YES 12.708 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
  ((addListToFM :: Ord b => FiniteMap (Maybe b) a  ->  [(Maybe b,a)]  ->  FiniteMap (Maybe b) a) :: Ord b => FiniteMap (Maybe b) a  ->  [(Maybe b,a)]  ->  FiniteMap (Maybe b) a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b


  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM fm key_elt_pairs addListToFM_C (\old new ->new) fm key_elt_pairs

  addListToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM_C combiner fm key_elt_pairs 
foldl add fm key_elt_pairs where 
add fmap (key,eltaddToFM_C combiner fmap key elt

  addToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM_C combiner EmptyFM key elt unitFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_key new_elt 
 | new_key < key = 
mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
 | new_key > key = 
mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
 | otherwise = 
Branch new_key (combiner elt new_elt) size fm_l fm_r

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt _ _ EmptyFM(key,elt)
findMax (Branch key elt _ _ fm_rfindMax fm_r

  findMin :: FiniteMap b a  ->  (b,a)
findMin (Branch key elt _ EmptyFM _) (key,elt)
findMin (Branch key elt _ fm_l _) findMin fm_l

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

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

  mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkBalBranch key elt fm_L fm_R 
 | size_l + size_r < 2 = 
mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l = 
case fm_R of
  Branch _ _ _ fm_rl fm_rr
 | sizeFM fm_rl < 2 * sizeFM fm_rr -> 
single_L fm_L fm_R
 | otherwise -> 
double_L fm_L fm_R
 | size_l > sIZE_RATIO * size_r = 
case fm_L of
  Branch _ _ _ fm_ll fm_lr
 | sizeFM fm_lr < 2 * sizeFM fm_ll -> 
single_R fm_L fm_R
 | otherwise -> 
double_R fm_L fm_R
 | otherwise = 
mkBranch 2 key elt fm_L fm_R where 
double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rrmkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
single_L fm_l (Branch key_r elt_r _ fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l _ fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

  mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBranch which key elt fm_l fm_r 
let 
result Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result
 where 
balance_ok True
left_ok 
case fm_l of
  EmptyFM-> True
  Branch left_key _ _ _ _-> 
let 
biggest_left_key fst (findMax fm_l)
in biggest_left_key < key
left_size sizeFM fm_l
right_ok 
case fm_r of
  EmptyFM-> True
  Branch right_key _ _ _ _-> 
let 
smallest_right_key fst (findMin fm_r)
in key < smallest_right_key
right_size sizeFM fm_r
unbox :: Int  ->  Int
unbox x x

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

  unitFM :: b  ->  a  ->  FiniteMap b a
unitFM key elt Branch key elt 1 emptyFM emptyFM


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

The following Lambda expression
\oldnewnew

is transformed to
addListToFM0 old new = new



↳ HASKELL
  ↳ LR
HASKELL
      ↳ CR

mainModule FiniteMap
  ((addListToFM :: Ord b => FiniteMap (Maybe b) a  ->  [(Maybe b,a)]  ->  FiniteMap (Maybe b) a) :: Ord b => FiniteMap (Maybe b) a  ->  [(Maybe b,a)]  ->  FiniteMap (Maybe b) a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a


  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b
addListToFM_C combiner fm key_elt_pairs 
foldl add fm key_elt_pairs where 
add fmap (key,eltaddToFM_C combiner fmap key elt

  addToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b
addToFM_C combiner EmptyFM key elt unitFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_key new_elt 
 | new_key < key = 
mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
 | new_key > key = 
mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
 | otherwise = 
Branch new_key (combiner elt new_elt) size fm_l fm_r

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

  findMax :: FiniteMap a b  ->  (a,b)
findMax (Branch key elt _ _ EmptyFM(key,elt)
findMax (Branch key elt _ _ fm_rfindMax fm_r

  findMin :: FiniteMap b a  ->  (b,a)
findMin (Branch key elt _ EmptyFM _) (key,elt)
findMin (Branch key elt _ fm_l _) findMin fm_l

