[], bdc))) → new_ltEs2(vyy2130010, vyy1510, bdc)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, gf), fc), app(app(ty_Either, bag), bah))) → new_ltEs3(vyy2130012, vyy1512, bag, bah)
new_compare20(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, fa, app(ty_Maybe, app(ty_Maybe, h))) → new_ltEs(vyy2130010, vyy1510, h)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), gf, app(ty_Maybe, gg), fd) → new_lt(vyy2130011, vyy1511, gg)
new_ltEs0(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(ty_Maybe, ca), cb) → new_lt(vyy2130010, vyy1510, ca)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, app(ty_[], gc)), fc), fd)) → new_lt2(vyy2130010, vyy1510, gc)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), gf, app(app(ty_Either, hf), hg), fd) → new_lt3(vyy2130011, vyy1511, hf, hg)
new_compare20(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, app(ty_Maybe, ef), bdf) → new_compare2(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, ef), ef)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), gf, fc, app(app(app(ty_@3, bac), bad), bae)) → new_ltEs1(vyy2130012, vyy1512, bac, bad, bae)
new_primCompAux(vyy2130000, vyy1500, vyy178, app(ty_[], bfc)) → new_compare1(vyy2130000, vyy1500, bfc)
new_compare20(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, app(app(app(ty_@3, bdg), bdh), bea), bdf) → new_compare21(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, bdg, bdh, bea), bdg, bdh, bea)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, gf), app(app(app(ty_@3, hb), hc), hd)), fd)) → new_lt1(vyy2130011, vyy1511, hb, hc, hd)
new_compare0(vyy213000, vyy150, eg, eh) → new_compare20(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, eg, eh), eg, eh)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, gf), app(app(ty_Either, hf), hg)), fd)) → new_lt3(vyy2130011, vyy1511, hf, hg)
new_compare20(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, fa, app(app(ty_@2, dd), app(ty_[], ec))) → new_ltEs2(vyy2130011, vyy1511, ec)
new_compare20(@2(:(vyy2130000, vyy2130001), vyy213001), @2(:(vyy1500, vyy1501), vyy151), False, app(ty_[], beb), bdf) → new_compare1(vyy2130001, vyy1501, beb)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, app(app(ty_@2, ff), fg)), fc), fd)) → new_lt0(vyy2130010, vyy1510, ff, fg)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, gf), app(app(ty_@2, gh), ha)), fd)) → new_lt0(vyy2130011, vyy1511, gh, ha)
new_ltEs0(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), dd, app(app(ty_Either, ed), ee)) → new_ltEs3(vyy2130011, vyy1511, ed, ee)
new_compare(vyy213000, vyy150, ef) → new_compare2(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, ef), ef)
new_ltEs0(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(app(ty_@2, cc), cd), cb) → new_lt0(vyy2130010, vyy1510, cc, cd)
new_compare20(@2(:(vyy2130000, vyy2130001), vyy213001), @2(:(vyy1500, vyy1501), vyy151), False, app(ty_[], beb), bdf) → new_primCompAux(vyy2130000, vyy1500, new_compare3(vyy2130001, vyy1501, beb), beb)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), gf, app(ty_[], he), fd) → new_lt2(vyy2130011, vyy1511, he)
new_compare22(vyy213000, vyy150, False, bec, bed) → new_ltEs3(vyy213000, vyy150, bec, bed)
new_ltEs3(Right(vyy2130010), Right(vyy1510), bcd, app(ty_[], bdc)) → new_ltEs2(vyy2130010, vyy1510, bdc)
new_compare20(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, fa, app(app(ty_@2, app(app(app(ty_@3, ce), cf), cg)), cb)) → new_lt1(vyy2130010, vyy1510, ce, cf, cg)
new_ltEs3(Right(vyy2130010), Right(vyy1510), bcd, app(app(app(ty_@3, bch), bda), bdb)) → new_ltEs1(vyy2130010, vyy1510, bch, bda, bdb)
new_compare20(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, fa, app(app(ty_@2, dd), app(app(ty_@2, df), dg))) → new_ltEs0(vyy2130011, vyy1511, df, dg)
new_compare20(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, fa, app(ty_Maybe, app(ty_[], bf))) → new_ltEs2(vyy2130010, vyy1510, bf)
new_compare20(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, fa, app(ty_[], bba)) → new_compare1(vyy213001, vyy151, bba)
new_lt2(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), beb) → new_compare1(vyy2130001, vyy1501, beb)
new_compare21(vyy213000, vyy150, False, bdg, bdh, bea) → new_ltEs1(vyy213000, vyy150, bdg, bdh, bea)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(ty_Maybe, fb), fc, fd) → new_lt(vyy2130010, vyy1510, fb)
new_compare20(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, fa, app(app(ty_@2, dd), app(ty_Maybe, de))) → new_ltEs(vyy2130011, vyy1511, de)
new_compare20(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, fa, app(app(ty_Either, bcd), app(app(ty_Either, bdd), bde))) → new_ltEs3(vyy2130010, vyy1510, bdd, bde)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, app(ty_Maybe, fb)), fc), fd)) → new_lt(vyy2130010, vyy1510, fb)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(app(ty_@2, ff), fg), fc, fd) → new_lt0(vyy2130010, vyy1510, ff, fg)
new_primCompAux(vyy2130000, vyy1500, vyy178, app(app(ty_@2, bef), beg)) → new_compare0(vyy2130000, vyy1500, bef, beg)
new_ltEs(Just(vyy2130010), Just(vyy1510), app(app(app(ty_@3, bc), bd), be)) → new_ltEs1(vyy2130010, vyy1510, bc, bd, be)
new_compare20(@2(vyy213000, @2(vyy2130010, vyy2130011)), @2(vyy150, @2(vyy1510, vyy1511)), False, fa, app(app(ty_@2, app(ty_[], da)), cb)) → new_lt2(vyy2130010, vyy1510, da)
new_ltEs(Just(vyy2130010), Just(vyy1510), app(ty_Maybe, h)) → new_ltEs(vyy2130010, vyy1510, h)
new_lt(vyy213000, vyy150, ef) → new_compare2(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, ef), ef)
new_compare20(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, fa, app(app(ty_Either, app(ty_[], bca)), bbc)) → new_ltEs2(vyy2130010, vyy1510, bca)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, gf), fc), app(app(ty_@2, baa), bab))) → new_ltEs0(vyy2130012, vyy1512, baa, bab)
new_lt2(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), beb) → new_primCompAux(vyy2130000, vyy1500, new_compare3(vyy2130001, vyy1501, beb), beb)
new_ltEs3(Left(vyy2130010), Left(vyy1510), app(ty_[], bca), bbc) → new_ltEs2(vyy2130010, vyy1510, bca)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), gf, fc, app(app(ty_Either, bag), bah)) → new_ltEs3(vyy2130012, vyy1512, bag, bah)
new_compare4(vyy213000, vyy150, bdg, bdh, bea) → new_compare21(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, bdg, bdh, bea), bdg, bdh, bea)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, gf), fc), app(ty_Maybe, hh))) → new_ltEs(vyy2130012, vyy1512, hh)
new_compare20(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, fa, app(ty_Maybe, app(app(app(ty_@3, bc), bd), be))) → new_ltEs1(vyy2130010, vyy1510, bc, bd, be)
new_compare20(@2(vyy213000, Just(vyy2130010)), @2(vyy150, Just(vyy1510)), False, fa, app(ty_Maybe, app(app(ty_Either, bg), bh))) → new_ltEs3(vyy2130010, vyy1510, bg, bh)
new_ltEs3(Left(vyy2130010), Left(vyy1510), app(app(app(ty_@3, bbf), bbg), bbh), bbc) → new_ltEs1(vyy2130010, vyy1510, bbf, bbg, bbh)
new_compare20(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, fa, app(app(ty_Either, bcd), app(app(app(ty_@3, bch), bda), bdb))) → new_ltEs1(vyy2130010, vyy1510, bch, bda, bdb)
new_ltEs0(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), dd, app(app(ty_@2, df), dg)) → new_ltEs0(vyy2130011, vyy1511, df, dg)
new_compare20(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, fa, app(app(ty_Either, app(app(ty_Either, bcb), bcc)), bbc)) → new_ltEs3(vyy2130010, vyy1510, bcb, bcc)
new_ltEs3(Left(vyy2130010), Left(vyy1510), app(app(ty_@2, bbd), bbe), bbc) → new_ltEs0(vyy2130010, vyy1510, bbd, bbe)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, app(app(app(ty_@3, fh), ga), gb)), fc), fd)) → new_lt1(vyy2130010, vyy1510, fh, ga, gb)
new_compare20(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, fa, app(app(ty_Either, app(app(ty_@2, bbd), bbe)), bbc)) → new_ltEs0(vyy2130010, vyy1510, bbd, bbe)
new_compare2(vyy213000, vyy150, False, ef) → new_ltEs(vyy213000, vyy150, ef)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), gf, fc, app(ty_[], baf)) → new_ltEs2(vyy2130012, vyy1512, baf)
new_compare20(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, fa, app(app(ty_Either, app(app(app(ty_@3, bbf), bbg), bbh)), bbc)) → new_ltEs1(vyy2130010, vyy1510, bbf, bbg, bbh)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), gf, fc, app(ty_Maybe, hh)) → new_ltEs(vyy2130012, vyy1512, hh)
new_compare5(vyy213000, vyy150, bec, bed) → new_compare22(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bec, bed), bec, bed)
new_compare20(@2(vyy213000, @3(vyy2130010, vyy2130011, vyy2130012)), @2(vyy150, @3(vyy1510, vyy1511, vyy1512)), False, fa, app(app(app(ty_@3, gf), fc), app(ty_[], baf))) → new_ltEs2(vyy2130012, vyy1512, baf)
new_compare20(@2(vyy213000, Right(vyy2130010)), @2(vyy150, Right(vyy1510)), False, fa, app(app(ty_Either, bcd), app(app(ty_@2, bcf), bcg))) → new_ltEs0(vyy2130010, vyy1510, bcf, bcg)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), gf, app(app(ty_@2, gh), ha), fd) → new_lt0(vyy2130011, vyy1511, gh, ha)
new_compare20(@2(vyy213000, Left(vyy2130010)), @2(vyy150, Left(vyy1510)), False, fa, app(app(ty_Either, app(ty_Maybe, bbb)), bbc)) → new_ltEs(vyy2130010, vyy1510, bbb)
new_ltEs3(Right(vyy2130010), Right(vyy1510), bcd, app(ty_Maybe, bce)) → new_ltEs(vyy2130010, vyy1510, bce)
new_compare20(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, app(app(ty_@2, eg), eh), bdf) → new_compare20(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, eg, eh), eg, eh)
new_lt1(vyy213000, vyy150, bdg, bdh, bea) → new_compare21(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, bdg, bdh, bea), bdg, bdh, bea)
new_ltEs0(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), dd, app(ty_[], ec)) → new_ltEs2(vyy2130011, vyy1511, ec)
new_ltEs3(Right(vyy2130010), Right(vyy1510), bcd, app(app(ty_@2, bcf), bcg)) → new_ltEs0(vyy2130010, vyy1510, bcf, bcg)
new_ltEs0(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), app(app(app(ty_@3, ce), cf), cg), cb) → new_lt1(vyy2130010, vyy1510, ce, cf, cg)
new_compare20(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, app(app(ty_Either, bec), bed), bdf) → new_compare22(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bec, bed), bec, bed)
new_primCompAux(vyy2130000, vyy1500, vyy178, app(app(app(ty_@3, beh), bfa), bfb)) → new_compare4(vyy2130000, vyy1500, beh, bfa, bfb)
new_primCompAux(vyy2130000, vyy1500, vyy178, app(ty_Maybe, bee)) → new_compare(vyy2130000, vyy1500, bee)
new_ltEs1(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), app(app(app(ty_@3, fh), ga), gb), fc, fd) → new_lt1(vyy2130010, vyy1510, fh, ga, gb)

The TRS R consists of the following rules:

new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, dda)) → new_esEs4(vyy3000, vyy400, dda)
new_esEs26(vyy2130010, vyy1510, app(ty_[], gc)) → new_esEs8(vyy2130010, vyy1510, gc)
new_esEs23(vyy3000, vyy400, app(app(ty_Either, daa), dab)) → new_esEs7(vyy3000, vyy400, daa, dab)
new_esEs23(vyy3000, vyy400, ty_Ordering) → new_esEs18(vyy3000, vyy400)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_Either, cag), cah), bhf) → new_esEs7(vyy3000, vyy400, cag, cah)
new_compare3(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), beb) → new_primCompAux0(vyy2130000, vyy1500, new_compare3(vyy2130001, vyy1501, beb), beb)
new_lt20(vyy2130010, vyy1510, ty_Int) → new_lt16(vyy2130010, vyy1510)
new_lt20(vyy2130010, vyy1510, app(app(app(ty_@3, fh), ga), gb)) → new_lt12(vyy2130010, vyy1510, fh, ga, gb)
new_ltEs17(False, False) → True
new_compare10(vyy213000, vyy150, True, bdg, bdh, bea) → LT
new_esEs18(LT, LT) → True
new_compare8(Integer(vyy2130000), Integer(vyy1500)) → new_primCmpInt(vyy2130000, vyy1500)
new_compare32(vyy2130000, vyy1500, ty_@0) → new_compare15(vyy2130000, vyy1500)
new_esEs25(vyy213000, vyy150, ty_Ordering) → new_esEs18(vyy213000, vyy150)
new_lt7(vyy2130010, vyy1510, app(ty_[], da)) → new_lt14(vyy2130010, vyy1510, da)
new_esEs17(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Maybe, cad), bhf) → new_esEs4(vyy3000, vyy400, cad)
new_esEs24(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Ordering) → new_ltEs5(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, ty_Float) → new_ltEs15(vyy2130011, vyy1511)
new_esEs9(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs26(vyy2130010, vyy1510, ty_Double) → new_esEs14(vyy2130010, vyy1510)
new_compare23(vyy213000, vyy150, False, bdg, bdh, bea) → new_compare10(vyy213000, vyy150, new_ltEs4(vyy213000, vyy150, bdg, bdh, bea), bdg, bdh, bea)
new_esEs9(vyy3000, vyy400, ty_@0) → new_esEs13(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, app(ty_Maybe, dah)) → new_esEs4(vyy3001, vyy401, dah)
new_esEs18(LT, EQ) → False
new_esEs18(EQ, LT) → False
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Integer) → new_ltEs11(vyy2130010, vyy1510)
new_esEs4(Nothing, Just(vyy400), dcc) → False
new_esEs4(Just(vyy3000), Nothing, dcc) → False
new_lt19(vyy213000, vyy150, app(app(ty_Either, bec), bed)) → new_lt18(vyy213000, vyy150, bec, bed)
new_ltEs5(EQ, GT) → True
new_ltEs20(vyy2130012, vyy1512, ty_@0) → new_ltEs8(vyy2130012, vyy1512)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs17(vyy3000, vyy400)
new_ltEs9(Nothing, Just(vyy1510), ccd) → True
new_compare31(vyy213000, vyy150, bdg, bdh, bea) → new_compare23(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, bdg, bdh, bea), bdg, bdh, bea)
new_esEs25(vyy213000, vyy150, ty_Char) → new_esEs17(vyy213000, vyy150)
new_ltEs18(vyy2130011, vyy1511, app(ty_Ratio, bhe)) → new_ltEs12(vyy2130011, vyy1511, bhe)
new_ltEs20(vyy2130012, vyy1512, ty_Double) → new_ltEs7(vyy2130012, vyy1512)
new_ltEs19(vyy213001, vyy151, app(ty_Ratio, dbe)) → new_ltEs12(vyy213001, vyy151, dbe)
new_compare32(vyy2130000, vyy1500, ty_Double) → new_compare6(vyy2130000, vyy1500)
new_compare112(vyy159, vyy160, vyy161, vyy162, True, dbf, dbg) → LT
new_compare32(vyy2130000, vyy1500, ty_Integer) → new_compare8(vyy2130000, vyy1500)
new_esEs21(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_primMulNat0(Zero, Zero) → Zero
new_esEs24(vyy3001, vyy401, ty_@0) → new_esEs13(vyy3001, vyy401)
new_esEs7(Right(vyy3000), Right(vyy400), cba, ty_Double) → new_esEs14(vyy3000, vyy400)
new_primCompAux0(vyy2130000, vyy1500, vyy178, beb) → new_primCompAux00(vyy178, new_compare32(vyy2130000, vyy1500, beb))