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

  
fmToList0 key elt rest (key,elt: rest

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

  mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBalBranch key elt fm_L fm_R 
 | size_l + size_r < 2 = 
mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l = 
case fm_R of
  Branch _ _ _ fm_rl fm_rr
 | sizeFM fm_rl < 2 * sizeFM fm_rr -> 
single_L fm_L fm_R
 | otherwise -> 
double_L fm_L fm_R
 | size_l > sIZE_RATIO * size_r = 
case fm_L of
  Branch _ _ _ fm_ll fm_lr
 | sizeFM fm_lr < 2 * sizeFM fm_ll -> 
single_R fm_L fm_R
 | otherwise -> 
double_R fm_L fm_R
 | otherwise = 
mkBranch 2 key elt fm_L fm_R where 
double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rrmkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
single_L fm_l (Branch key_r elt_r _ fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l _ fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

  mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkBranch which key elt fm_l fm_r 
let 
result Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result
 where 
balance_ok True
left_ok 
case fm_l of
  EmptyFM-> True
  Branch left_key _ _ _ _-> 
let 
biggest_left_key fst (findMax fm_l)
in biggest_left_key < key
left_size sizeFM fm_l
right_ok 
case fm_r of
  EmptyFM-> True
  Branch right_key _ _ _ _-> 
let 
smallest_right_key fst (findMin fm_r)
in key < smallest_right_key
right_size sizeFM fm_r
unbox :: Int  ->  Int
unbox x x

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

  unitFM :: b  ->  a  ->  FiniteMap b a
unitFM key elt Branch key elt 1 emptyFM emptyFM


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Case Reductions:
The following Case expression
case fm_l of
 EmptyFM → True
 Branch left_key _ _ _ _ → 
let 
biggest_left_key  = fst (findMax fm_l)
in biggest_left_key < key

is transformed to
left_ok0 fm_l key EmptyFM = True
left_ok0 fm_l key (Branch left_key _ _ _ _) = 
let 
biggest_left_key  = fst (findMax fm_l)
in biggest_left_key < key

The following Case expression
case fm_r of
 EmptyFM → True
 Branch right_key _ _ _ _ → 
let 
smallest_right_key  = fst (findMin fm_r)
in key < smallest_right_key

is transformed to
right_ok0 fm_r key EmptyFM = True
right_ok0 fm_r key (Branch right_key _ _ _ _) = 
let 
smallest_right_key  = fst (findMin fm_r)
in key < smallest_right_key

The following Case expression
case fm_R of
 Branch _ _ _ fm_rl fm_rr
 | sizeFM fm_rl < 2 * sizeFM fm_rr
 → single_L fm_L fm_R
 | otherwise
 → double_L fm_L fm_R

is transformed to
mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)
 | sizeFM fm_rl < 2 * sizeFM fm_rr
 = single_L fm_L fm_R
 | otherwise
 = double_L fm_L fm_R

The following Case expression
case fm_L of
 Branch _ _ _ fm_ll fm_lr
 | sizeFM fm_lr < 2 * sizeFM fm_ll
 → single_R fm_L fm_R
 | otherwise
 → double_R fm_L fm_R

is transformed to
mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)
 | sizeFM fm_lr < 2 * sizeFM fm_ll
 = single_R fm_L fm_R
 | otherwise
 = double_R fm_L fm_R

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
  ((addListToFM :: Ord b => FiniteMap (Maybe b) a  ->  [(Maybe b,a)]  ->  FiniteMap (Maybe b) a) :: Ord b => FiniteMap (Maybe b) a  ->  [(Maybe b,a)]  ->  FiniteMap (Maybe 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

  addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM_C combiner fm key_elt_pairs 
foldl add fm key_elt_pairs where 
add fmap (key,eltaddToFM_C combiner fmap key elt

  addToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM_C combiner EmptyFM key elt unitFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_key new_elt 
 | new_key < key = 
mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
 | new_key > key = 
mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
 | otherwise = 
Branch new_key (combiner elt new_elt) size fm_l fm_r

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt _ _ EmptyFM(key,elt)
findMax (Branch key elt _ _ fm_rfindMax fm_r

  findMin :: FiniteMap a b  ->  (a,b)
findMin (Branch key elt _ EmptyFM _) (key,elt)
findMin (Branch key elt _ fm_l _) findMin fm_l

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

  
fmToList0 key elt rest (key,elt: rest

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

  mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkBalBranch key elt fm_L fm_R 
 | size_l + size_r < 2 = 
mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l = 
mkBalBranch0 fm_L fm_R fm_R
 | size_l > sIZE_RATIO * size_r = 
mkBalBranch1 fm_L fm_R fm_L
 | otherwise = 
mkBranch 2 key elt fm_L fm_R where 
double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rrmkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr
 | sizeFM fm_rl < 2 * sizeFM fm_rr = 
single_L fm_L fm_R
 | otherwise = 
double_L fm_L fm_R
mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr
 | sizeFM fm_lr < 2 * sizeFM fm_ll = 
single_R fm_L fm_R
 | otherwise = 
double_R fm_L fm_R
single_L fm_l (Branch key_r elt_r _ fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l _ fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

  mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkBranch which key elt fm_l fm_r 
let 
result Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result
 where 
balance_ok True
left_ok left_ok0 fm_l key fm_l
left_ok0 fm_l key EmptyFM True
left_ok0 fm_l key (Branch left_key _ _ _ _) 
let 
biggest_left_key fst (findMax fm_l)
in biggest_left_key < key
left_size sizeFM fm_l
right_ok right_ok0 fm_r key fm_r
right_ok0 fm_r key EmptyFM True
right_ok0 fm_r key (Branch right_key _ _ _ _) 
let 
smallest_right_key fst (findMin fm_r)
in key < smallest_right_key
right_size sizeFM fm_r
unbox :: Int  ->  Int
unbox x x

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

  unitFM :: a  ->  b  ->  FiniteMap a b
unitFM key elt Branch key elt 1 emptyFM emptyFM


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
  ((addListToFM :: Ord a => FiniteMap (Maybe a) b  ->  [(Maybe a,b)]  ->  FiniteMap (Maybe a) b) :: Ord a => FiniteMap (Maybe a) b  ->  [(Maybe a,b)]  ->  FiniteMap (Maybe 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

  addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b
addListToFM_C combiner fm key_elt_pairs 
foldl add fm key_elt_pairs where 
add fmap (key,eltaddToFM_C combiner fmap key elt

  addToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b
addToFM_C combiner EmptyFM key elt unitFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_key new_elt 
 | new_key < key = 
mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
 | new_key > key = 
mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
 | otherwise = 
Branch new_key (combiner elt new_elt) size fm_l fm_r

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

  findMax :: FiniteMap a b  ->  (a,b)
findMax (Branch key elt _ _ EmptyFM(key,elt)
findMax (Branch key elt _ _ fm_rfindMax fm_r

  findMin :: FiniteMap a b  ->  (a,b)
findMin (Branch key elt _ EmptyFM _) (key,elt)
findMin (Branch key elt _ fm_l _) findMin fm_l

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

  
fmToList0 key elt rest (key,elt: rest

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

  mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBalBranch key elt fm_L fm_R 
 | size_l + size_r < 2 = 
mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l = 
mkBalBranch0 fm_L fm_R fm_R
 | size_l > sIZE_RATIO * size_r = 
mkBalBranch1 fm_L fm_R fm_L
 | otherwise = 
mkBranch 2 key elt fm_L fm_R where 
double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rrmkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr
 | sizeFM fm_rl < 2 * sizeFM fm_rr = 
single_L fm_L fm_R
 | otherwise = 
double_L fm_L fm_R
mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr
 | sizeFM fm_lr < 2 * sizeFM fm_ll = 
single_R fm_L fm_R
 | otherwise = 
double_R fm_L fm_R
single_L fm_l (Branch key_r elt_r _ fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l _ fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

  mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkBranch which key elt fm_l fm_r 
let 
result Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result
 where 
balance_ok True
left_ok left_ok0 fm_l key fm_l
left_ok0 fm_l key EmptyFM True
left_ok0 fm_l key (Branch left_key _ _ _ _) 
let 
biggest_left_key fst (findMax fm_l)
in biggest_left_key < key
left_size sizeFM fm_l
right_ok right_ok0 fm_r key fm_r
right_ok0 fm_r key EmptyFM True
right_ok0 fm_r key (Branch right_key _ _ _ _) 
let 
smallest_right_key fst (findMin fm_r)
in key < smallest_right_key
right_size sizeFM fm_r
unbox :: Int  ->  Int
unbox x x

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

  unitFM :: b  ->  a  ->  FiniteMap b a
unitFM key elt Branch key elt 1 emptyFM emptyFM