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs6(vyy3000, vyy400, dcf, dcg, dch)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Double, bhf) → new_esEs14(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, app(ty_Ratio, cdg)) → new_esEs16(vyy3000, vyy400, cdg)
new_esEs20(vyy3000, vyy400, app(ty_Maybe, cdf)) → new_esEs4(vyy3000, vyy400, cdf)
new_lt20(vyy2130010, vyy1510, ty_Integer) → new_lt4(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, app(ty_[], ec)) → new_ltEs13(vyy2130011, vyy1511, ec)
new_compare26(vyy213000, vyy150, False) → new_compare19(vyy213000, vyy150, new_ltEs5(vyy213000, vyy150))
new_ltEs13(vyy213001, vyy151, bba) → new_not(new_esEs18(new_compare3(vyy213001, vyy151, bba), GT))
new_lt21(vyy2130011, vyy1511, ty_Float) → new_lt15(vyy2130011, vyy1511)
new_esEs22(vyy3002, vyy402, ty_Char) → new_esEs17(vyy3002, vyy402)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_lt17(vyy213000, vyy150) → new_esEs18(new_compare29(vyy213000, vyy150), LT)
new_lt21(vyy2130011, vyy1511, ty_@0) → new_lt9(vyy2130011, vyy1511)
new_ltEs20(vyy2130012, vyy1512, ty_Char) → new_ltEs14(vyy2130012, vyy1512)
new_lt20(vyy2130010, vyy1510, app(app(ty_@2, ff), fg)) → new_lt11(vyy2130010, vyy1510, ff, fg)
new_compare32(vyy2130000, vyy1500, ty_Ordering) → new_compare30(vyy2130000, vyy1500)
new_esEs23(vyy3000, vyy400, app(ty_Maybe, chf)) → new_esEs4(vyy3000, vyy400, chf)
new_ltEs9(Just(vyy2130010), Just(vyy1510), app(app(ty_Either, bg), bh)) → new_ltEs6(vyy2130010, vyy1510, bg, bh)
new_esEs20(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, ty_@0) → new_esEs13(vyy3000, vyy400)
new_esEs22(vyy3002, vyy402, ty_Bool) → new_esEs10(vyy3002, vyy402)
new_lt7(vyy2130010, vyy1510, ty_Ordering) → new_lt13(vyy2130010, vyy1510)
new_lt19(vyy213000, vyy150, ty_Bool) → new_lt17(vyy213000, vyy150)
new_ltEs6(Left(vyy2130010), Left(vyy1510), app(app(ty_Either, bcb), bcc), bbc) → new_ltEs6(vyy2130010, vyy1510, bcb, bcc)
new_ltEs18(vyy2130011, vyy1511, app(app(app(ty_@3, dh), ea), eb)) → new_ltEs4(vyy2130011, vyy1511, dh, ea, eb)
new_ltEs18(vyy2130011, vyy1511, ty_Char) → new_ltEs14(vyy2130011, vyy1511)
new_esEs22(vyy3002, vyy402, app(app(ty_@2, cfe), cff)) → new_esEs5(vyy3002, vyy402, cfe, cff)
new_esEs24(vyy3001, vyy401, app(app(ty_@2, dac), dad)) → new_esEs5(vyy3001, vyy401, dac, dad)
new_ltEs5(EQ, LT) → False
new_esEs27(vyy2130011, vyy1511, ty_Bool) → new_esEs10(vyy2130011, vyy1511)
new_ltEs8(vyy213001, vyy151) → new_not(new_esEs18(new_compare15(vyy213001, vyy151), GT))
new_esEs15(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs18(LT, GT) → False
new_esEs18(GT, LT) → False
new_esEs25(vyy213000, vyy150, ty_Double) → new_esEs14(vyy213000, vyy150)
new_esEs26(vyy2130010, vyy1510, app(ty_Maybe, fb)) → new_esEs4(vyy2130010, vyy1510, fb)
new_esEs22(vyy3002, vyy402, app(ty_[], cgd)) → new_esEs8(vyy3002, vyy402, cgd)
new_esEs27(vyy2130011, vyy1511, ty_Double) → new_esEs14(vyy2130011, vyy1511)
new_esEs22(vyy3002, vyy402, app(app(ty_Either, cge), cgf)) → new_esEs7(vyy3002, vyy402, cge, cgf)
new_esEs29(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_lt19(vyy213000, vyy150, ty_Float) → new_lt15(vyy213000, vyy150)
new_lt4(vyy213000, vyy150) → new_esEs18(new_compare8(vyy213000, vyy150), LT)
new_pePe(False, vyy177) → vyy177
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs12(vyy3000, vyy400)
new_esEs26(vyy2130010, vyy1510, ty_Bool) → new_esEs10(vyy2130010, vyy1510)
new_esEs27(vyy2130011, vyy1511, app(ty_[], he)) → new_esEs8(vyy2130011, vyy1511, he)
new_esEs7(Left(vyy3000), Right(vyy400), cba, bhf) → False
new_esEs7(Right(vyy3000), Left(vyy400), cba, bhf) → False
new_esEs27(vyy2130011, vyy1511, ty_Float) → new_esEs11(vyy2130011, vyy1511)
new_ltEs4(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), gf, fc, fd) → new_pePe(new_lt20(vyy2130010, vyy1510, gf), new_asAs(new_esEs26(vyy2130010, vyy1510, gf), new_pePe(new_lt21(vyy2130011, vyy1511, fc), new_asAs(new_esEs27(vyy2130011, vyy1511, fc), new_ltEs20(vyy2130012, vyy1512, fd)))))
new_esEs27(vyy2130011, vyy1511, app(app(ty_Either, hf), hg)) → new_esEs7(vyy2130011, vyy1511, hf, hg)
new_lt7(vyy2130010, vyy1510, ty_@0) → new_lt9(vyy2130010, vyy1510)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Float, bbc) → new_ltEs15(vyy2130010, vyy1510)
new_ltEs10(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), dd, cb) → new_pePe(new_lt7(vyy2130010, vyy1510, dd), new_asAs(new_esEs19(vyy2130010, vyy1510, dd), new_ltEs18(vyy2130011, vyy1511, cb)))
new_esEs26(vyy2130010, vyy1510, ty_@0) → new_esEs13(vyy2130010, vyy1510)
new_esEs7(Right(vyy3000), Right(vyy400), cba, app(ty_Ratio, cbh)) → new_esEs16(vyy3000, vyy400, cbh)
new_esEs9(vyy3000, vyy400, ty_Ordering) → new_esEs18(vyy3000, vyy400)
new_lt7(vyy2130010, vyy1510, app(ty_Ratio, bhd)) → new_lt5(vyy2130010, vyy1510, bhd)
new_lt7(vyy2130010, vyy1510, app(ty_Maybe, ca)) → new_lt10(vyy2130010, vyy1510, ca)
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, app(ty_[], bdc)) → new_ltEs13(vyy2130010, vyy1510, bdc)
new_compare23(vyy213000, vyy150, True, bdg, bdh, bea) → EQ
new_compare29(vyy213000, vyy150) → new_compare25(vyy213000, vyy150, new_esEs10(vyy213000, vyy150))
new_ltEs20(vyy2130012, vyy1512, app(ty_[], baf)) → new_ltEs13(vyy2130012, vyy1512, baf)
new_esEs11(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs12(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare15(@0, @0) → EQ
new_lt19(vyy213000, vyy150, app(ty_Maybe, ef)) → new_lt10(vyy213000, vyy150, ef)
new_ltEs18(vyy2130011, vyy1511, ty_Int) → new_ltEs16(vyy2130011, vyy1511)
new_esEs19(vyy2130010, vyy1510, app(app(ty_Either, db), dc)) → new_esEs7(vyy2130010, vyy1510, db, dc)
new_esEs9(vyy3000, vyy400, app(ty_Ratio, bge)) → new_esEs16(vyy3000, vyy400, bge)
new_esEs20(vyy3000, vyy400, app(app(ty_@2, cda), cdb)) → new_esEs5(vyy3000, vyy400, cda, cdb)
new_compare19(vyy213000, vyy150, True) → LT
new_ltEs6(Left(vyy2130010), Left(vyy1510), app(app(ty_@2, bbd), bbe), bbc) → new_ltEs10(vyy2130010, vyy1510, bbd, bbe)
new_esEs23(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_compare27(vyy213000, vyy150, False, ef) → new_compare110(vyy213000, vyy150, new_ltEs9(vyy213000, vyy150, ef), ef)
new_esEs7(Right(vyy3000), Right(vyy400), cba, app(app(ty_@2, cbb), cbc)) → new_esEs5(vyy3000, vyy400, cbb, cbc)
new_primCmpNat0(Zero, Succ(vyy15000)) → LT
new_esEs7(Left(vyy3000), Left(vyy400), ty_Int, bhf) → new_esEs12(vyy3000, vyy400)
new_ltEs9(Just(vyy2130010), Just(vyy1510), app(app(app(ty_@3, bc), bd), be)) → new_ltEs4(vyy2130010, vyy1510, bc, bd, be)
new_ltEs19(vyy213001, vyy151, ty_Float) → new_ltEs15(vyy213001, vyy151)
new_esEs20(vyy3000, vyy400, app(ty_[], cdh)) → new_esEs8(vyy3000, vyy400, cdh)
new_ltEs16(vyy213001, vyy151) → new_not(new_esEs18(new_compare7(vyy213001, vyy151), GT))
new_compare17(Float(vyy2130000, vyy2130001), Float(vyy1500, vyy1501)) → new_compare7(new_sr(vyy2130000, vyy1500), new_sr(vyy2130001, vyy1501))
new_esEs20(vyy3000, vyy400, ty_Ordering) → new_esEs18(vyy3000, vyy400)
new_esEs19(vyy2130010, vyy1510, app(ty_Maybe, ca)) → new_esEs4(vyy2130010, vyy1510, ca)
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_ltEs19(vyy213001, vyy151, app(app(app(ty_@3, gf), fc), fd)) → new_ltEs4(vyy213001, vyy151, gf, fc, fd)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs10(vyy3000, vyy400)
new_ltEs20(vyy2130012, vyy1512, app(ty_Maybe, hh)) → new_ltEs9(vyy2130012, vyy1512, hh)
new_esEs24(vyy3001, vyy401, app(app(ty_Either, dbc), dbd)) → new_esEs7(vyy3001, vyy401, dbc, dbd)
new_esEs20(vyy3000, vyy400, app(app(app(ty_@3, cdc), cdd), cde)) → new_esEs6(vyy3000, vyy400, cdc, cdd, cde)
new_compare12(:%(vyy2130000, vyy2130001), :%(vyy1500, vyy1501), ty_Integer) → new_compare8(new_sr0(vyy2130000, vyy1501), new_sr0(vyy1500, vyy2130001))
new_lt19(vyy213000, vyy150, app(app(ty_@2, eg), eh)) → new_lt11(vyy213000, vyy150, eg, eh)
new_lt6(vyy213000, vyy150) → new_esEs18(new_compare13(vyy213000, vyy150), LT)
new_pePe(True, vyy177) → True
new_primEqNat0(Zero, Zero) → True
new_esEs27(vyy2130011, vyy1511, ty_Ordering) → new_esEs18(vyy2130011, vyy1511)
new_compare26(vyy213000, vyy150, True) → EQ
new_esEs26(vyy2130010, vyy1510, ty_Char) → new_esEs17(vyy2130010, vyy1510)
new_esEs19(vyy2130010, vyy1510, ty_Bool) → new_esEs10(vyy2130010, vyy1510)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_@2, bhg), bhh), bhf) → new_esEs5(vyy3000, vyy400, bhg, bhh)
new_primMulNat0(Succ(vyy300000), Succ(vyy40000)) → new_primPlusNat1(new_primMulNat0(vyy300000, Succ(vyy40000)), vyy40000)
new_lt21(vyy2130011, vyy1511, ty_Int) → new_lt16(vyy2130011, vyy1511)
new_esEs19(vyy2130010, vyy1510, ty_Int) → new_esEs12(vyy2130010, vyy1510)
new_compare111(vyy159, vyy160, vyy161, vyy162, False, vyy164, dbf, dbg) → new_compare112(vyy159, vyy160, vyy161, vyy162, vyy164, dbf, dbg)
new_esEs7(Right(vyy3000), Right(vyy400), cba, ty_Ordering) → new_esEs18(vyy3000, vyy400)
new_esEs7(Right(vyy3000), Right(vyy400), cba, app(app(app(ty_@3, cbd), cbe), cbf)) → new_esEs6(vyy3000, vyy400, cbd, cbe, cbf)
new_sr(vyy3000, vyy400) → new_primMulInt(vyy3000, vyy400)
new_lt7(vyy2130010, vyy1510, ty_Int) → new_lt16(vyy2130010, vyy1510)
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, ty_Double) → new_ltEs7(vyy2130010, vyy1510)
new_compare7(vyy213000, vyy150) → new_primCmpInt(vyy213000, vyy150)
new_esEs26(vyy2130010, vyy1510, ty_Int) → new_esEs12(vyy2130010, vyy1510)
new_ltEs9(Just(vyy2130010), Just(vyy1510), app(ty_[], bf)) → new_ltEs13(vyy2130010, vyy1510, bf)
new_ltEs20(vyy2130012, vyy1512, app(app(ty_Either, bag), bah)) → new_ltEs6(vyy2130012, vyy1512, bag, bah)
new_esEs7(Right(vyy3000), Right(vyy400), cba, app(app(ty_Either, ccb), ccc)) → new_esEs7(vyy3000, vyy400, ccb, ccc)
new_esEs26(vyy2130010, vyy1510, app(app(app(ty_@3, fh), ga), gb)) → new_esEs6(vyy2130010, vyy1510, fh, ga, gb)
new_ltEs5(LT, LT) → True
new_esEs18(EQ, GT) → False
new_esEs18(GT, EQ) → False
new_esEs26(vyy2130010, vyy1510, ty_Float) → new_esEs11(vyy2130010, vyy1510)
new_ltEs19(vyy213001, vyy151, app(ty_Maybe, ccd)) → new_ltEs9(vyy213001, vyy151, ccd)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_compare32(vyy2130000, vyy1500, app(ty_Ratio, ddg)) → new_compare12(vyy2130000, vyy1500, ddg)
new_ltEs18(vyy2130011, vyy1511, ty_Double) → new_ltEs7(vyy2130011, vyy1511)
new_compare30(vyy213000, vyy150) → new_compare26(vyy213000, vyy150, new_esEs18(vyy213000, vyy150))
new_ltEs20(vyy2130012, vyy1512, ty_Int) → new_ltEs16(vyy2130012, vyy1512)
new_esEs29(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare25(vyy213000, vyy150, True) → EQ
new_ltEs20(vyy2130012, vyy1512, app(app(app(ty_@3, bac), bad), bae)) → new_ltEs4(vyy2130012, vyy1512, bac, bad, bae)
new_compare28(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, fa, bdf) → new_compare111(vyy213000, vyy213001, vyy150, vyy151, new_lt19(vyy213000, vyy150, fa), new_asAs(new_esEs25(vyy213000, vyy150, fa), new_ltEs19(vyy213001, vyy151, bdf)), fa, bdf)
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, ty_Ordering) → new_ltEs5(vyy2130010, vyy1510)
new_esEs7(Right(vyy3000), Right(vyy400), cba, ty_Char) → new_esEs17(vyy3000, vyy400)
new_ltEs20(vyy2130012, vyy1512, ty_Integer) → new_ltEs11(vyy2130012, vyy1512)
new_ltEs19(vyy213001, vyy151, app(app(ty_@2, dd), cb)) → new_ltEs10(vyy213001, vyy151, dd, cb)
new_esEs22(vyy3002, vyy402, app(app(app(ty_@3, cfg), cfh), cga)) → new_esEs6(vyy3002, vyy402, cfg, cfh, cga)
new_compare10(vyy213000, vyy150, False, bdg, bdh, bea) → GT
new_lt20(vyy2130010, vyy1510, ty_Char) → new_lt6(vyy2130010, vyy1510)
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Float) → new_ltEs15(vyy2130010, vyy1510)
new_ltEs17(True, False) → False
new_lt13(vyy213000, vyy150) → new_esEs18(new_compare30(vyy213000, vyy150), LT)
new_compare3([], :(vyy1500, vyy1501), beb) → LT
new_esEs21(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, ty_Char) → new_ltEs14(vyy2130010, vyy1510)
new_esEs9(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy3001, vyy401, ty_Bool) → new_esEs10(vyy3001, vyy401)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Integer, bhf) → new_esEs15(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, app(app(app(ty_@3, dae), daf), dag)) → new_esEs6(vyy3001, vyy401, dae, daf, dag)
new_compare3(:(vyy2130000, vyy2130001), [], beb) → GT
new_esEs27(vyy2130011, vyy1511, ty_Int) → new_esEs12(vyy2130011, vyy1511)
new_lt7(vyy2130010, vyy1510, ty_Double) → new_lt8(vyy2130010, vyy1510)
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, app(ty_Ratio, bhc)) → new_ltEs12(vyy2130010, vyy1510, bhc)
new_esEs8([], [], bff) → True
new_compare18(vyy213000, vyy150, False) → GT
new_esEs9(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_ltEs6(Left(vyy2130010), Left(vyy1510), app(ty_[], bca), bbc) → new_ltEs13(vyy2130010, vyy1510, bca)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs13(vyy3000, vyy400)
new_primPlusNat1(Zero, vyy40000) → Succ(vyy40000)
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, ty_Float) → new_ltEs15(vyy2130010, vyy1510)
new_compare9(vyy213000, vyy150, bec, bed) → new_compare24(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, bec, bed), bec, bed)
new_lt20(vyy2130010, vyy1510, ty_Ordering) → new_lt13(vyy2130010, vyy1510)
new_compare24(vyy213000, vyy150, True, bec, bed) → EQ
new_esEs10(False, False) → True
new_esEs22(vyy3002, vyy402, ty_Int) → new_esEs12(vyy3002, vyy402)
new_compare12(:%(vyy2130000, vyy2130001), :%(vyy1500, vyy1501), ty_Int) → new_compare7(new_sr(vyy2130000, vyy1501), new_sr(vyy1500, vyy2130001))
new_esEs26(vyy2130010, vyy1510, app(app(ty_Either, gd), ge)) → new_esEs7(vyy2130010, vyy1510, gd, ge)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs24(vyy3001, vyy401, ty_Ordering) → new_esEs18(vyy3001, vyy401)
new_ltEs19(vyy213001, vyy151, ty_Double) → new_ltEs7(vyy213001, vyy151)
new_ltEs18(vyy2130011, vyy1511, app(app(ty_@2, df), dg)) → new_ltEs10(vyy2130011, vyy1511, df, dg)
new_lt20(vyy2130010, vyy1510, ty_Double) → new_lt8(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, ty_@0) → new_ltEs8(vyy2130011, vyy1511)
new_primCmpNat0(Succ(vyy21300000), Succ(vyy15000)) → new_primCmpNat0(vyy21300000, vyy15000)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, ddd), dde)) → new_esEs7(vyy3000, vyy400, ddd, dde)
new_compare32(vyy2130000, vyy1500, ty_Int) → new_compare7(vyy2130000, vyy1500)
new_esEs22(vyy3002, vyy402, app(ty_Maybe, cgb)) → new_esEs4(vyy3002, vyy402, cgb)
new_ltEs5(EQ, EQ) → True
new_ltEs18(vyy2130011, vyy1511, app(app(ty_Either, ed), ee)) → new_ltEs6(vyy2130011, vyy1511, ed, ee)
new_esEs25(vyy213000, vyy150, app(ty_Maybe, ef)) → new_esEs4(vyy213000, vyy150, ef)
new_compare32(vyy2130000, vyy1500, ty_Float) → new_compare17(vyy2130000, vyy1500)
new_lt7(vyy2130010, vyy1510, app(app(ty_@2, cc), cd)) → new_lt11(vyy2130010, vyy1510, cc, cd)
new_lt21(vyy2130011, vyy1511, app(ty_Ratio, dca)) → new_lt5(vyy2130011, vyy1511, dca)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare14(vyy213000, vyy150, ef) → new_compare27(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, ef), ef)
new_lt14(vyy213000, vyy150, beb) → new_esEs18(new_compare3(vyy213000, vyy150, beb), LT)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, dcd), dce)) → new_esEs5(vyy3000, vyy400, dcd, dce)
new_esEs24(vyy3001, vyy401, app(ty_Ratio, dba)) → new_esEs16(vyy3001, vyy401, dba)
new_esEs9(vyy3000, vyy400, app(ty_[], bgf)) → new_esEs8(vyy3000, vyy400, bgf)
new_ltEs18(vyy2130011, vyy1511, app(ty_Maybe, de)) → new_ltEs9(vyy2130011, vyy1511, de)
new_esEs23(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs25(vyy213000, vyy150, app(ty_[], beb)) → new_esEs8(vyy213000, vyy150, beb)
new_esEs26(vyy2130010, vyy1510, ty_Integer) → new_esEs15(vyy2130010, vyy1510)
new_esEs7(Right(vyy3000), Right(vyy400), cba, ty_Float) → new_esEs11(vyy3000, vyy400)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_esEs23(vyy3000, vyy400, app(ty_[], chh)) → new_esEs8(vyy3000, vyy400, chh)
new_esEs19(vyy2130010, vyy1510, app(app(app(ty_@3, ce), cf), cg)) → new_esEs6(vyy2130010, vyy1510, ce, cf, cg)
new_lt21(vyy2130011, vyy1511, ty_Char) → new_lt6(vyy2130011, vyy1511)
new_esEs5(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cgg, cgh) → new_asAs(new_esEs23(vyy3000, vyy400, cgg), new_esEs24(vyy3001, vyy401, cgh))
new_esEs7(Left(vyy3000), Left(vyy400), ty_Ordering, bhf) → new_esEs18(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_compare6(Double(vyy2130000, vyy2130001), Double(vyy1500, vyy1501)) → new_compare7(new_sr(vyy2130000, vyy1500), new_sr(vyy2130001, vyy1501))
new_primCompAux00(vyy185, LT) → LT
new_primCmpInt(Neg(Succ(vyy21300000)), Neg(vyy1500)) → new_primCmpNat0(vyy1500, Succ(vyy21300000))
new_compare32(vyy2130000, vyy1500, ty_Bool) → new_compare29(vyy2130000, vyy1500)
new_ltEs6(Left(vyy2130010), Right(vyy1510), bcd, bbc) → True
new_esEs9(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_compare32(vyy2130000, vyy1500, ty_Char) → new_compare13(vyy2130000, vyy1500)
new_ltEs6(Right(vyy2130010), Left(vyy1510), bcd, bbc) → False
new_lt20(vyy2130010, vyy1510, app(ty_Ratio, dbh)) → new_lt5(vyy2130010, vyy1510, dbh)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], ddc)) → new_esEs8(vyy3000, vyy400, ddc)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Ordering, bbc) → new_ltEs5(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, ty_Integer) → new_ltEs11(vyy2130011, vyy1511)
new_lt7(vyy2130010, vyy1510, ty_Float) → new_lt15(vyy2130010, vyy1510)
new_primPlusNat0(Succ(vyy13100), Zero) → Succ(vyy13100)
new_primPlusNat0(Zero, Succ(vyy400000)) → Succ(vyy400000)
new_ltEs5(GT, LT) → False
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Bool) → new_ltEs17(vyy2130010, vyy1510)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Char) → new_ltEs14(vyy2130010, vyy1510)
new_primCmpNat0(Succ(vyy21300000), Zero) → GT
new_compare18(vyy213000, vyy150, True) → LT
new_esEs23(vyy3000, vyy400, app(app(ty_@2, cha), chb)) → new_esEs5(vyy3000, vyy400, cha, chb)
new_ltEs9(Just(vyy2130010), Just(vyy1510), app(ty_Maybe, h)) → new_ltEs9(vyy2130010, vyy1510, h)
new_ltEs20(vyy2130012, vyy1512, ty_Ordering) → new_ltEs5(vyy2130012, vyy1512)
new_esEs21(vyy3001, vyy401, ty_@0) → new_esEs13(vyy3001, vyy401)
new_esEs19(vyy2130010, vyy1510, ty_@0) → new_esEs13(vyy2130010, vyy1510)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy15000))) → LT
new_compare19(vyy213000, vyy150, False) → GT
new_compare11(vyy213000, vyy150, True, bec, bed) → LT
new_lt15(vyy213000, vyy150) → new_esEs18(new_compare17(vyy213000, vyy150), LT)
new_sr0(Integer(vyy15000), Integer(vyy21300010)) → Integer(new_primMulInt(vyy15000, vyy21300010))
new_lt7(vyy2130010, vyy1510, ty_Bool) → new_lt17(vyy2130010, vyy1510)
new_ltEs11(vyy213001, vyy151) → new_not(new_esEs18(new_compare8(vyy213001, vyy151), GT))
new_compare28(vyy21300, vyy15, True, fa, bdf) → EQ
new_lt21(vyy2130011, vyy1511, app(ty_Maybe, gg)) → new_lt10(vyy2130011, vyy1511, gg)
new_lt21(vyy2130011, vyy1511, app(app(ty_@2, gh), ha)) → new_lt11(vyy2130011, vyy1511, gh, ha)
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_esEs25(vyy213000, vyy150, ty_@0) → new_esEs13(vyy213000, vyy150)
new_esEs26(vyy2130010, vyy1510, app(ty_Ratio, dbh)) → new_esEs16(vyy2130010, vyy1510, dbh)
new_ltEs20(vyy2130012, vyy1512, ty_Float) → new_ltEs15(vyy2130012, vyy1512)
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, app(app(app(ty_@3, bch), bda), bdb)) → new_ltEs4(vyy2130010, vyy1510, bch, bda, bdb)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_esEs13(@0, @0) → True
new_esEs21(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_ltEs9(Just(vyy2130010), Nothing, ccd) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy15000))) → new_primCmpNat0(Zero, Succ(vyy15000))
new_primCompAux00(vyy185, EQ) → vyy185
new_lt5(vyy213000, vyy150, bha) → new_esEs18(new_compare12(vyy213000, vyy150, bha), LT)
new_esEs7(Right(vyy3000), Right(vyy400), cba, ty_@0) → new_esEs13(vyy3000, vyy400)
new_esEs7(Right(vyy3000), Right(vyy400), cba, app(ty_Maybe, cbg)) → new_esEs4(vyy3000, vyy400, cbg)
new_esEs20(vyy3000, vyy400, ty_Bool) → new_esEs10(vyy3000, vyy400)
new_esEs26(vyy2130010, vyy1510, ty_Ordering) → new_esEs18(vyy2130010, vyy1510)
new_esEs21(vyy3001, vyy401, ty_Ordering) → new_esEs18(vyy3001, vyy401)
new_esEs27(vyy2130011, vyy1511, app(ty_Ratio, dca)) → new_esEs16(vyy2130011, vyy1511, dca)
new_esEs26(vyy2130010, vyy1510, app(app(ty_@2, ff), fg)) → new_esEs5(vyy2130010, vyy1510, ff, fg)
new_compare32(vyy2130000, vyy1500, app(app(app(ty_@3, beh), bfa), bfb)) → new_compare31(vyy2130000, vyy1500, beh, bfa, bfb)
new_esEs25(vyy213000, vyy150, ty_Bool) → new_esEs10(vyy213000, vyy150)
new_lt21(vyy2130011, vyy1511, ty_Bool) → new_lt17(vyy2130011, vyy1511)
new_esEs21(vyy3001, vyy401, app(app(ty_@2, cec), ced)) → new_esEs5(vyy3001, vyy401, cec, ced)
new_esEs23(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_not(False) → True
new_esEs9(vyy3000, vyy400, ty_Bool) → new_esEs10(vyy3000, vyy400)
new_primCmpInt(Pos(Succ(vyy21300000)), Pos(vyy1500)) → new_primCmpNat0(Succ(vyy21300000), vyy1500)
new_compare110(vyy213000, vyy150, True, ef) → LT
new_esEs22(vyy3002, vyy402, ty_Float) → new_esEs11(vyy3002, vyy402)
new_ltEs9(Nothing, Nothing, ccd) → True
new_lt9(vyy213000, vyy150) → new_esEs18(new_compare15(vyy213000, vyy150), LT)
new_esEs19(vyy2130010, vyy1510, ty_Char) → new_esEs17(vyy2130010, vyy1510)
new_esEs25(vyy213000, vyy150, ty_Integer) → new_esEs15(vyy213000, vyy150)
new_ltEs12(vyy213001, vyy151, dbe) → new_not(new_esEs18(new_compare12(vyy213001, vyy151, dbe), GT))
new_ltEs14(vyy213001, vyy151) → new_not(new_esEs18(new_compare13(vyy213001, vyy151), GT))
new_esEs25(vyy213000, vyy150, app(ty_Ratio, bha)) → new_esEs16(vyy213000, vyy150, bha)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs18(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, app(ty_[], dbb)) → new_esEs8(vyy3001, vyy401, dbb)
new_compare24(vyy213000, vyy150, False, bec, bed) → new_compare11(vyy213000, vyy150, new_ltEs6(vyy213000, vyy150, bec, bed), bec, bed)
new_lt19(vyy213000, vyy150, app(app(app(ty_@3, bdg), bdh), bea)) → new_lt12(vyy213000, vyy150, bdg, bdh, bea)
new_lt8(vyy213000, vyy150) → new_esEs18(new_compare6(vyy213000, vyy150), LT)
new_lt19(vyy213000, vyy150, ty_Integer) → new_lt4(vyy213000, vyy150)
new_esEs18(GT, GT) → True
new_lt21(vyy2130011, vyy1511, ty_Double) → new_lt8(vyy2130011, vyy1511)
new_compare11(vyy213000, vyy150, False, bec, bed) → GT
new_ltEs6(Left(vyy2130010), Left(vyy1510), app(app(app(ty_@3, bbf), bbg), bbh), bbc) → new_ltEs4(vyy2130010, vyy1510, bbf, bbg, bbh)
new_lt19(vyy213000, vyy150, ty_Char) → new_lt6(vyy213000, vyy150)
new_primCmpInt(Pos(Succ(vyy21300000)), Neg(vyy1500)) → GT
new_esEs7(Left(vyy3000), Left(vyy400), ty_Bool, bhf) → new_esEs10(vyy3000, vyy400)
new_primMulInt(Pos(vyy30000), Pos(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, ty_@0) → new_ltEs8(vyy2130010, vyy1510)
new_ltEs6(Left(vyy2130010), Left(vyy1510), app(ty_Maybe, bbb), bbc) → new_ltEs9(vyy2130010, vyy1510, bbb)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Float, bhf) → new_esEs11(vyy3000, vyy400)
new_esEs27(vyy2130011, vyy1511, ty_Char) → new_esEs17(vyy2130011, vyy1511)
new_ltEs5(LT, GT) → True
new_esEs10(True, True) → True
new_esEs7(Right(vyy3000), Right(vyy400), cba, ty_Int) → new_esEs12(vyy3000, vyy400)
new_ltEs20(vyy2130012, vyy1512, ty_Bool) → new_ltEs17(vyy2130012, vyy1512)
new_lt7(vyy2130010, vyy1510, app(app(app(ty_@3, ce), cf), cg)) → new_lt12(vyy2130010, vyy1510, ce, cf, cg)
new_primMulInt(Neg(vyy30000), Neg(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_esEs20(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_lt20(vyy2130010, vyy1510, app(app(ty_Either, gd), ge)) → new_lt18(vyy2130010, vyy1510, gd, ge)
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Int) → new_ltEs16(vyy2130010, vyy1510)
new_esEs22(vyy3002, vyy402, ty_Ordering) → new_esEs18(vyy3002, vyy402)
new_lt20(vyy2130010, vyy1510, app(ty_Maybe, fb)) → new_lt10(vyy2130010, vyy1510, fb)
new_esEs22(vyy3002, vyy402, ty_Double) → new_esEs14(vyy3002, vyy402)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, dcc) → True
new_ltEs18(vyy2130011, vyy1511, ty_Bool) → new_ltEs17(vyy2130011, vyy1511)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Char, bhf) → new_esEs17(vyy3000, vyy400)
new_esEs25(vyy213000, vyy150, ty_Int) → new_esEs12(vyy213000, vyy150)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, ddb)) → new_esEs16(vyy3000, vyy400, ddb)
new_compare112(vyy159, vyy160, vyy161, vyy162, False, dbf, dbg) → GT
new_esEs27(vyy2130011, vyy1511, app(app(app(ty_@3, hb), hc), hd)) → new_esEs6(vyy2130011, vyy1511, hb, hc, hd)
new_lt19(vyy213000, vyy150, app(ty_Ratio, bha)) → new_lt5(vyy213000, vyy150, bha)
new_esEs27(vyy2130011, vyy1511, app(app(ty_@2, gh), ha)) → new_esEs5(vyy2130011, vyy1511, gh, ha)
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_[], caf), bhf) → new_esEs8(vyy3000, vyy400, caf)
new_esEs27(vyy2130011, vyy1511, app(ty_Maybe, gg)) → new_esEs4(vyy2130011, vyy1511, gg)
new_esEs21(vyy3001, vyy401, app(app(ty_Either, cfc), cfd)) → new_esEs7(vyy3001, vyy401, cfc, cfd)
new_ltEs9(Just(vyy2130010), Just(vyy1510), app(app(ty_@2, ba), bb)) → new_ltEs10(vyy2130010, vyy1510, ba, bb)
new_primPlusNat1(Succ(vyy1310), vyy40000) → Succ(Succ(new_primPlusNat0(vyy1310, vyy40000)))
new_esEs8(:(vyy3000, vyy3001), :(vyy400, vyy401), bff) → new_asAs(new_esEs9(vyy3000, vyy400, bff), new_esEs8(vyy3001, vyy401, bff))
new_lt21(vyy2130011, vyy1511, ty_Integer) → new_lt4(vyy2130011, vyy1511)
new_lt20(vyy2130010, vyy1510, ty_@0) → new_lt9(vyy2130010, vyy1510)
new_esEs21(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy15000))) → new_primCmpNat0(Succ(vyy15000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy15000))) → GT
new_ltEs6(Left(vyy2130010), Left(vyy1510), app(ty_Ratio, bhb), bbc) → new_ltEs12(vyy2130010, vyy1510, bhb)
new_compare13(Char(vyy2130000), Char(vyy1500)) → new_primCmpNat0(vyy2130000, vyy1500)
new_compare110(vyy213000, vyy150, False, ef) → GT
new_esEs12(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_lt21(vyy2130011, vyy1511, app(ty_[], he)) → new_lt14(vyy2130011, vyy1511, he)
new_ltEs19(vyy213001, vyy151, ty_Bool) → new_ltEs17(vyy213001, vyy151)
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Double) → new_ltEs7(vyy2130010, vyy1510)
new_esEs19(vyy2130010, vyy1510, ty_Double) → new_esEs14(vyy2130010, vyy1510)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Char, bbc) → new_ltEs14(vyy2130010, vyy1510)
new_ltEs19(vyy213001, vyy151, ty_Char) → new_ltEs14(vyy213001, vyy151)
new_esEs19(vyy2130010, vyy1510, ty_Float) → new_esEs11(vyy2130010, vyy1510)
new_ltEs19(vyy213001, vyy151, ty_Integer) → new_ltEs11(vyy213001, vyy151)
new_esEs9(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_esEs21(vyy3001, vyy401, app(ty_Maybe, ceh)) → new_esEs4(vyy3001, vyy401, ceh)
new_compare25(vyy213000, vyy150, False) → new_compare18(vyy213000, vyy150, new_ltEs17(vyy213000, vyy150))
new_esEs23(vyy3000, vyy400, app(ty_Ratio, chg)) → new_esEs16(vyy3000, vyy400, chg)
new_esEs20(vyy3000, vyy400, app(app(ty_Either, cea), ceb)) → new_esEs7(vyy3000, vyy400, cea, ceb)
new_esEs22(vyy3002, vyy402, app(ty_Ratio, cgc)) → new_esEs16(vyy3002, vyy402, cgc)
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, app(app(ty_Either, bdd), bde)) → new_ltEs6(vyy2130010, vyy1510, bdd, bde)
new_compare32(vyy2130000, vyy1500, app(app(ty_Either, bfd), bfe)) → new_compare9(vyy2130000, vyy1500, bfd, bfe)
new_esEs19(vyy2130010, vyy1510, app(app(ty_@2, cc), cd)) → new_esEs5(vyy2130010, vyy1510, cc, cd)
new_esEs9(vyy3000, vyy400, app(app(ty_@2, bfg), bfh)) → new_esEs5(vyy3000, vyy400, bfg, bfh)
new_esEs19(vyy2130010, vyy1510, app(ty_Ratio, bhd)) → new_esEs16(vyy2130010, vyy1510, bhd)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, ty_Bool) → new_ltEs17(vyy2130010, vyy1510)
new_lt19(vyy213000, vyy150, ty_Ordering) → new_lt13(vyy213000, vyy150)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs14(vyy3000, vyy400)
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, ty_Integer) → new_ltEs11(vyy2130010, vyy1510)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Bool, bbc) → new_ltEs17(vyy2130010, vyy1510)
new_asAs(False, vyy111) → False
new_esEs14(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs12(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare3([], [], beb) → EQ
new_primMulInt(Pos(vyy30000), Neg(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulInt(Neg(vyy30000), Pos(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulNat0(Zero, Succ(vyy40000)) → Zero