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
  ((addListToFM :: Ord a => FiniteMap (Maybe a) b  ->  [(Maybe a,b)]  ->  FiniteMap (Maybe a) b) :: Ord a => FiniteMap (Maybe a) b  ->  [(Maybe a,b)]  ->  FiniteMap (Maybe a) b)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b


  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b
addListToFM_C combiner fm key_elt_pairs 
foldl add fm key_elt_pairs where 
add fmap (key,eltaddToFM_C combiner fmap key elt

  addToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b
addToFM_C combiner EmptyFM key elt unitFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_key new_elt 
 | new_key < key = 
mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
 | new_key > key = 
mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
 | otherwise = 
Branch new_key (combiner elt new_elt) size fm_l fm_r

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vuv vuw EmptyFM(key,elt)
findMax (Branch key elt vux vuy fm_rfindMax fm_r

  findMin :: FiniteMap a b  ->  (a,b)
findMin (Branch key elt wz EmptyFM xu(key,elt)
findMin (Branch key elt xv fm_l xwfindMin fm_l

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

  
fmToList0 key elt rest (key,elt: rest

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

  mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBalBranch key elt fm_L fm_R 
 | size_l + size_r < 2 = 
mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l = 
mkBalBranch0 fm_L fm_R fm_R
 | size_l > sIZE_RATIO * size_r = 
mkBalBranch1 fm_L fm_R fm_L
 | otherwise = 
mkBranch 2 key elt fm_L fm_R where 
double_L fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlr) fm_rrmkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch zx zy zz fm_rl fm_rr
 | sizeFM fm_rl < 2 * sizeFM fm_rr = 
single_L fm_L fm_R
 | otherwise = 
double_L fm_L fm_R
mkBalBranch1 fm_L fm_R (Branch yy yz zu fm_ll fm_lr
 | sizeFM fm_lr < 2 * sizeFM fm_ll = 
single_R fm_L fm_R
 | otherwise = 
double_R fm_L fm_R
single_L fm_l (Branch key_r elt_r vuu fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l yv fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

  mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBranch which key elt fm_l fm_r 
let 
result Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result
 where 
balance_ok True
left_ok left_ok0 fm_l key fm_l
left_ok0 fm_l key EmptyFM True
left_ok0 fm_l key (Branch left_key vw vx vy vz
let 
biggest_left_key fst (findMax fm_l)
in biggest_left_key < key
left_size sizeFM fm_l
right_ok right_ok0 fm_r key fm_r
right_ok0 fm_r key EmptyFM True
right_ok0 fm_r key (Branch right_key wu wv ww wx
let 
smallest_right_key fst (findMin fm_r)
in key < smallest_right_key
right_size sizeFM fm_r
unbox :: Int  ->  Int
unbox x x

  sIZE_RATIO :: Int
sIZE_RATIO 5

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch xx xy size xz yusize

  unitFM :: a  ->  b  ->  FiniteMap a b
unitFM key elt Branch key elt 1 emptyFM emptyFM


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Cond Reductions:
The following Function with conditions
mkBalBranch1 fm_L fm_R (Branch yy yz zu fm_ll fm_lr)
 | sizeFM fm_lr < 2 * sizeFM fm_ll
 = single_R fm_L fm_R
 | otherwise
 = double_R fm_L fm_R

is transformed to
mkBalBranch1 fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr)

mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr True = double_R fm_L fm_R

mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr otherwise

mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

The following Function with conditions
mkBalBranch0 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)
 | sizeFM fm_rl < 2 * sizeFM fm_rr
 = single_L fm_L fm_R
 | otherwise
 = double_L fm_L fm_R

is transformed to
mkBalBranch0 fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)

mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr True = double_L fm_L fm_R

mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr otherwise

mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

The following Function with conditions
mkBalBranch key elt fm_L fm_R
 | size_l + size_r < 2
 = mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l
 = mkBalBranch0 fm_L fm_R fm_R
 | size_l > sIZE_RATIO * size_r
 = mkBalBranch1 fm_L fm_R fm_L
 | otherwise
 = mkBranch 2 key elt fm_L fm_R
where 
double_L fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlrfm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)
 | sizeFM fm_rl < 2 * sizeFM fm_rr
 = single_L fm_L fm_R
 | otherwise
 = double_L fm_L fm_R
mkBalBranch1 fm_L fm_R (Branch yy yz zu fm_ll fm_lr)
 | sizeFM fm_lr < 2 * sizeFM fm_ll
 = single_R fm_L fm_R
 | otherwise
 = double_R fm_L fm_R
single_L fm_l (Branch key_r elt_r vuu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rlfm_rr
single_R (Branch key_l elt_l yv fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

is transformed to
mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R

mkBalBranch6 key elt fm_L fm_R = 
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2)
where 
double_L fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlrfm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)
mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr)
mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)
mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R
mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L
mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise
mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R
mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r)
mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l)
single_L fm_l (Branch key_r elt_r vuu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rlfm_rr
single_R (Branch key_l elt_l yv fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