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_ltEs18(vyy2130011, vyy1511, ty_Ordering) → new_ltEs5(vyy2130011, vyy1511)
new_esEs7(Right(vyy3000), Right(vyy400), cba, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_compare111(vyy159, vyy160, vyy161, vyy162, True, vyy164, dbf, dbg) → new_compare112(vyy159, vyy160, vyy161, vyy162, True, dbf, dbg)
new_esEs23(vyy3000, vyy400, app(app(app(ty_@3, chc), chd), che)) → new_esEs6(vyy3000, vyy400, chc, chd, che)
new_ltEs5(LT, EQ) → True
new_lt20(vyy2130010, vyy1510, app(ty_[], gc)) → new_lt14(vyy2130010, vyy1510, gc)
new_esEs9(vyy3000, vyy400, app(ty_Maybe, bgd)) → new_esEs4(vyy3000, vyy400, bgd)
new_lt21(vyy2130011, vyy1511, ty_Ordering) → new_lt13(vyy2130011, vyy1511)
new_lt19(vyy213000, vyy150, ty_Double) → new_lt8(vyy213000, vyy150)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Int, bbc) → new_ltEs16(vyy2130010, vyy1510)
new_esEs24(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_esEs27(vyy2130011, vyy1511, ty_@0) → new_esEs13(vyy2130011, vyy1511)
new_compare16(vyy213000, vyy150, eg, eh) → new_compare28(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, eg, eh), eg, eh)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_ltEs15(vyy213001, vyy151) → new_not(new_esEs18(new_compare17(vyy213001, vyy151), GT))
new_ltEs17(True, True) → True
new_esEs21(vyy3001, vyy401, app(ty_[], cfb)) → new_esEs8(vyy3001, vyy401, cfb)
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, app(ty_Maybe, bce)) → new_ltEs9(vyy2130010, vyy1510, bce)
new_ltEs20(vyy2130012, vyy1512, app(ty_Ratio, dcb)) → new_ltEs12(vyy2130012, vyy1512, dcb)
new_esEs25(vyy213000, vyy150, app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs6(vyy213000, vyy150, bdg, bdh, bea)
new_lt11(vyy213000, vyy150, eg, eh) → new_esEs18(new_compare16(vyy213000, vyy150, eg, eh), LT)
new_ltEs7(vyy213001, vyy151) → new_not(new_esEs18(new_compare6(vyy213001, vyy151), GT))
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, ty_Bool) → new_esEs10(vyy3000, vyy400)
new_ltEs19(vyy213001, vyy151, ty_Int) → new_ltEs16(vyy213001, vyy151)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, caa), cab), cac), bhf) → new_esEs6(vyy3000, vyy400, caa, cab, cac)
new_lt19(vyy213000, vyy150, app(ty_[], beb)) → new_lt14(vyy213000, vyy150, beb)
new_esEs21(vyy3001, vyy401, app(ty_Ratio, cfa)) → new_esEs16(vyy3001, vyy401, cfa)
new_ltEs19(vyy213001, vyy151, ty_@0) → new_ltEs8(vyy213001, vyy151)
new_lt7(vyy2130010, vyy1510, ty_Char) → new_lt6(vyy2130010, vyy1510)
new_esEs19(vyy2130010, vyy1510, ty_Ordering) → new_esEs18(vyy2130010, vyy1510)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Double, bbc) → new_ltEs7(vyy2130010, vyy1510)
new_esEs25(vyy213000, vyy150, app(app(ty_@2, eg), eh)) → new_esEs5(vyy213000, vyy150, eg, eh)
new_esEs20(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_esEs6(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), ccf, ccg, cch) → new_asAs(new_esEs20(vyy3000, vyy400, ccf), new_asAs(new_esEs21(vyy3001, vyy401, ccg), new_esEs22(vyy3002, vyy402, cch)))
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Ratio, cae), bhf) → new_esEs16(vyy3000, vyy400, cae)
new_ltEs17(False, True) → True
new_lt10(vyy213000, vyy150, ef) → new_esEs18(new_compare14(vyy213000, vyy150, ef), LT)
new_lt7(vyy2130010, vyy1510, ty_Integer) → new_lt4(vyy2130010, vyy1510)
new_compare32(vyy2130000, vyy1500, app(ty_[], bfc)) → new_compare3(vyy2130000, vyy1500, bfc)
new_lt18(vyy213000, vyy150, bec, bed) → new_esEs18(new_compare9(vyy213000, vyy150, bec, bed), LT)
new_lt21(vyy2130011, vyy1511, app(app(ty_Either, hf), hg)) → new_lt18(vyy2130011, vyy1511, hf, hg)
new_lt12(vyy213000, vyy150, bdg, bdh, bea) → new_esEs18(new_compare31(vyy213000, vyy150, bdg, bdh, bea), LT)
new_compare27(vyy213000, vyy150, True, ef) → EQ
new_esEs21(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_@0, bbc) → new_ltEs8(vyy2130010, vyy1510)
new_esEs20(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy13100), Succ(vyy400000)) → Succ(Succ(new_primPlusNat0(vyy13100, vyy400000)))
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_esEs22(vyy3002, vyy402, ty_@0) → new_esEs13(vyy3002, vyy402)
new_esEs9(vyy3000, vyy400, app(app(app(ty_@3, bga), bgb), bgc)) → new_esEs6(vyy3000, vyy400, bga, bgb, bgc)
new_ltEs19(vyy213001, vyy151, ty_Ordering) → new_ltEs5(vyy213001, vyy151)
new_esEs22(vyy3002, vyy402, ty_Integer) → new_esEs15(vyy3002, vyy402)
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, app(app(ty_@2, bcf), bcg)) → new_ltEs10(vyy2130010, vyy1510, bcf, bcg)
new_esEs21(vyy3001, vyy401, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs6(vyy3001, vyy401, cee, cef, ceg)
new_esEs19(vyy2130010, vyy1510, ty_Integer) → new_esEs15(vyy2130010, vyy1510)
new_esEs7(Right(vyy3000), Right(vyy400), cba, app(ty_[], cca)) → new_esEs8(vyy3000, vyy400, cca)
new_lt20(vyy2130010, vyy1510, ty_Float) → new_lt15(vyy2130010, vyy1510)
new_asAs(True, vyy111) → vyy111
new_ltEs5(GT, GT) → True
new_esEs10(True, False) → False
new_esEs10(False, True) → False
new_esEs25(vyy213000, vyy150, ty_Float) → new_esEs11(vyy213000, vyy150)
new_lt20(vyy2130010, vyy1510, ty_Bool) → new_lt17(vyy2130010, vyy1510)
new_lt19(vyy213000, vyy150, ty_@0) → new_lt9(vyy213000, vyy150)
new_esEs19(vyy2130010, vyy1510, app(ty_[], da)) → new_esEs8(vyy2130010, vyy1510, da)
new_esEs9(vyy3000, vyy400, app(app(ty_Either, bgg), bgh)) → new_esEs7(vyy3000, vyy400, bgg, bgh)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs7(Left(vyy3000), Left(vyy400), ty_@0, bhf) → new_esEs13(vyy3000, vyy400)
new_compare32(vyy2130000, vyy1500, app(app(ty_@2, bef), beg)) → new_compare16(vyy2130000, vyy1500, bef, beg)
new_lt19(vyy213000, vyy150, ty_Int) → new_lt16(vyy213000, vyy150)
new_esEs21(vyy3001, vyy401, ty_Bool) → new_esEs10(vyy3001, vyy401)
new_lt16(vyy213000, vyy150) → new_esEs18(new_compare7(vyy213000, vyy150), LT)
new_esEs16(:%(vyy3000, vyy3001), :%(vyy400, vyy401), ddf) → new_asAs(new_esEs28(vyy3000, vyy400, ddf), new_esEs29(vyy3001, vyy401, ddf))
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_@0) → new_ltEs8(vyy2130010, vyy1510)
new_lt21(vyy2130011, vyy1511, app(app(app(ty_@3, hb), hc), hd)) → new_lt12(vyy2130011, vyy1511, hb, hc, hd)
new_primCompAux00(vyy185, GT) → GT
new_esEs25(vyy213000, vyy150, app(app(ty_Either, bec), bed)) → new_esEs7(vyy213000, vyy150, bec, bed)
new_compare32(vyy2130000, vyy1500, app(ty_Maybe, bee)) → new_compare14(vyy2130000, vyy1500, bee)
new_esEs7(Right(vyy3000), Right(vyy400), cba, ty_Bool) → new_esEs10(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs20(vyy3000, vyy400, ty_@0) → new_esEs13(vyy3000, vyy400)
new_ltEs9(Just(vyy2130010), Just(vyy1510), app(ty_Ratio, cce)) → new_ltEs12(vyy2130010, vyy1510, cce)
new_esEs8(:(vyy3000, vyy3001), [], bff) → False
new_esEs8([], :(vyy400, vyy401), bff) → False
new_ltEs5(GT, EQ) → False
new_ltEs20(vyy2130012, vyy1512, app(app(ty_@2, baa), bab)) → new_ltEs10(vyy2130012, vyy1512, baa, bab)
new_ltEs19(vyy213001, vyy151, app(app(ty_Either, bcd), bbc)) → new_ltEs6(vyy213001, vyy151, bcd, bbc)
new_ltEs19(vyy213001, vyy151, app(ty_[], bba)) → new_ltEs13(vyy213001, vyy151, bba)
new_lt7(vyy2130010, vyy1510, app(app(ty_Either, db), dc)) → new_lt18(vyy2130010, vyy1510, db, dc)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs27(vyy2130011, vyy1511, ty_Integer) → new_esEs15(vyy2130011, vyy1511)
new_esEs18(EQ, EQ) → True
new_primCmpInt(Neg(Succ(vyy21300000)), Pos(vyy1500)) → LT
new_esEs24(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_not(True) → False
new_ltEs6(Right(vyy2130010), Right(vyy1510), bcd, ty_Int) → new_ltEs16(vyy2130010, vyy1510)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Integer, bbc) → new_ltEs11(vyy2130010, vyy1510)

The set Q consists of the following terms:

new_esEs13(@0, @0)
new_esEs21(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(True, x0)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(LT, LT)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs23(x0, x1, ty_Bool)
new_compare15(@0, @0)
new_compare24(x0, x1, True, x2, x3)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt16(x0, x1)
new_ltEs15(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare18(x0, x1, True)
new_esEs26(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_lt7(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare111(x0, x1, x2, x3, True, x4, x5, x6)
new_compare13(Char(x0), Char(x1))
new_lt7(x0, x1, app(ty_[], x2))
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt18(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_@0)
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_esEs27(x0, x1, ty_Bool)
new_compare30(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_lt21(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, True)
new_esEs23(x0, x1, ty_Double)
new_lt12(x0, x1, x2, x3, x4)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Char(x0), Char(x1))
new_compare27(x0, x1, False, x2)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(EQ, GT)
new_esEs18(GT, EQ)
new_esEs22(x0, x1, ty_Char)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(x0, x1, x2)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primMulNat0(Zero, Succ(x0))
new_compare3(:(x0, x1), :(x2, x3), x4)
new_esEs27(x0, x1, ty_@0)
new_ltEs6(Left(x0), Left(x1), ty_Char, x2)
new_compare29(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, ty_Int)
new_esEs18(EQ, EQ)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt21(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt11(x0, x1, x2, x3)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Int)
new_compare23(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs17(False, False)
new_esEs23(x0, x1, ty_Int)
new_ltEs5(LT, EQ)
new_ltEs5(EQ, LT)
new_compare28(x0, x1, True, x2, x3)
new_lt19(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Char)
new_primEqNat0(Zero, Zero)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt21(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, False, x2, x3, x4)
new_compare11(x0, x1, True, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(x0, x1, ty_@0)
new_compare3([], [], x0)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Nothing, x1)
new_esEs22(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs10(True, False)
new_esEs10(False, True)
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare18(x0, x1, False)
new_compare28(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_esEs26(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare26(x0, x1, True)
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Float)
new_ltEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare111(x0, x1, x2, x3, False, x4, x5, x6)
new_esEs25(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_ltEs14(x0, x1)
new_esEs25(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Bool)
new_ltEs17(True, True)
new_sr0(Integer(x0), Integer(x1))
new_ltEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt13(x0, x1)
new_compare3(:(x0, x1), [], x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_pePe(True, x0)
new_compare7(x0, x1)
new_esEs19(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Ordering)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare3([], :(x0, x1), x2)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_Double)
new_esEs9(x0, x1, ty_@0)
new_primPlusNat1(Zero, x0)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2, x3)
new_esEs9(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(x0, x1, ty_Integer)
new_compare12(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs20(x0, x1, ty_Ordering)
new_compare16(x0, x1, x2, x3)
new_lt7(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_ltEs18(x0, x1, ty_Int)
new_primPlusNat0(Zero, Zero)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs10(True, True)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Ordering)
new_ltEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_compare32(x0, x1, ty_Bool)
new_lt9(x0, x1)
new_compare6(Double(x0, x1), Double(x2, x3))
new_compare32(x0, x1, app(ty_Ratio, x2))
new_esEs18(GT, GT)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare32(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_ltEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs4(Nothing, Nothing, x0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt21(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Char)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Float)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs21(x0, x1, ty_Ordering)
new_compare19(x0, x1, False)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_compare32(x0, x1, ty_@0)
new_ltEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs8(x0, x1)
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare11(x0, x1, False, x2, x3)
new_esEs8(:(x0, x1), [], x2)
new_esEs12(x0, x1)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_asAs(False, x0)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare32(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_primPlusNat1(Succ(x0), x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs9(Nothing, Nothing, x0)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs23(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_@0)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs24(x0, x1, ty_@0)
new_compare10(x0, x1, True, x2, x3, x4)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs9(Nothing, Just(x0), x1)
new_esEs28(x0, x1, ty_Integer)
new_ltEs11(x0, x1)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare8(Integer(x0), Integer(x1))
new_ltEs18(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_lt7(x0, x1, ty_Char)
new_compare12(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt5(x0, x1, x2)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Double)
new_ltEs16(x0, x1)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_esEs20(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Int)
new_compare10(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, ty_Float)
new_ltEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_compare112(x0, x1, x2, x3, True, x4, x5)
new_ltEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Double)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Integer)
new_primCompAux00(x0, GT)
new_ltEs19(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_esEs4(Nothing, Just(x0), x1)
new_compare32(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare26(x0, x1, False)
new_esEs22(x0, x1, ty_Int)
new_esEs10(False, False)
new_esEs29(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_compare17(Float(x0, x1), Float(x2, x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Char)
new_ltEs19(x0, x1, ty_Double)
new_esEs8([], :(x0, x1), x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_compare25(x0, x1, True)
new_esEs8(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs9(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs18(LT, EQ)
new_esEs18(EQ, LT)
new_esEs21(x0, x1, ty_Float)
new_lt14(x0, x1, x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs5(GT, GT)
new_ltEs6(Left(x0), Left(x1), ty_Double, x2)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Int)
new_lt7(x0, x1, ty_Int)
new_ltEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primPlusNat0(Zero, Succ(x0))
new_compare32(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Int)
new_compare9(x0, x1, x2, x3)
new_lt4(x0, x1)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_esEs25(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Integer)
new_esEs15(Integer(x0), Integer(x1))
new_not(True)
new_esEs21(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Double)
new_ltEs6(Left(x0), Right(x1), x2, x3)
new_ltEs6(Right(x0), Left(x1), x2, x3)
new_esEs20(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Just(x0), Nothing, x1)
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt21(x0, x1, ty_Integer)
new_not(False)
new_esEs24(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs17(False, True)
new_ltEs17(True, False)
new_lt8(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCompAux00(x0, LT)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(EQ, EQ)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare14(x0, x1, x2)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare32(x0, x1, app(ty_[], x2))
new_sr(x0, x1)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_Ordering)
new_primMulNat0(Succ(x0), Zero)
new_compare32(x0, x1, ty_Int)
new_ltEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare32(x0, x1, ty_Integer)
new_esEs18(GT, LT)
new_esEs18(LT, GT)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primCompAux00(x0, EQ)
new_lt15(x0, x1)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_primPlusNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_compare25(x0, x1, False)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqNat0(Succ(x0), Zero)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs9(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_lt7(x0, x1, ty_Double)
new_compare27(x0, x1, True, x2)
new_esEs25(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Float)
new_pePe(False, x0)
new_lt21(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Float)
new_ltEs18(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs19(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Bool)
new_esEs8([], [], x0)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt21(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs9(x0, x1, ty_Float)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Bool)
new_lt7(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs18(x0, x1, ty_Double)
new_compare112(x0, x1, x2, x3, False, x4, x5)
new_ltEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs5(LT, LT)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs20(x0, x1, ty_@0)
new_compare31(x0, x1, x2, x3, x4)
new_ltEs13(x0, x1, 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_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_GE1(vyy113, vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, h, ba, bb) → new_foldFM_GE10(vyy113, vyy15, vyy16, vyy2130, vyy2131, vyy2132, vyy2133, vyy2134, new_esEs18(new_compare28(vyy2130, @2(vyy15, vyy16), new_esEs5(vyy2130, @2(vyy15, vyy16), h, ba), h, ba), 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_GE1(new_fmToList_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_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_esEs4(Just(vyy3000), Just(vyy400), app(ty_Maybe, dcc)) → new_esEs4(vyy3000, vyy400, dcc)
new_esEs26(vyy2130010, vyy1510, app(ty_[], cgf)) → new_esEs8(vyy2130010, vyy1510, cgf)
new_esEs23(vyy3000, vyy400, app(app(ty_Either, cdc), cdd)) → new_esEs7(vyy3000, vyy400, cdc, cdd)
new_esEs23(vyy3000, vyy400, ty_Ordering) → new_esEs18(vyy3000, vyy400)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_Either, bce), bcf), bbd) → new_esEs7(vyy3000, vyy400, bce, bcf)
new_compare3(:(vyy2130000, vyy2130001), :(vyy1500, vyy1501), bfe) → new_primCompAux0(vyy2130000, vyy1500, new_compare3(vyy2130001, vyy1501, bfe), bfe)
new_lt20(vyy2130010, vyy1510, ty_Int) → new_lt16(vyy2130010, vyy1510)
new_lt20(vyy2130010, vyy1510, app(app(app(ty_@3, cgb), cgc), cgd)) → new_lt12(vyy2130010, vyy1510, cgb, cgc, cgd)
new_ltEs17(False, False) → True
new_compare10(vyy213000, vyy150, True, bc, bd, be) → LT
new_esEs18(LT, LT) → True
new_compare8(Integer(vyy2130000), Integer(vyy1500)) → new_primCmpInt(vyy2130000, vyy1500)
new_compare32(vyy2130000, vyy1500, ty_@0) → new_compare15(vyy2130000, vyy1500)
new_esEs25(vyy213000, vyy150, ty_Ordering) → new_esEs18(vyy213000, vyy150)
new_lt7(vyy2130010, vyy1510, app(ty_[], he)) → new_lt14(vyy2130010, vyy1510, he)
new_esEs17(Char(vyy3000), Char(vyy400)) → new_primEqNat0(vyy3000, vyy400)
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Maybe, bcb), bbd) → new_esEs4(vyy3000, vyy400, bcb)
new_esEs24(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
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_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Ordering) → new_ltEs5(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, ty_Float) → new_ltEs15(vyy2130011, vyy1511)
new_esEs9(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs26(vyy2130010, vyy1510, ty_Double) → new_esEs14(vyy2130010, vyy1510)
new_esEs9(vyy3000, vyy400, ty_@0) → new_esEs13(vyy3000, vyy400)
new_compare23(vyy213000, vyy150, False, bc, bd, be) → new_compare10(vyy213000, vyy150, new_ltEs4(vyy213000, vyy150, bc, bd, be), bc, bd, be)
new_esEs24(vyy3001, vyy401, app(ty_Maybe, ceb)) → new_esEs4(vyy3001, vyy401, ceb)
new_esEs18(LT, EQ) → False
new_esEs18(EQ, LT) → False
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Integer) → new_ltEs11(vyy2130010, vyy1510)
new_esEs4(Nothing, Just(vyy400), dbe) → False
new_esEs4(Just(vyy3000), Nothing, dbe) → False
new_lt19(vyy213000, vyy150, app(app(ty_Either, db), dc)) → new_lt18(vyy213000, vyy150, db, dc)
new_ltEs5(EQ, GT) → True
new_ltEs20(vyy2130012, vyy1512, ty_@0) → new_ltEs8(vyy2130012, vyy1512)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Char) → new_esEs17(vyy3000, vyy400)
new_ltEs9(Nothing, Just(vyy1510), beb) → True
new_compare31(vyy213000, vyy150, bc, bd, be) → new_compare23(vyy213000, vyy150, new_esEs6(vyy213000, vyy150, bc, bd, be), bc, bd, be)
new_esEs25(vyy213000, vyy150, ty_Char) → new_esEs17(vyy213000, vyy150)
new_ltEs18(vyy2130011, vyy1511, app(ty_Ratio, baf)) → new_ltEs12(vyy2130011, vyy1511, baf)
new_ltEs20(vyy2130012, vyy1512, ty_Double) → new_ltEs7(vyy2130012, vyy1512)
new_ltEs19(vyy213001, vyy151, app(ty_Ratio, cfd)) → new_ltEs12(vyy213001, vyy151, cfd)
new_fmToList_GE0(vyy210, vyy211, vyy112, h, ba, bb) → :(@2(vyy210, vyy211), vyy112)
new_compare32(vyy2130000, vyy1500, ty_Double) → new_compare6(vyy2130000, vyy1500)
new_compare112(vyy159, vyy160, vyy161, vyy162, True, cfe, cff) → LT
new_compare32(vyy2130000, vyy1500, ty_Integer) → new_compare8(vyy2130000, vyy1500)
new_esEs21(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_primMulNat0(Zero, Zero) → Zero
new_esEs24(vyy3001, vyy401, ty_@0) → new_esEs13(vyy3001, vyy401)
new_esEs7(Right(vyy3000), Right(vyy400), bcg, ty_Double) → new_esEs14(vyy3000, vyy400)
new_primCompAux0(vyy2130000, vyy1500, vyy178, bfe) → new_primCompAux00(vyy178, new_compare32(vyy2130000, vyy1500, bfe))
new_esEs4(Just(vyy3000), Just(vyy400), app(app(app(ty_@3, dbh), dca), dcb)) → new_esEs6(vyy3000, vyy400, dbh, dca, dcb)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Double, bbd) → new_esEs14(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, app(ty_Ratio, bha)) → new_esEs16(vyy3000, vyy400, bha)
new_esEs20(vyy3000, vyy400, app(ty_Maybe, bgh)) → new_esEs4(vyy3000, vyy400, bgh)
new_lt20(vyy2130010, vyy1510, ty_Integer) → new_lt4(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, app(ty_[], bag)) → new_ltEs13(vyy2130011, vyy1511, bag)
new_compare26(vyy213000, vyy150, False) → new_compare19(vyy213000, vyy150, new_ltEs5(vyy213000, vyy150))
new_ltEs13(vyy213001, vyy151, bbc) → new_not(new_esEs18(new_compare3(vyy213001, vyy151, bbc), GT))
new_lt21(vyy2130011, vyy1511, ty_Float) → new_lt15(vyy2130011, vyy1511)
new_esEs22(vyy3002, vyy402, ty_Char) → new_esEs17(vyy3002, vyy402)
new_esEs24(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_lt17(vyy213000, vyy150) → new_esEs18(new_compare29(vyy213000, vyy150), LT)
new_lt21(vyy2130011, vyy1511, ty_@0) → new_lt9(vyy2130011, vyy1511)
new_ltEs20(vyy2130012, vyy1512, ty_Char) → new_ltEs14(vyy2130012, vyy1512)
new_lt20(vyy2130010, vyy1510, app(app(ty_@2, cfh), cga)) → new_lt11(vyy2130010, vyy1510, cfh, cga)
new_compare32(vyy2130000, vyy1500, ty_Ordering) → new_compare30(vyy2130000, vyy1500)
new_esEs23(vyy3000, vyy400, app(ty_Maybe, cch)) → new_esEs4(vyy3000, vyy400, cch)
new_ltEs9(Just(vyy2130010), Just(vyy1510), app(app(ty_Either, bfc), bfd)) → new_ltEs6(vyy2130010, vyy1510, bfc, bfd)
new_esEs20(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, ty_@0) → new_esEs13(vyy3000, vyy400)
new_esEs22(vyy3002, vyy402, ty_Bool) → new_esEs10(vyy3002, vyy402)
new_lt7(vyy2130010, vyy1510, ty_Ordering) → new_lt13(vyy2130010, vyy1510)
new_lt19(vyy213000, vyy150, ty_Bool) → new_lt17(vyy213000, vyy150)
new_ltEs6(Left(vyy2130010), Left(vyy1510), app(app(ty_Either, ef), eg), de) → new_ltEs6(vyy2130010, vyy1510, ef, eg)
new_ltEs18(vyy2130011, vyy1511, app(app(app(ty_@3, bac), bad), bae)) → new_ltEs4(vyy2130011, vyy1511, bac, bad, bae)
new_ltEs18(vyy2130011, vyy1511, ty_Char) → new_ltEs14(vyy2130011, vyy1511)
new_esEs22(vyy3002, vyy402, app(app(ty_@2, cag), cah)) → new_esEs5(vyy3002, vyy402, cag, cah)
new_esEs24(vyy3001, vyy401, app(app(ty_@2, cde), cdf)) → new_esEs5(vyy3001, vyy401, cde, cdf)
new_ltEs5(EQ, LT) → False
new_esEs27(vyy2130011, vyy1511, ty_Bool) → new_esEs10(vyy2130011, vyy1511)
new_ltEs8(vyy213001, vyy151) → new_not(new_esEs18(new_compare15(vyy213001, vyy151), GT))
new_esEs15(Integer(vyy3000), Integer(vyy400)) → new_primEqInt(vyy3000, vyy400)
new_esEs18(LT, GT) → False
new_esEs18(GT, LT) → False
new_esEs25(vyy213000, vyy150, ty_Double) → new_esEs14(vyy213000, vyy150)
new_esEs26(vyy2130010, vyy1510, app(ty_Maybe, cfg)) → new_esEs4(vyy2130010, vyy1510, cfg)
new_esEs22(vyy3002, vyy402, app(ty_[], cbf)) → new_esEs8(vyy3002, vyy402, cbf)
new_esEs27(vyy2130011, vyy1511, ty_Double) → new_esEs14(vyy2130011, vyy1511)
new_esEs22(vyy3002, vyy402, app(app(ty_Either, cbg), cbh)) → new_esEs7(vyy3002, vyy402, cbg, cbh)
new_esEs29(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_lt19(vyy213000, vyy150, ty_Float) → new_lt15(vyy213000, vyy150)
new_lt4(vyy213000, vyy150) → new_esEs18(new_compare8(vyy213000, vyy150), LT)
new_pePe(False, vyy177) → vyy177
new_esEs4(Just(vyy3000), Just(vyy400), ty_Int) → new_esEs12(vyy3000, vyy400)
new_esEs26(vyy2130010, vyy1510, ty_Bool) → new_esEs10(vyy2130010, vyy1510)
new_esEs27(vyy2130011, vyy1511, app(ty_[], chh)) → new_esEs8(vyy2130011, vyy1511, chh)
new_esEs7(Left(vyy3000), Right(vyy400), bcg, bbd) → False
new_esEs7(Right(vyy3000), Left(vyy400), bcg, bbd) → False
new_esEs27(vyy2130011, vyy1511, ty_Float) → new_esEs11(vyy2130011, vyy1511)
new_ltEs4(@3(vyy2130010, vyy2130011, vyy2130012), @3(vyy1510, vyy1511, vyy1512), cfa, cfb, cfc) → new_pePe(new_lt20(vyy2130010, vyy1510, cfa), new_asAs(new_esEs26(vyy2130010, vyy1510, cfa), new_pePe(new_lt21(vyy2130011, vyy1511, cfb), new_asAs(new_esEs27(vyy2130011, vyy1511, cfb), new_ltEs20(vyy2130012, vyy1512, cfc)))))
new_esEs27(vyy2130011, vyy1511, app(app(ty_Either, daa), dab)) → new_esEs7(vyy2130011, vyy1511, daa, dab)
new_lt7(vyy2130010, vyy1510, ty_@0) → new_lt9(vyy2130010, vyy1510)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Float, de) → new_ltEs15(vyy2130010, vyy1510)
new_ltEs10(@2(vyy2130010, vyy2130011), @2(vyy1510, vyy1511), gd, ge) → new_pePe(new_lt7(vyy2130010, vyy1510, gd), new_asAs(new_esEs19(vyy2130010, vyy1510, gd), new_ltEs18(vyy2130011, vyy1511, ge)))
new_esEs26(vyy2130010, vyy1510, ty_@0) → new_esEs13(vyy2130010, vyy1510)
new_esEs7(Right(vyy3000), Right(vyy400), bcg, app(ty_Ratio, bdf)) → new_esEs16(vyy3000, vyy400, bdf)
new_esEs9(vyy3000, vyy400, ty_Ordering) → new_esEs18(vyy3000, vyy400)
new_lt7(vyy2130010, vyy1510, app(ty_Ratio, hd)) → new_lt5(vyy2130010, vyy1510, hd)
new_lt7(vyy2130010, vyy1510, app(ty_Maybe, gf)) → new_lt10(vyy2130010, vyy1510, gf)
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, app(ty_[], ga)) → new_ltEs13(vyy2130010, vyy1510, ga)
new_compare23(vyy213000, vyy150, True, bc, bd, be) → EQ
new_compare29(vyy213000, vyy150) → new_compare25(vyy213000, vyy150, new_esEs10(vyy213000, vyy150))
new_ltEs20(vyy2130012, vyy1512, app(ty_[], dbb)) → new_ltEs13(vyy2130012, vyy1512, dbb)
new_esEs11(Float(vyy3000, vyy3001), Float(vyy400, vyy401)) → new_esEs12(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare15(@0, @0) → EQ
new_lt19(vyy213000, vyy150, app(ty_Maybe, bbb)) → new_lt10(vyy213000, vyy150, bbb)
new_ltEs18(vyy2130011, vyy1511, ty_Int) → new_ltEs16(vyy2130011, vyy1511)
new_esEs19(vyy2130010, vyy1510, app(app(ty_Either, hf), hg)) → new_esEs7(vyy2130010, vyy1510, hf, hg)
new_esEs9(vyy3000, vyy400, app(ty_Ratio, ce)) → new_esEs16(vyy3000, vyy400, ce)
new_esEs20(vyy3000, vyy400, app(app(ty_@2, bgc), bgd)) → new_esEs5(vyy3000, vyy400, bgc, bgd)
new_compare19(vyy213000, vyy150, True) → LT
new_ltEs6(Left(vyy2130010), Left(vyy1510), app(app(ty_@2, dg), dh), de) → new_ltEs10(vyy2130010, vyy1510, dg, dh)
new_esEs23(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_compare27(vyy213000, vyy150, False, bbb) → new_compare110(vyy213000, vyy150, new_ltEs9(vyy213000, vyy150, bbb), bbb)
new_esEs7(Right(vyy3000), Right(vyy400), bcg, app(app(ty_@2, bch), bda)) → new_esEs5(vyy3000, vyy400, bch, bda)
new_primCmpNat0(Zero, Succ(vyy15000)) → LT
new_esEs7(Left(vyy3000), Left(vyy400), ty_Int, bbd) → new_esEs12(vyy3000, vyy400)