The following Function with conditions
addToFM_C combiner EmptyFM key elt = unitFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_key new_elt
 | new_key < key
 = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_eltfm_r
 | new_key > key
 = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
 | otherwise
 = Branch new_key (combiner elt new_eltsize fm_l fm_r

is transformed to
addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_rnew_key new_elt

addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise

addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_eltsize fm_l fm_r

addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_eltfm_r
addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key)

addToFM_C3 combiner (Branch key elt size fm_l fm_rnew_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key)

addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 wuu wuv wuw wux = addToFM_C3 wuu wuv wuw wux

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

is transformed to
compare x y = compare3 x y

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

gcd'1 True x wuy = x
gcd'1 wuz wvu wvv = gcd'0 wvu wvv

gcd'2 x wuy = gcd'1 (wuy == 0) x wuy
gcd'2 wvw wvx = gcd'0 wvw wvx

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 wvy wvz = gcd3 wvy wvz
gcd x y = gcd0 x y

gcd0 x y = 
gcd' (abs x) (abs y)
where 
gcd' x wuy = gcd'2 x wuy
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x wuy = x
gcd'1 wuz wvu wvv = gcd'0 wvu wvv
gcd'2 x wuy = gcd'1 (wuy == 0) x wuy
gcd'2 wvw wvx = gcd'0 wvw wvx

gcd1 True wvy wvz = error []
gcd1 wwu wwv www = gcd0 wwv www

gcd2 True wvy wvz = gcd1 (wvz == 0) wvy wvz
gcd2 wwx wwy wwz = gcd0 wwy wwz

gcd3 wvy wvz = gcd2 (wvy == 0) wvy wvz
gcd3 wxu wxv = gcd0 wxu wxv

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

is transformed to
absReal x = absReal2 x

absReal0 x True = `negate` x

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

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

  addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM_C combiner fm key_elt_pairs 
foldl add fm key_elt_pairs where 
add fmap (key,eltaddToFM_C combiner fmap key elt

  addToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM_C combiner EmptyFM key elt addToFM_C4 combiner EmptyFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_key new_elt addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt

  
addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True Branch new_key (combiner elt new_elt) size fm_l fm_r

  
addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise

  
addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key)

  
addToFM_C3 combiner (Branch key elt size fm_l fm_rnew_key new_elt addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key)

  
addToFM_C4 combiner EmptyFM key elt unitFM key elt
addToFM_C4 wuu wuv wuw wux addToFM_C3 wuu wuv wuw wux

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

  findMax :: FiniteMap a b  ->  (a,b)
findMax (Branch key elt vuv vuw EmptyFM(key,elt)
findMax (Branch key elt vux vuy fm_rfindMax fm_r

  findMin :: FiniteMap b a  ->  (b,a)
findMin (Branch key elt wz EmptyFM xu(key,elt)
findMin (Branch key elt xv fm_l xwfindMin fm_l

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

  
fmToList0 key elt rest (key,elt: rest

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

  mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBalBranch key elt fm_L fm_R mkBalBranch6 key elt fm_L fm_R

  
mkBalBranch6 key elt fm_L fm_R 
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where 
double_L fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlr) fm_rrmkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch zx zy zz fm_rl fm_rrmkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)
mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr True double_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr True single_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr False mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rrmkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr)
mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr True double_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr True single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr False mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)
mkBalBranch2 key elt fm_L fm_R True mkBranch 2 key elt fm_L fm_R
mkBalBranch3 key elt fm_L fm_R True mkBalBranch1 fm_L fm_R fm_L
mkBalBranch3 key elt fm_L fm_R False mkBalBranch2 key elt fm_L fm_R otherwise
mkBalBranch4 key elt fm_L fm_R True mkBalBranch0 fm_L fm_R fm_R
mkBalBranch4 key elt fm_L fm_R False mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r)
mkBalBranch5 key elt fm_L fm_R True mkBranch 1 key elt fm_L fm_R
mkBalBranch5 key elt fm_L fm_R False mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l)
single_L fm_l (Branch key_r elt_r vuu fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l yv fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

  mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkBranch which key elt fm_l fm_r 
let 
result Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result
 where 
balance_ok True
left_ok left_ok0 fm_l key fm_l
left_ok0 fm_l key EmptyFM True
left_ok0 fm_l key (Branch left_key vw vx vy vz
let 
biggest_left_key fst (findMax fm_l)
in biggest_left_key < key
left_size sizeFM fm_l
right_ok right_ok0 fm_r key fm_r
right_ok0 fm_r key EmptyFM True
right_ok0 fm_r key (Branch right_key wu wv ww wx
let 
smallest_right_key fst (findMin fm_r)
in key < smallest_right_key
right_size sizeFM fm_r
unbox :: Int  ->  Int
unbox x x

  sIZE_RATIO :: Int
sIZE_RATIO 5

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch xx xy size xz yusize

  unitFM :: a  ->  b  ->  FiniteMap a b
unitFM key elt Branch key elt 1 emptyFM emptyFM


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Let/Where Reductions:
The bindings of the following Let/Where expression
let 
result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result
where 
balance_ok  = True
left_ok  = left_ok0 fm_l key fm_l
left_ok0 fm_l key EmptyFM = True
left_ok0 fm_l key (Branch left_key vw vx vy vz) = 
let 
biggest_left_key  = fst (findMax fm_l)
in biggest_left_key < key
left_size  = sizeFM fm_l
right_ok  = right_ok0 fm_r key fm_r
right_ok0 fm_r key EmptyFM = True
right_ok0 fm_r key (Branch right_key wu wv ww wx) = 
let 
smallest_right_key  = fst (findMin fm_r)
in key < smallest_right_key
right_size  = sizeFM fm_r
unbox x = x

are unpacked to the following functions on top level
mkBranchRight_ok wxw wxx wxy = mkBranchRight_ok0 wxw wxx wxy wxw wxx wxw

mkBranchRight_size wxw wxx wxy = sizeFM wxw

mkBranchLeft_ok0 wxw wxx wxy fm_l key EmptyFM = True
mkBranchLeft_ok0 wxw wxx wxy fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

mkBranchRight_ok0 wxw wxx wxy fm_r key EmptyFM = True
mkBranchRight_ok0 wxw wxx wxy fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

mkBranchLeft_size wxw wxx wxy = sizeFM wxy

mkBranchBalance_ok wxw wxx wxy = True

mkBranchUnbox wxw wxx wxy x = x

mkBranchLeft_ok wxw wxx wxy = mkBranchLeft_ok0 wxw wxx wxy wxy wxx wxy

The bindings of the following Let/Where expression
let 
result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result

are unpacked to the following functions on top level
mkBranchResult wxz wyu wyv wyw = Branch wxz wyu (mkBranchUnbox wyv wxz wyw (1 + mkBranchLeft_size wyv wxz wyw + mkBranchRight_size wyv wxz wyw)) wyw wyv

The bindings of the following Let/Where expression
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2)
where 
double_L fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlrfm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)
mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr)
mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)
mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R
mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L
mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise
mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R
mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r)
mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l)
single_L fm_l (Branch key_r elt_r vuu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rlfm_rr
single_R (Branch key_l elt_l yv fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

are unpacked to the following functions on top level
mkBalBranch6Single_L wyx wyy wyz wzu fm_l (Branch key_r elt_r vuu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 wyx wyy fm_l fm_rlfm_rr

mkBalBranch6Double_L wyx wyy wyz wzu fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlrfm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 wyx wyy fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

mkBalBranch6MkBalBranch2 wyx wyy wyz wzu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

mkBalBranch6Size_l wyx wyy wyz wzu = sizeFM wyz

mkBalBranch6MkBalBranch0 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rr)

mkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

mkBalBranch6Double_R wyx wyy wyz wzu (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 wyx wyy fm_lrr fm_r)

mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 wyx wyy wyz wzu fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R (mkBalBranch6Size_l wyx wyy wyz wzu > sIZE_RATIO * mkBalBranch6Size_r wyx wyy wyz wzu)

mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr True = mkBalBranch6Single_L wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr False = mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr otherwise

mkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

mkBalBranch6Size_r wyx wyy wyz wzu = sizeFM wzu

mkBalBranch6Single_R wyx wyy wyz wzu (Branch key_l elt_l yv fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 wyx wyy fm_lr fm_r)

mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr True = mkBalBranch6Double_R wyx wyy wyz wzu fm_L fm_R

mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr True = mkBalBranch6Single_R wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr False = mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr otherwise

mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 wyx wyy wyz wzu key elt fm_L fm_R otherwise

mkBalBranch6MkBalBranch5 wyx wyy wyz wzu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 wyx wyy wyz wzu key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R (mkBalBranch6Size_r wyx wyy wyz wzu > sIZE_RATIO * mkBalBranch6Size_l wyx wyy wyz wzu)

mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr True = mkBalBranch6Double_L wyx wyy wyz wzu fm_L fm_R

mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lr)

The bindings of the following Let/Where expression
foldl add fm key_elt_pairs
where 
add fmap (key,elt) = addToFM_C combiner fmap key elt

are unpacked to the following functions on top level
addListToFM_CAdd wzv fmap (key,elt) = addToFM_C wzv fmap key elt

The bindings of the following Let/Where expression
let 
biggest_left_key  = fst (findMax fm_l)
in biggest_left_key < key

are unpacked to the following functions on top level
mkBranchLeft_ok0Biggest_left_key wzw = fst (findMax wzw)

The bindings of the following Let/Where expression
let 
smallest_right_key  = fst (findMin fm_r)
in key < smallest_right_key

are unpacked to the following functions on top level
mkBranchRight_ok0Smallest_right_key wzx = fst (findMin wzx)

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 wzy wzz = gcd wzy wzz

reduce2Reduce0 wzy wzz x y True = x `quot` reduce2D wzy wzz :% (y `quot` reduce2D wzy wzz)

reduce2Reduce1 wzy wzz x y True = error []
reduce2Reduce1 wzy wzz x y False = reduce2Reduce0 wzy wzz x y otherwise

The bindings of the following Let/Where expression
gcd' (abs x) (abs y)
where 
gcd' x wuy = gcd'2 x wuy
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x wuy = x
gcd'1 wuz wvu wvv = gcd'0 wvu wvv
gcd'2 x wuy = gcd'1 (wuy == 0) x wuy
gcd'2 wvw wvx = gcd'0 wvw wvx

are unpacked to the following functions on top level
gcd0Gcd'1 True x wuy = x
gcd0Gcd'1 wuz wvu wvv = gcd0Gcd'0 wvu wvv

gcd0Gcd' x wuy = gcd0Gcd'2 x wuy
gcd0Gcd' x y = gcd0Gcd'0 x y

gcd0Gcd'2 x wuy = gcd0Gcd'1 (wuy == 0) x wuy
gcd0Gcd'2 wvw wvx = gcd0Gcd'0 wvw wvx

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
  ((addListToFM :: Ord a => FiniteMap (Maybe a) b  ->  [(Maybe a,b)]  ->  FiniteMap (Maybe a) b) :: Ord a => FiniteMap (Maybe a) b  ->  [(Maybe a,b)]  ->  FiniteMap (Maybe 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 b a) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  addListToFM :: Ord a => FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b
addListToFM_C combiner fm key_elt_pairs foldl (addListToFM_CAdd combiner) fm key_elt_pairs

  
addListToFM_CAdd wzv fmap (key,eltaddToFM_C wzv fmap key elt

  addToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b
addToFM_C combiner EmptyFM key elt addToFM_C4 combiner EmptyFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_key new_elt addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt

  
addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True Branch new_key (combiner elt new_elt) size fm_l fm_r

  
addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise

  
addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key)

  
addToFM_C3 combiner (Branch key elt size fm_l fm_rnew_key new_elt addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key)

  
addToFM_C4 combiner EmptyFM key elt unitFM key elt
addToFM_C4 wuu wuv wuw wux addToFM_C3 wuu wuv wuw wux