new_ltEs9(Just(vyy2130010), Just(vyy1510), app(app(app(ty_@3, bef), beg), beh)) → new_ltEs4(vyy2130010, vyy1510, bef, beg, beh)
new_ltEs19(vyy213001, vyy151, ty_Float) → new_ltEs15(vyy213001, vyy151)
new_esEs20(vyy3000, vyy400, app(ty_[], bhb)) → new_esEs8(vyy3000, vyy400, bhb)
new_ltEs16(vyy213001, vyy151) → new_not(new_esEs18(new_compare7(vyy213001, vyy151), GT))
new_compare17(Float(vyy2130000, vyy2130001), Float(vyy1500, vyy1501)) → new_compare7(new_sr(vyy2130000, vyy1500), new_sr(vyy2130001, vyy1501))
new_esEs20(vyy3000, vyy400, ty_Ordering) → new_esEs18(vyy3000, vyy400)
new_esEs19(vyy2130010, vyy1510, app(ty_Maybe, gf)) → new_esEs4(vyy2130010, vyy1510, gf)
new_foldFM_GE0(vyy61, vyy15, vyy16, EmptyFM, h, ba, bb) → vyy61
new_esEs24(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_ltEs19(vyy213001, vyy151, app(app(app(ty_@3, cfa), cfb), cfc)) → new_ltEs4(vyy213001, vyy151, cfa, cfb, cfc)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Float) → new_esEs11(vyy3000, vyy400)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Bool) → new_esEs10(vyy3000, vyy400)
new_ltEs20(vyy2130012, vyy1512, app(ty_Maybe, dac)) → new_ltEs9(vyy2130012, vyy1512, dac)
new_esEs24(vyy3001, vyy401, app(app(ty_Either, cee), cef)) → new_esEs7(vyy3001, vyy401, cee, cef)
new_esEs20(vyy3000, vyy400, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs6(vyy3000, vyy400, bge, bgf, bgg)
new_compare12(:%(vyy2130000, vyy2130001), :%(vyy1500, vyy1501), ty_Integer) → new_compare8(new_sr0(vyy2130000, vyy1501), new_sr0(vyy1500, vyy2130001))
new_lt19(vyy213000, vyy150, app(app(ty_@2, bff), bfg)) → new_lt11(vyy213000, vyy150, bff, bfg)
new_lt6(vyy213000, vyy150) → new_esEs18(new_compare13(vyy213000, vyy150), LT)
new_pePe(True, vyy177) → True
new_primEqNat0(Zero, Zero) → True
new_esEs27(vyy2130011, vyy1511, ty_Ordering) → new_esEs18(vyy2130011, vyy1511)
new_compare26(vyy213000, vyy150, True) → EQ
new_esEs26(vyy2130010, vyy1510, ty_Char) → new_esEs17(vyy2130010, vyy1510)
new_esEs19(vyy2130010, vyy1510, ty_Bool) → new_esEs10(vyy2130010, vyy1510)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(ty_@2, bbe), bbf), bbd) → new_esEs5(vyy3000, vyy400, bbe, bbf)
new_primMulNat0(Succ(vyy300000), Succ(vyy40000)) → new_primPlusNat1(new_primMulNat0(vyy300000, Succ(vyy40000)), vyy40000)
new_lt21(vyy2130011, vyy1511, ty_Int) → new_lt16(vyy2130011, vyy1511)
new_esEs19(vyy2130010, vyy1510, ty_Int) → new_esEs12(vyy2130010, vyy1510)
new_compare111(vyy159, vyy160, vyy161, vyy162, False, vyy164, cfe, cff) → new_compare112(vyy159, vyy160, vyy161, vyy162, vyy164, cfe, cff)
new_esEs7(Right(vyy3000), Right(vyy400), bcg, ty_Ordering) → new_esEs18(vyy3000, vyy400)
new_esEs7(Right(vyy3000), Right(vyy400), bcg, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs6(vyy3000, vyy400, bdb, bdc, bdd)
new_sr(vyy3000, vyy400) → new_primMulInt(vyy3000, vyy400)
new_lt7(vyy2130010, vyy1510, ty_Int) → new_lt16(vyy2130010, vyy1510)
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, ty_Double) → new_ltEs7(vyy2130010, vyy1510)
new_compare7(vyy213000, vyy150) → new_primCmpInt(vyy213000, vyy150)
new_esEs26(vyy2130010, vyy1510, ty_Int) → new_esEs12(vyy2130010, vyy1510)
new_ltEs9(Just(vyy2130010), Just(vyy1510), app(ty_[], bfb)) → new_ltEs13(vyy2130010, vyy1510, bfb)
new_ltEs20(vyy2130012, vyy1512, app(app(ty_Either, dbc), dbd)) → new_ltEs6(vyy2130012, vyy1512, dbc, dbd)
new_esEs7(Right(vyy3000), Right(vyy400), bcg, app(app(ty_Either, bdh), bea)) → new_esEs7(vyy3000, vyy400, bdh, bea)
new_esEs26(vyy2130010, vyy1510, app(app(app(ty_@3, cgb), cgc), cgd)) → new_esEs6(vyy2130010, vyy1510, cgb, cgc, cgd)
new_ltEs5(LT, LT) → True
new_esEs18(EQ, GT) → False
new_esEs18(GT, EQ) → False
new_esEs26(vyy2130010, vyy1510, ty_Float) → new_esEs11(vyy2130010, vyy1510)
new_ltEs19(vyy213001, vyy151, app(ty_Maybe, beb)) → new_ltEs9(vyy213001, vyy151, beb)
new_esEs23(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_compare32(vyy2130000, vyy1500, app(ty_Ratio, ddg)) → new_compare12(vyy2130000, vyy1500, ddg)
new_ltEs18(vyy2130011, vyy1511, ty_Double) → new_ltEs7(vyy2130011, vyy1511)
new_compare30(vyy213000, vyy150) → new_compare26(vyy213000, vyy150, new_esEs18(vyy213000, vyy150))
new_ltEs20(vyy2130012, vyy1512, ty_Int) → new_ltEs16(vyy2130012, vyy1512)
new_esEs29(vyy3001, vyy401, ty_Int) → new_esEs12(vyy3001, vyy401)
new_primEqInt(Neg(Succ(vyy30000)), Neg(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare25(vyy213000, vyy150, True) → EQ
new_ltEs20(vyy2130012, vyy1512, app(app(app(ty_@3, daf), dag), dah)) → new_ltEs4(vyy2130012, vyy1512, daf, dag, dah)
new_compare28(@2(vyy213000, vyy213001), @2(vyy150, vyy151), False, ceg, ceh) → new_compare111(vyy213000, vyy213001, vyy150, vyy151, new_lt19(vyy213000, vyy150, ceg), new_asAs(new_esEs25(vyy213000, vyy150, ceg), new_ltEs19(vyy213001, vyy151, ceh)), ceg, ceh)
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, ty_Ordering) → new_ltEs5(vyy2130010, vyy1510)
new_esEs7(Right(vyy3000), Right(vyy400), bcg, ty_Char) → new_esEs17(vyy3000, vyy400)
new_ltEs20(vyy2130012, vyy1512, ty_Integer) → new_ltEs11(vyy2130012, vyy1512)
new_ltEs19(vyy213001, vyy151, app(app(ty_@2, gd), ge)) → new_ltEs10(vyy213001, vyy151, gd, ge)
new_esEs22(vyy3002, vyy402, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs6(vyy3002, vyy402, cba, cbb, cbc)
new_compare10(vyy213000, vyy150, False, bc, bd, be) → GT
new_lt20(vyy2130010, vyy1510, ty_Char) → new_lt6(vyy2130010, vyy1510)
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Float) → new_ltEs15(vyy2130010, vyy1510)
new_ltEs17(True, False) → False
new_lt13(vyy213000, vyy150) → new_esEs18(new_compare30(vyy213000, vyy150), LT)
new_compare3([], :(vyy1500, vyy1501), bfe) → LT
new_esEs21(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, ty_Char) → new_ltEs14(vyy2130010, vyy1510)
new_esEs9(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs24(vyy3001, vyy401, ty_Bool) → new_esEs10(vyy3001, vyy401)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Integer, bbd) → new_esEs15(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs6(vyy3001, vyy401, cdg, cdh, cea)
new_compare3(:(vyy2130000, vyy2130001), [], bfe) → GT
new_esEs27(vyy2130011, vyy1511, ty_Int) → new_esEs12(vyy2130011, vyy1511)
new_lt7(vyy2130010, vyy1510, ty_Double) → new_lt8(vyy2130010, vyy1510)
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, app(ty_Ratio, fh)) → new_ltEs12(vyy2130010, vyy1510, fh)
new_esEs8([], [], bf) → True
new_compare18(vyy213000, vyy150, False) → GT
new_esEs9(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_ltEs6(Left(vyy2130010), Left(vyy1510), app(ty_[], ee), de) → new_ltEs13(vyy2130010, vyy1510, ee)
new_primEqInt(Neg(Zero), Neg(Succ(vyy4000))) → False
new_primEqInt(Neg(Succ(vyy30000)), Neg(Zero)) → False
new_esEs4(Just(vyy3000), Just(vyy400), ty_@0) → new_esEs13(vyy3000, vyy400)
new_primPlusNat1(Zero, vyy40000) → Succ(vyy40000)
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, ty_Float) → new_ltEs15(vyy2130010, vyy1510)
new_compare9(vyy213000, vyy150, db, dc) → new_compare24(vyy213000, vyy150, new_esEs7(vyy213000, vyy150, db, dc), db, dc)
new_lt20(vyy2130010, vyy1510, ty_Ordering) → new_lt13(vyy2130010, vyy1510)
new_compare24(vyy213000, vyy150, True, db, dc) → EQ
new_esEs10(False, False) → True
new_esEs22(vyy3002, vyy402, ty_Int) → new_esEs12(vyy3002, vyy402)
new_compare12(:%(vyy2130000, vyy2130001), :%(vyy1500, vyy1501), ty_Int) → new_compare7(new_sr(vyy2130000, vyy1501), new_sr(vyy1500, vyy2130001))
new_esEs26(vyy2130010, vyy1510, app(app(ty_Either, cgg), cgh)) → new_esEs7(vyy2130010, vyy1510, cgg, cgh)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs24(vyy3001, vyy401, ty_Ordering) → new_esEs18(vyy3001, vyy401)
new_ltEs19(vyy213001, vyy151, ty_Double) → new_ltEs7(vyy213001, vyy151)
new_ltEs18(vyy2130011, vyy1511, app(app(ty_@2, baa), bab)) → new_ltEs10(vyy2130011, vyy1511, baa, bab)
new_lt20(vyy2130010, vyy1510, ty_Double) → new_lt8(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, ty_@0) → new_ltEs8(vyy2130011, vyy1511)
new_primCmpNat0(Succ(vyy21300000), Succ(vyy15000)) → new_primCmpNat0(vyy21300000, vyy15000)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_Either, dcf), dcg)) → new_esEs7(vyy3000, vyy400, dcf, dcg)
new_compare32(vyy2130000, vyy1500, ty_Int) → new_compare7(vyy2130000, vyy1500)
new_esEs22(vyy3002, vyy402, app(ty_Maybe, cbd)) → new_esEs4(vyy3002, vyy402, cbd)
new_ltEs5(EQ, EQ) → True
new_ltEs18(vyy2130011, vyy1511, app(app(ty_Either, bah), bba)) → new_ltEs6(vyy2130011, vyy1511, bah, bba)
new_esEs25(vyy213000, vyy150, app(ty_Maybe, bbb)) → new_esEs4(vyy213000, vyy150, bbb)
new_compare32(vyy2130000, vyy1500, ty_Float) → new_compare17(vyy2130000, vyy1500)
new_lt7(vyy2130010, vyy1510, app(app(ty_@2, gg), gh)) → new_lt11(vyy2130010, vyy1510, gg, gh)
new_lt21(vyy2130011, vyy1511, app(ty_Ratio, chg)) → new_lt5(vyy2130011, vyy1511, chg)
new_primEqInt(Pos(Succ(vyy30000)), Pos(Succ(vyy4000))) → new_primEqNat0(vyy30000, vyy4000)
new_compare14(vyy213000, vyy150, bbb) → new_compare27(vyy213000, vyy150, new_esEs4(vyy213000, vyy150, bbb), bbb)
new_lt14(vyy213000, vyy150, bfe) → new_esEs18(new_compare3(vyy213000, vyy150, bfe), LT)
new_esEs4(Just(vyy3000), Just(vyy400), app(app(ty_@2, dbf), dbg)) → new_esEs5(vyy3000, vyy400, dbf, dbg)
new_esEs24(vyy3001, vyy401, app(ty_Ratio, cec)) → new_esEs16(vyy3001, vyy401, cec)
new_esEs9(vyy3000, vyy400, app(ty_[], cf)) → new_esEs8(vyy3000, vyy400, cf)
new_ltEs18(vyy2130011, vyy1511, app(ty_Maybe, hh)) → new_ltEs9(vyy2130011, vyy1511, hh)
new_esEs23(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_esEs25(vyy213000, vyy150, app(ty_[], bfe)) → new_esEs8(vyy213000, vyy150, bfe)
new_esEs26(vyy2130010, vyy1510, ty_Integer) → new_esEs15(vyy2130010, vyy1510)
new_esEs7(Right(vyy3000), Right(vyy400), bcg, ty_Float) → new_esEs11(vyy3000, vyy400)
new_primEqNat0(Succ(vyy30000), Succ(vyy4000)) → new_primEqNat0(vyy30000, vyy4000)
new_esEs23(vyy3000, vyy400, app(ty_[], cdb)) → new_esEs8(vyy3000, vyy400, cdb)
new_esEs19(vyy2130010, vyy1510, app(app(app(ty_@3, ha), hb), hc)) → new_esEs6(vyy2130010, vyy1510, ha, hb, hc)
new_lt21(vyy2130011, vyy1511, ty_Char) → new_lt6(vyy2130011, vyy1511)
new_esEs5(@2(vyy3000, vyy3001), @2(vyy400, vyy401), cca, ccb) → new_asAs(new_esEs23(vyy3000, vyy400, cca), new_esEs24(vyy3001, vyy401, ccb))
new_esEs7(Left(vyy3000), Left(vyy400), ty_Ordering, bbd) → new_esEs18(vyy3000, vyy400)
new_esEs20(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_compare6(Double(vyy2130000, vyy2130001), Double(vyy1500, vyy1501)) → new_compare7(new_sr(vyy2130000, vyy1500), new_sr(vyy2130001, vyy1501))
new_primCompAux00(vyy185, LT) → LT
new_primCmpInt(Neg(Succ(vyy21300000)), Neg(vyy1500)) → new_primCmpNat0(vyy1500, Succ(vyy21300000))
new_compare32(vyy2130000, vyy1500, ty_Bool) → new_compare29(vyy2130000, vyy1500)
new_ltEs6(Left(vyy2130010), Right(vyy1510), eh, de) → True
new_esEs9(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_compare32(vyy2130000, vyy1500, ty_Char) → new_compare13(vyy2130000, vyy1500)
new_ltEs6(Right(vyy2130010), Left(vyy1510), eh, de) → False
new_lt20(vyy2130010, vyy1510, app(ty_Ratio, cge)) → new_lt5(vyy2130010, vyy1510, cge)
new_primEqInt(Pos(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Succ(vyy30000)), Pos(Zero)) → False
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_[], dce)) → new_esEs8(vyy3000, vyy400, dce)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Ordering, de) → new_ltEs5(vyy2130010, vyy1510)
new_ltEs18(vyy2130011, vyy1511, ty_Integer) → new_ltEs11(vyy2130011, vyy1511)
new_lt7(vyy2130010, vyy1510, ty_Float) → new_lt15(vyy2130010, vyy1510)
new_primPlusNat0(Succ(vyy13100), Zero) → Succ(vyy13100)
new_primPlusNat0(Zero, Succ(vyy400000)) → Succ(vyy400000)
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_ltEs5(GT, LT) → False
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Bool) → new_ltEs17(vyy2130010, vyy1510)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Char) → new_ltEs14(vyy2130010, vyy1510)
new_primCmpNat0(Succ(vyy21300000), Zero) → GT
new_compare18(vyy213000, vyy150, True) → LT
new_esEs23(vyy3000, vyy400, app(app(ty_@2, ccc), ccd)) → new_esEs5(vyy3000, vyy400, ccc, ccd)
new_ltEs9(Just(vyy2130010), Just(vyy1510), app(ty_Maybe, bec)) → new_ltEs9(vyy2130010, vyy1510, bec)
new_ltEs20(vyy2130012, vyy1512, ty_Ordering) → new_ltEs5(vyy2130012, vyy1512)
new_esEs21(vyy3001, vyy401, ty_@0) → new_esEs13(vyy3001, vyy401)
new_esEs19(vyy2130010, vyy1510, ty_@0) → new_esEs13(vyy2130010, vyy1510)
new_primCmpInt(Neg(Zero), Pos(Succ(vyy15000))) → LT
new_compare19(vyy213000, vyy150, False) → GT
new_compare11(vyy213000, vyy150, True, db, dc) → LT
new_lt15(vyy213000, vyy150) → new_esEs18(new_compare17(vyy213000, vyy150), LT)
new_sr0(Integer(vyy15000), Integer(vyy21300010)) → Integer(new_primMulInt(vyy15000, vyy21300010))
new_lt7(vyy2130010, vyy1510, ty_Bool) → new_lt17(vyy2130010, vyy1510)
new_ltEs11(vyy213001, vyy151) → new_not(new_esEs18(new_compare8(vyy213001, vyy151), GT))
new_compare28(vyy21300, vyy15, True, ceg, ceh) → EQ
new_lt21(vyy2130011, vyy1511, app(ty_Maybe, cha)) → new_lt10(vyy2130011, vyy1511, cha)
new_lt21(vyy2130011, vyy1511, app(app(ty_@2, chb), chc)) → new_lt11(vyy2130011, vyy1511, chb, chc)
new_primEqInt(Neg(Succ(vyy30000)), Pos(vyy400)) → False
new_primEqInt(Pos(Succ(vyy30000)), Neg(vyy400)) → False
new_esEs25(vyy213000, vyy150, ty_@0) → new_esEs13(vyy213000, vyy150)
new_foldFM_GE11(vyy61, vyy15, vyy16, vyy210, vyy211, vyy212, EmptyFM, vyy214, False, h, ba, bb) → new_fmToList_GE0(vyy210, vyy211, new_foldFM_GE0(vyy61, vyy15, vyy16, vyy214, h, ba, bb), h, ba, bb)
new_esEs26(vyy2130010, vyy1510, app(ty_Ratio, cge)) → new_esEs16(vyy2130010, vyy1510, cge)
new_ltEs20(vyy2130012, vyy1512, ty_Float) → new_ltEs15(vyy2130012, vyy1512)
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, app(app(app(ty_@3, fd), ff), fg)) → new_ltEs4(vyy2130010, vyy1510, fd, ff, fg)
new_primEqInt(Neg(Zero), Pos(Succ(vyy4000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(vyy4000))) → False
new_esEs13(@0, @0) → True
new_esEs21(vyy3001, vyy401, ty_Integer) → new_esEs15(vyy3001, vyy401)
new_ltEs9(Just(vyy2130010), Nothing, beb) → False
new_primCmpInt(Pos(Zero), Pos(Succ(vyy15000))) → new_primCmpNat0(Zero, Succ(vyy15000))
new_primCompAux00(vyy185, EQ) → vyy185