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

  findMax :: FiniteMap a b  ->  (a,b)
findMax (Branch key elt vuv vuw EmptyFM(key,elt)
findMax (Branch key elt vux vuy fm_rfindMax fm_r

  findMin :: FiniteMap a b  ->  (a,b)
findMin (Branch key elt wz EmptyFM xu(key,elt)
findMin (Branch key elt xv fm_l xwfindMin fm_l

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

  
fmToList0 key elt rest (key,elt: rest

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

  mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBalBranch key elt fm_L fm_R mkBalBranch6 key elt fm_L fm_R

  
mkBalBranch6 key elt fm_L fm_R mkBalBranch6MkBalBranch5 key elt fm_L fm_R key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_L fm_R + mkBalBranch6Size_r key elt fm_L fm_R < 2)

  
mkBalBranch6Double_L wyx wyy wyz wzu fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlr) fm_rrmkBranch 5 key_rl elt_rl (mkBranch 6 wyx wyy fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R wyx wyy wyz wzu (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 wyx wyy fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rrmkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr True mkBalBranch6Double_L wyx wyy wyz wzu fm_L fm_R

  
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr True mkBalBranch6Single_L wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr False mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rrmkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr True mkBalBranch6Double_R wyx wyy wyz wzu fm_L fm_R

  
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr True mkBalBranch6Single_R wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr False mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 wyx wyy wyz wzu key elt fm_L fm_R True mkBranch 2 key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R True mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R False mkBalBranch6MkBalBranch2 wyx wyy wyz wzu key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R True mkBalBranch6MkBalBranch0 wyx wyy wyz wzu fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R False mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R (mkBalBranch6Size_l wyx wyy wyz wzu > sIZE_RATIO * mkBalBranch6Size_r wyx wyy wyz wzu)

  
mkBalBranch6MkBalBranch5 wyx wyy wyz wzu key elt fm_L fm_R True mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 wyx wyy wyz wzu key elt fm_L fm_R False mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R (mkBalBranch6Size_r wyx wyy wyz wzu > sIZE_RATIO * mkBalBranch6Size_l wyx wyy wyz wzu)

  
mkBalBranch6Single_L wyx wyy wyz wzu fm_l (Branch key_r elt_r vuu fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 wyx wyy fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R wyx wyy wyz wzu (Branch key_l elt_l yv fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 wyx wyy fm_lr fm_r)

  
mkBalBranch6Size_l wyx wyy wyz wzu sizeFM wyz

  
mkBalBranch6Size_r wyx wyy wyz wzu sizeFM wzu

  mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkBranch which key elt fm_l fm_r mkBranchResult key elt fm_r fm_l

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxy wxx wxy

  
mkBranchLeft_ok0 wxw wxx wxy fm_l key EmptyFM True
mkBranchLeft_ok0 wxw wxx wxy fm_l key (Branch left_key vw vx vy vzmkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key wzw fst (findMax wzw)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxy

  
mkBranchResult wxz wyu wyv wyw Branch wxz wyu (mkBranchUnbox wyv wxz wyw (1 + mkBranchLeft_size wyv wxz wyw + mkBranchRight_size wyv wxz wyw)) wyw wyv

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxw wxx wxw

  
mkBranchRight_ok0 wxw wxx wxy fm_r key EmptyFM True
mkBranchRight_ok0 wxw wxx wxy fm_r key (Branch right_key wu wv ww wxkey < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key wzx fst (findMin wzx)

  
mkBranchRight_size wxw wxx wxy sizeFM wxw

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)))
mkBranchUnbox wxw wxx wxy x x

  sIZE_RATIO :: Int
sIZE_RATIO 5

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch xx xy size xz yusize

  unitFM :: b  ->  a  ->  FiniteMap b a
unitFM key elt Branch key elt 1 emptyFM emptyFM


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
  (addListToFM :: Ord b => FiniteMap (Maybe b) a  ->  [(Maybe b,a)]  ->  FiniteMap (Maybe b) a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b


  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  addListToFM :: Ord a => FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b
addListToFM_C combiner fm key_elt_pairs foldl (addListToFM_CAdd combiner) fm key_elt_pairs

  
addListToFM_CAdd wzv fmap (key,eltaddToFM_C wzv fmap key elt

  addToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM_C combiner EmptyFM key elt addToFM_C4 combiner EmptyFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_key new_elt addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt

  
addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True Branch new_key (combiner elt new_elt) size fm_l