new_lt5(vyy213000, vyy150, dd) → new_esEs18(new_compare12(vyy213000, vyy150, dd), LT)
new_esEs7(Right(vyy3000), Right(vyy400), bcg, ty_@0) → new_esEs13(vyy3000, vyy400)
new_esEs7(Right(vyy3000), Right(vyy400), bcg, app(ty_Maybe, bde)) → new_esEs4(vyy3000, vyy400, bde)
new_esEs20(vyy3000, vyy400, ty_Bool) → new_esEs10(vyy3000, vyy400)
new_foldFM_GE11(vyy61, vyy15, vyy16, vyy210, vyy211, vyy212, Branch(vyy2130, vyy2131, vyy2132, vyy2133, vyy2134), vyy214, False, h, ba, bb) → new_foldFM_GE12(new_fmToList_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_esEs26(vyy2130010, vyy1510, ty_Ordering) → new_esEs18(vyy2130010, vyy1510)
new_esEs21(vyy3001, vyy401, ty_Ordering) → new_esEs18(vyy3001, vyy401)
new_esEs27(vyy2130011, vyy1511, app(ty_Ratio, chg)) → new_esEs16(vyy2130011, vyy1511, chg)
new_esEs26(vyy2130010, vyy1510, app(app(ty_@2, cfh), cga)) → new_esEs5(vyy2130010, vyy1510, cfh, cga)
new_compare32(vyy2130000, vyy1500, app(app(app(ty_@3, ddd), dde), ddf)) → new_compare31(vyy2130000, vyy1500, ddd, dde, ddf)
new_esEs25(vyy213000, vyy150, ty_Bool) → new_esEs10(vyy213000, vyy150)
new_lt21(vyy2130011, vyy1511, ty_Bool) → new_lt17(vyy2130011, vyy1511)
new_esEs21(vyy3001, vyy401, app(app(ty_@2, bhe), bhf)) → new_esEs5(vyy3001, vyy401, bhe, bhf)
new_esEs23(vyy3000, vyy400, ty_Float) → new_esEs11(vyy3000, vyy400)
new_not(False) → True
new_esEs9(vyy3000, vyy400, ty_Bool) → new_esEs10(vyy3000, vyy400)
new_primCmpInt(Pos(Succ(vyy21300000)), Pos(vyy1500)) → new_primCmpNat0(Succ(vyy21300000), vyy1500)
new_compare110(vyy213000, vyy150, True, bbb) → LT
new_esEs22(vyy3002, vyy402, ty_Float) → new_esEs11(vyy3002, vyy402)
new_ltEs9(Nothing, Nothing, beb) → True
new_lt9(vyy213000, vyy150) → new_esEs18(new_compare15(vyy213000, vyy150), LT)
new_esEs19(vyy2130010, vyy1510, ty_Char) → new_esEs17(vyy2130010, vyy1510)
new_esEs25(vyy213000, vyy150, ty_Integer) → new_esEs15(vyy213000, vyy150)
new_ltEs12(vyy213001, vyy151, cfd) → new_not(new_esEs18(new_compare12(vyy213001, vyy151, cfd), GT))
new_ltEs14(vyy213001, vyy151) → new_not(new_esEs18(new_compare13(vyy213001, vyy151), GT))
new_esEs25(vyy213000, vyy150, app(ty_Ratio, dd)) → new_esEs16(vyy213000, vyy150, dd)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Ordering) → new_esEs18(vyy3000, vyy400)
new_esEs24(vyy3001, vyy401, app(ty_[], ced)) → new_esEs8(vyy3001, vyy401, ced)
new_compare24(vyy213000, vyy150, False, db, dc) → new_compare11(vyy213000, vyy150, new_ltEs6(vyy213000, vyy150, db, dc), db, dc)
new_lt19(vyy213000, vyy150, app(app(app(ty_@3, bc), bd), be)) → new_lt12(vyy213000, vyy150, bc, bd, be)
new_lt8(vyy213000, vyy150) → new_esEs18(new_compare6(vyy213000, vyy150), LT)
new_lt19(vyy213000, vyy150, ty_Integer) → new_lt4(vyy213000, vyy150)
new_esEs18(GT, GT) → True
new_lt21(vyy2130011, vyy1511, ty_Double) → new_lt8(vyy2130011, vyy1511)
new_compare11(vyy213000, vyy150, False, db, dc) → GT
new_ltEs6(Left(vyy2130010), Left(vyy1510), app(app(app(ty_@3, ea), eb), ec), de) → new_ltEs4(vyy2130010, vyy1510, ea, eb, ec)
new_lt19(vyy213000, vyy150, ty_Char) → new_lt6(vyy213000, vyy150)
new_primCmpInt(Pos(Succ(vyy21300000)), Neg(vyy1500)) → GT
new_esEs7(Left(vyy3000), Left(vyy400), ty_Bool, bbd) → new_esEs10(vyy3000, vyy400)
new_primMulInt(Pos(vyy30000), Pos(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, ty_@0) → new_ltEs8(vyy2130010, vyy1510)
new_ltEs6(Left(vyy2130010), Left(vyy1510), app(ty_Maybe, df), de) → new_ltEs9(vyy2130010, vyy1510, df)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Float, bbd) → new_esEs11(vyy3000, vyy400)
new_esEs27(vyy2130011, vyy1511, ty_Char) → new_esEs17(vyy2130011, vyy1511)
new_ltEs5(LT, GT) → True
new_esEs10(True, True) → True
new_esEs7(Right(vyy3000), Right(vyy400), bcg, ty_Int) → new_esEs12(vyy3000, vyy400)
new_ltEs20(vyy2130012, vyy1512, ty_Bool) → new_ltEs17(vyy2130012, vyy1512)
new_lt7(vyy2130010, vyy1510, app(app(app(ty_@3, ha), hb), hc)) → new_lt12(vyy2130010, vyy1510, ha, hb, hc)
new_primMulInt(Neg(vyy30000), Neg(vyy4000)) → Pos(new_primMulNat0(vyy30000, vyy4000))
new_esEs20(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_primEqNat0(Zero, Succ(vyy4000)) → False
new_primEqNat0(Succ(vyy30000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_lt20(vyy2130010, vyy1510, app(app(ty_Either, cgg), cgh)) → new_lt18(vyy2130010, vyy1510, cgg, cgh)
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Int) → new_ltEs16(vyy2130010, vyy1510)
new_esEs22(vyy3002, vyy402, ty_Ordering) → new_esEs18(vyy3002, vyy402)
new_lt20(vyy2130010, vyy1510, app(ty_Maybe, cfg)) → new_lt10(vyy2130010, vyy1510, cfg)
new_esEs22(vyy3002, vyy402, ty_Double) → new_esEs14(vyy3002, vyy402)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, dbe) → True
new_ltEs18(vyy2130011, vyy1511, ty_Bool) → new_ltEs17(vyy2130011, vyy1511)
new_esEs7(Left(vyy3000), Left(vyy400), ty_Char, bbd) → new_esEs17(vyy3000, vyy400)
new_esEs25(vyy213000, vyy150, ty_Int) → new_esEs12(vyy213000, vyy150)
new_esEs4(Just(vyy3000), Just(vyy400), app(ty_Ratio, dcd)) → new_esEs16(vyy3000, vyy400, dcd)
new_compare112(vyy159, vyy160, vyy161, vyy162, False, cfe, cff) → GT
new_esEs27(vyy2130011, vyy1511, app(app(app(ty_@3, chd), che), chf)) → new_esEs6(vyy2130011, vyy1511, chd, che, chf)
new_lt19(vyy213000, vyy150, app(ty_Ratio, dd)) → new_lt5(vyy213000, vyy150, dd)
new_esEs27(vyy2130011, vyy1511, app(app(ty_@2, chb), chc)) → new_esEs5(vyy2130011, vyy1511, chb, chc)
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_[], bcd), bbd) → new_esEs8(vyy3000, vyy400, bcd)
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_esEs18(new_compare28(vyy2130, @2(vyy15, vyy16), new_esEs5(vyy2130, @2(vyy15, vyy16), h, ba), h, ba), LT), h, ba, bb)
new_esEs27(vyy2130011, vyy1511, app(ty_Maybe, cha)) → new_esEs4(vyy2130011, vyy1511, cha)
new_esEs21(vyy3001, vyy401, app(app(ty_Either, cae), caf)) → new_esEs7(vyy3001, vyy401, cae, caf)
new_ltEs9(Just(vyy2130010), Just(vyy1510), app(app(ty_@2, bed), bee)) → new_ltEs10(vyy2130010, vyy1510, bed, bee)
new_primPlusNat1(Succ(vyy1310), vyy40000) → Succ(Succ(new_primPlusNat0(vyy1310, vyy40000)))
new_esEs8(:(vyy3000, vyy3001), :(vyy400, vyy401), bf) → new_asAs(new_esEs9(vyy3000, vyy400, bf), new_esEs8(vyy3001, vyy401, bf))
new_lt21(vyy2130011, vyy1511, ty_Integer) → new_lt4(vyy2130011, vyy1511)
new_lt20(vyy2130010, vyy1510, ty_@0) → new_lt9(vyy2130010, vyy1510)
new_esEs21(vyy3001, vyy401, ty_Char) → new_esEs17(vyy3001, vyy401)
new_primCmpInt(Neg(Zero), Neg(Succ(vyy15000))) → new_primCmpNat0(Succ(vyy15000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vyy15000))) → GT
new_ltEs6(Left(vyy2130010), Left(vyy1510), app(ty_Ratio, ed), de) → new_ltEs12(vyy2130010, vyy1510, ed)
new_compare13(Char(vyy2130000), Char(vyy1500)) → new_primCmpNat0(vyy2130000, vyy1500)
new_compare110(vyy213000, vyy150, False, bbb) → GT
new_esEs12(vyy300, vyy40) → new_primEqInt(vyy300, vyy40)
new_lt21(vyy2130011, vyy1511, app(ty_[], chh)) → new_lt14(vyy2130011, vyy1511, chh)
new_ltEs19(vyy213001, vyy151, ty_Bool) → new_ltEs17(vyy213001, vyy151)
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_Double) → new_ltEs7(vyy2130010, vyy1510)
new_esEs19(vyy2130010, vyy1510, ty_Double) → new_esEs14(vyy2130010, vyy1510)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Char, de) → new_ltEs14(vyy2130010, vyy1510)
new_ltEs19(vyy213001, vyy151, ty_Char) → new_ltEs14(vyy213001, vyy151)
new_esEs19(vyy2130010, vyy1510, ty_Float) → new_esEs11(vyy2130010, vyy1510)
new_ltEs19(vyy213001, vyy151, ty_Integer) → new_ltEs11(vyy213001, vyy151)
new_esEs9(vyy3000, vyy400, ty_Double) → new_esEs14(vyy3000, vyy400)
new_esEs21(vyy3001, vyy401, app(ty_Maybe, cab)) → new_esEs4(vyy3001, vyy401, cab)
new_compare25(vyy213000, vyy150, False) → new_compare18(vyy213000, vyy150, new_ltEs17(vyy213000, vyy150))
new_esEs23(vyy3000, vyy400, app(ty_Ratio, cda)) → new_esEs16(vyy3000, vyy400, cda)
new_esEs20(vyy3000, vyy400, app(app(ty_Either, bhc), bhd)) → new_esEs7(vyy3000, vyy400, bhc, bhd)
new_esEs22(vyy3002, vyy402, app(ty_Ratio, cbe)) → new_esEs16(vyy3002, vyy402, cbe)
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, app(app(ty_Either, gb), gc)) → new_ltEs6(vyy2130010, vyy1510, gb, gc)
new_compare32(vyy2130000, vyy1500, app(app(ty_Either, dea), deb)) → new_compare9(vyy2130000, vyy1500, dea, deb)
new_esEs19(vyy2130010, vyy1510, app(app(ty_@2, gg), gh)) → new_esEs5(vyy2130010, vyy1510, gg, gh)
new_esEs9(vyy3000, vyy400, app(app(ty_@2, bg), bh)) → new_esEs5(vyy3000, vyy400, bg, bh)
new_esEs19(vyy2130010, vyy1510, app(ty_Ratio, hd)) → new_esEs16(vyy2130010, vyy1510, hd)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, ty_Bool) → new_ltEs17(vyy2130010, vyy1510)
new_lt19(vyy213000, vyy150, ty_Ordering) → new_lt13(vyy213000, vyy150)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Double) → new_esEs14(vyy3000, vyy400)
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, ty_Integer) → new_ltEs11(vyy2130010, vyy1510)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Bool, de) → new_ltEs17(vyy2130010, vyy1510)
new_asAs(False, vyy111) → False
new_esEs14(Double(vyy3000, vyy3001), Double(vyy400, vyy401)) → new_esEs12(new_sr(vyy3000, vyy400), new_sr(vyy3001, vyy401))
new_compare3([], [], bfe) → EQ
new_primMulInt(Pos(vyy30000), Neg(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulInt(Neg(vyy30000), Pos(vyy4000)) → Neg(new_primMulNat0(vyy30000, vyy4000))
new_primMulNat0(Zero, Succ(vyy40000)) → Zero
new_primMulNat0(Succ(vyy300000), Zero) → Zero
new_ltEs18(vyy2130011, vyy1511, ty_Ordering) → new_ltEs5(vyy2130011, vyy1511)
new_esEs7(Right(vyy3000), Right(vyy400), bcg, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_compare111(vyy159, vyy160, vyy161, vyy162, True, vyy164, cfe, cff) → new_compare112(vyy159, vyy160, vyy161, vyy162, True, cfe, cff)
new_esEs23(vyy3000, vyy400, app(app(app(ty_@3, cce), ccf), ccg)) → new_esEs6(vyy3000, vyy400, cce, ccf, ccg)
new_ltEs5(LT, EQ) → True
new_lt20(vyy2130010, vyy1510, app(ty_[], cgf)) → new_lt14(vyy2130010, vyy1510, cgf)
new_esEs9(vyy3000, vyy400, app(ty_Maybe, cd)) → new_esEs4(vyy3000, vyy400, cd)
new_lt21(vyy2130011, vyy1511, ty_Ordering) → new_lt13(vyy2130011, vyy1511)
new_lt19(vyy213000, vyy150, ty_Double) → new_lt8(vyy213000, vyy150)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Int, de) → new_ltEs16(vyy2130010, vyy1510)
new_esEs24(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_esEs27(vyy2130011, vyy1511, ty_@0) → new_esEs13(vyy2130011, vyy1511)
new_compare16(vyy213000, vyy150, bff, bfg) → new_compare28(vyy213000, vyy150, new_esEs5(vyy213000, vyy150, bff, bfg), bff, bfg)
new_esEs28(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_ltEs15(vyy213001, vyy151) → new_not(new_esEs18(new_compare17(vyy213001, vyy151), GT))
new_ltEs17(True, True) → True
new_esEs21(vyy3001, vyy401, app(ty_[], cad)) → new_esEs8(vyy3001, vyy401, cad)
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, app(ty_Maybe, fa)) → new_ltEs9(vyy2130010, vyy1510, fa)
new_ltEs20(vyy2130012, vyy1512, app(ty_Ratio, dba)) → new_ltEs12(vyy2130012, vyy1512, dba)
new_esEs25(vyy213000, vyy150, app(app(app(ty_@3, bc), bd), be)) → new_esEs6(vyy213000, vyy150, bc, bd, be)
new_lt11(vyy213000, vyy150, bff, bfg) → new_esEs18(new_compare16(vyy213000, vyy150, bff, bfg), LT)
new_ltEs7(vyy213001, vyy151) → new_not(new_esEs18(new_compare6(vyy213001, vyy151), GT))
new_esEs23(vyy3000, vyy400, ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs23(vyy3000, vyy400, ty_Bool) → new_esEs10(vyy3000, vyy400)
new_ltEs19(vyy213001, vyy151, ty_Int) → new_ltEs16(vyy213001, vyy151)
new_esEs7(Left(vyy3000), Left(vyy400), app(app(app(ty_@3, bbg), bbh), bca), bbd) → new_esEs6(vyy3000, vyy400, bbg, bbh, bca)
new_lt19(vyy213000, vyy150, app(ty_[], bfe)) → new_lt14(vyy213000, vyy150, bfe)
new_esEs21(vyy3001, vyy401, app(ty_Ratio, cac)) → new_esEs16(vyy3001, vyy401, cac)
new_ltEs19(vyy213001, vyy151, ty_@0) → new_ltEs8(vyy213001, vyy151)
new_lt7(vyy2130010, vyy1510, ty_Char) → new_lt6(vyy2130010, vyy1510)
new_esEs19(vyy2130010, vyy1510, ty_Ordering) → new_esEs18(vyy2130010, vyy1510)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Double, de) → new_ltEs7(vyy2130010, vyy1510)
new_esEs25(vyy213000, vyy150, app(app(ty_@2, bff), bfg)) → new_esEs5(vyy213000, vyy150, bff, bfg)
new_esEs20(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_esEs6(@3(vyy3000, vyy3001, vyy3002), @3(vyy400, vyy401, vyy402), bfh, bga, bgb) → new_asAs(new_esEs20(vyy3000, vyy400, bfh), new_asAs(new_esEs21(vyy3001, vyy401, bga), new_esEs22(vyy3002, vyy402, bgb)))
new_esEs7(Left(vyy3000), Left(vyy400), app(ty_Ratio, bcc), bbd) → new_esEs16(vyy3000, vyy400, bcc)
new_ltEs17(False, True) → True
new_lt10(vyy213000, vyy150, bbb) → new_esEs18(new_compare14(vyy213000, vyy150, bbb), LT)
new_lt7(vyy2130010, vyy1510, ty_Integer) → new_lt4(vyy2130010, vyy1510)
new_compare32(vyy2130000, vyy1500, app(ty_[], ddh)) → new_compare3(vyy2130000, vyy1500, ddh)
new_lt18(vyy213000, vyy150, db, dc) → new_esEs18(new_compare9(vyy213000, vyy150, db, dc), LT)
new_lt21(vyy2130011, vyy1511, app(app(ty_Either, daa), dab)) → new_lt18(vyy2130011, vyy1511, daa, dab)
new_lt12(vyy213000, vyy150, bc, bd, be) → new_esEs18(new_compare31(vyy213000, vyy150, bc, bd, be), LT)
new_compare27(vyy213000, vyy150, True, bbb) → EQ
new_esEs21(vyy3001, vyy401, ty_Float) → new_esEs11(vyy3001, vyy401)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_@0, de) → new_ltEs8(vyy2130010, vyy1510)
new_esEs20(vyy3000, vyy400, ty_Char) → new_esEs17(vyy3000, vyy400)
new_primPlusNat0(Succ(vyy13100), Succ(vyy400000)) → Succ(Succ(new_primPlusNat0(vyy13100, vyy400000)))
new_esEs28(vyy3000, vyy400, ty_Int) → new_esEs12(vyy3000, vyy400)
new_esEs22(vyy3002, vyy402, ty_@0) → new_esEs13(vyy3002, vyy402)
new_esEs9(vyy3000, vyy400, app(app(app(ty_@3, ca), cb), cc)) → new_esEs6(vyy3000, vyy400, ca, cb, cc)
new_ltEs19(vyy213001, vyy151, ty_Ordering) → new_ltEs5(vyy213001, vyy151)
new_esEs22(vyy3002, vyy402, ty_Integer) → new_esEs15(vyy3002, vyy402)
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, app(app(ty_@2, fb), fc)) → new_ltEs10(vyy2130010, vyy1510, fb, fc)
new_esEs21(vyy3001, vyy401, app(app(app(ty_@3, bhg), bhh), caa)) → new_esEs6(vyy3001, vyy401, bhg, bhh, caa)
new_esEs19(vyy2130010, vyy1510, ty_Integer) → new_esEs15(vyy2130010, vyy1510)
new_esEs7(Right(vyy3000), Right(vyy400), bcg, app(ty_[], bdg)) → new_esEs8(vyy3000, vyy400, bdg)
new_lt20(vyy2130010, vyy1510, ty_Float) → new_lt15(vyy2130010, vyy1510)
new_asAs(True, vyy111) → vyy111
new_ltEs5(GT, GT) → True
new_esEs10(True, False) → False
new_esEs10(False, True) → False
new_esEs25(vyy213000, vyy150, ty_Float) → new_esEs11(vyy213000, vyy150)
new_lt20(vyy2130010, vyy1510, ty_Bool) → new_lt17(vyy2130010, vyy1510)
new_lt19(vyy213000, vyy150, ty_@0) → new_lt9(vyy213000, vyy150)
new_esEs19(vyy2130010, vyy1510, app(ty_[], he)) → new_esEs8(vyy2130010, vyy1510, he)
new_esEs9(vyy3000, vyy400, app(app(ty_Either, cg), da)) → new_esEs7(vyy3000, vyy400, cg, da)
new_esEs4(Just(vyy3000), Just(vyy400), ty_Integer) → new_esEs15(vyy3000, vyy400)
new_esEs7(Left(vyy3000), Left(vyy400), ty_@0, bbd) → new_esEs13(vyy3000, vyy400)
new_compare32(vyy2130000, vyy1500, app(app(ty_@2, ddb), ddc)) → new_compare16(vyy2130000, vyy1500, ddb, ddc)
new_lt19(vyy213000, vyy150, ty_Int) → new_lt16(vyy213000, vyy150)
new_esEs21(vyy3001, vyy401, ty_Bool) → new_esEs10(vyy3001, vyy401)
new_lt16(vyy213000, vyy150) → new_esEs18(new_compare7(vyy213000, vyy150), LT)
new_esEs16(:%(vyy3000, vyy3001), :%(vyy400, vyy401), dch) → new_asAs(new_esEs28(vyy3000, vyy400, dch), new_esEs29(vyy3001, vyy401, dch))
new_ltEs9(Just(vyy2130010), Just(vyy1510), ty_@0) → new_ltEs8(vyy2130010, vyy1510)
new_lt21(vyy2130011, vyy1511, app(app(app(ty_@3, chd), che), chf)) → new_lt12(vyy2130011, vyy1511, chd, che, chf)
new_primCompAux00(vyy185, GT) → GT
new_esEs25(vyy213000, vyy150, app(app(ty_Either, db), dc)) → new_esEs7(vyy213000, vyy150, db, dc)
new_compare32(vyy2130000, vyy1500, app(ty_Maybe, dda)) → new_compare14(vyy2130000, vyy1500, dda)
new_esEs7(Right(vyy3000), Right(vyy400), bcg, ty_Bool) → new_esEs10(vyy3000, vyy400)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs20(vyy3000, vyy400, ty_@0) → new_esEs13(vyy3000, vyy400)
new_ltEs9(Just(vyy2130010), Just(vyy1510), app(ty_Ratio, bfa)) → new_ltEs12(vyy2130010, vyy1510, bfa)
new_esEs8(:(vyy3000, vyy3001), [], bf) → False
new_esEs8([], :(vyy400, vyy401), bf) → False
new_ltEs5(GT, EQ) → False
new_ltEs20(vyy2130012, vyy1512, app(app(ty_@2, dad), dae)) → new_ltEs10(vyy2130012, vyy1512, dad, dae)
new_ltEs19(vyy213001, vyy151, app(app(ty_Either, eh), de)) → new_ltEs6(vyy213001, vyy151, eh, de)
new_ltEs19(vyy213001, vyy151, app(ty_[], bbc)) → new_ltEs13(vyy213001, vyy151, bbc)
new_lt7(vyy2130010, vyy1510, app(app(ty_Either, hf), hg)) → new_lt18(vyy2130010, vyy1510, hf, hg)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs27(vyy2130011, vyy1511, ty_Integer) → new_esEs15(vyy2130011, vyy1511)
new_esEs18(EQ, EQ) → True
new_primCmpInt(Neg(Succ(vyy21300000)), Pos(vyy1500)) → LT
new_esEs24(vyy3001, vyy401, ty_Double) → new_esEs14(vyy3001, vyy401)
new_not(True) → False
new_ltEs6(Right(vyy2130010), Right(vyy1510), eh, ty_Int) → new_ltEs16(vyy2130010, vyy1510)
new_ltEs6(Left(vyy2130010), Left(vyy1510), ty_Integer, de) → new_ltEs11(vyy2130010, vyy1510)

The set Q consists of the following terms:

new_esEs13(@0, @0)
new_esEs21(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Char)
new_asAs(True, x0)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_ltEs9(Nothing, Just(x0), x1)
new_esEs18(LT, LT)
new_compare111(x0, x1, x2, x3, True, x4, x5, x6)
new_esEs23(x0, x1, ty_Bool)
new_compare15(@0, @0)
new_ltEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare3(:(x0, x1), :(x2, x3), x4)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt16(x0, x1)
new_ltEs15(x0, x1)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare27(x0, x1, False, x2)
new_compare18(x0, x1, True)
new_esEs26(x0, x1, ty_@0)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_lt7(x0, x1, ty_@0)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt18(x0, x1, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_compare13(Char(x0), Char(x1))
new_ltEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Int)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs5(GT, EQ)
new_ltEs5(EQ, GT)
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_compare30(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_ltEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, True)
new_esEs23(x0, x1, ty_Double)
new_ltEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs23(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Nothing, x1)
new_esEs17(Char(x0), Char(x1))
new_lt7(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, x2, x3, x4)
new_esEs18(EQ, GT)
new_esEs18(GT, EQ)
new_esEs22(x0, x1, ty_Char)
new_ltEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primMulNat0(Zero, Succ(x0))
new_lt21(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Int)
new_esEs18(EQ, EQ)
new_lt21(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs17(False, False)
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Int)
new_ltEs5(LT, EQ)
new_ltEs5(EQ, LT)
new_lt19(x0, x1, ty_Char)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Integer)
new_compare10(x0, x1, False, x2, x3, x4)
new_esEs19(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_[], x2))
new_compare32(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare112(x0, x1, x2, x3, True, x4, x5)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Zero, Zero)
new_ltEs9(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(True, False)
new_esEs10(False, True)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare18(x0, x1, False)
new_compare10(x0, x1, True, x2, x3, x4)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_compare26(x0, x1, True)
new_esEs25(x0, x1, ty_Float)
new_lt10(x0, x1, x2)
new_esEs25(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1)
new_compare27(x0, x1, True, x2)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare3(:(x0, x1), [], x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs25(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Bool)
new_ltEs17(True, True)
new_sr0(Integer(x0), Integer(x1))
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_lt13(x0, x1)
new_compare23(x0, x1, True, x2, x3, x4)
new_ltEs6(Right(x0), Right(x1), x2, ty_Char)
new_lt12(x0, x1, x2, x3, x4)
new_compare3([], [], x0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_pePe(True, x0)
new_ltEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare7(x0, x1)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs19(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Ordering)
new_compare32(x0, x1, ty_Char)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_lt7(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_Double)
new_esEs9(x0, x1, ty_@0)
new_compare11(x0, x1, True, x2, x3)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primPlusNat1(Zero, x0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Char)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(x0, x1, ty_Integer)
new_compare12(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_compare111(x0, x1, x2, x3, False, x4, x5, x6)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare23(x0, x1, False, x2, x3, x4)
new_lt7(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_ltEs18(x0, x1, ty_Int)
new_primPlusNat0(Zero, Zero)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs10(True, True)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt7(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Char)
new_ltEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Integer)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_compare32(x0, x1, ty_Bool)
new_lt9(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs18(x0, x1, app(ty_[], x2))
new_compare32(x0, x1, app(ty_Ratio, x2))
new_esEs18(GT, GT)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare32(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare112(x0, x1, x2, x3, False, x4, x5)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs24(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Bool)
new_compare11(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_Int)
new_foldFM_GE11(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9, x10)
new_ltEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs19(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt21(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Char)
new_compare14(x0, x1, x2)
new_esEs4(Just(x0), Just(x1), ty_Int)
new_ltEs18(x0, x1, ty_Float)
new_compare28(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs26(x0, x1, ty_Double)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, x2, x3)
new_ltEs20(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare28(x0, x1, True, x2, x3)
new_esEs8(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs21(x0, x1, ty_Ordering)
new_compare19(x0, x1, False)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_compare32(x0, x1, ty_@0)
new_ltEs8(x0, x1)
new_compare9(x0, x1, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs12(x0, x1)
new_asAs(False, x0)
new_primPlusNat1(Succ(x0), x1)
new_esEs21(x0, x1, ty_Char)
new_compare110(x0, x1, False, x2)
new_ltEs20(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_foldFM_GE0(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10)
new_lt19(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs24(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs18(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Integer)
new_ltEs11(x0, x1)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare8(Integer(x0), Integer(x1))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs18(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs21(x0, x1, ty_Int)
new_lt7(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare12(:%(x0, x1), :%(x2, x3), ty_Int)
new_foldFM_GE11(x0, x1, x2, x3, x4, x5, EmptyFM, x6, False, x7, x8, x9)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs6(Left(x0), Right(x1), x2, x3)
new_ltEs6(Right(x0), Left(x1), x2, x3)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, ty_Double)
new_ltEs16(x0, x1)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_esEs20(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Zero, Succ(x0))
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Int)
new_ltEs13(x0, x1, x2)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs19(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(GT, LT)
new_ltEs5(LT, GT)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Double)
new_esEs8(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_Integer)
new_primCompAux00(x0, GT)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_compare32(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_foldFM_GE11(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, False, x12, x13, x14)
new_ltEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(x0, x1, False)
new_esEs22(x0, x1, ty_Int)
new_esEs10(False, False)
new_esEs29(x0, x1, ty_Integer)
new_esEs8([], [], x0)
new_esEs27(x0, x1, ty_Integer)
new_compare17(Float(x0, x1), Float(x2, x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare25(x0, x1, True)
new_ltEs6(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs9(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs18(LT, EQ)
new_esEs18(EQ, LT)
new_esEs21(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(GT, GT)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_lt19(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_fmToList_GE0(x0, x1, x2, x3, x4, x5)
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Float)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_lt7(x0, x1, ty_Int)
new_ltEs12(x0, x1, x2)
new_primPlusNat0(Zero, Succ(x0))
new_compare32(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Int)
new_lt4(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, ty_Bool)
new_ltEs7(x0, x1)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_esEs15(Integer(x0), Integer(x1))
new_not(True)
new_esEs4(Nothing, Just(x0), x1)
new_esEs21(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Float)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt21(x0, x1, ty_Integer)
new_not(False)
new_compare16(x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(Right(x0), Right(x1), x2, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs17(False, True)
new_ltEs17(True, False)
new_lt8(x0, x1)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_foldFM_GE12(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCompAux00(x0, LT)
new_compare24(x0, x1, True, x2, x3)
new_ltEs5(EQ, EQ)
new_lt19(x0, x1, ty_Ordering)
new_lt7(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr(x0, x1)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_Ordering)
new_primMulNat0(Succ(x0), Zero)
new_compare32(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare32(x0, x1, ty_Integer)
new_esEs18(GT, LT)
new_esEs18(LT, GT)
new_primCompAux00(x0, EQ)
new_lt15(x0, x1)
new_esEs23(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs11(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, ty_Char)
new_primPlusNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, app(ty_[], x2))
new_compare25(x0, x1, False)
new_compare110(x0, x1, True, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare3([], :(x0, x1), x2)
new_esEs25(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqNat0(Succ(x0), Zero)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_lt7(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_ltEs9(Nothing, Nothing, x0)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs9(x0, x1, ty_Ordering)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_lt7(x0, x1, ty_Double)
new_compare32(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_foldFM_GE0(x0, x1, x2, EmptyFM, x3, x4, x5)
new_esEs19(x0, x1, ty_Float)
new_pePe(False, x0)
new_lt21(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Float)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs19(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Char)
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs8([], :(x0, x1), x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Float)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_ltEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs9(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Bool)
new_lt5(x0, x1, x2)
new_lt7(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs18(x0, x1, ty_Double)
new_ltEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, ty_@0)

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: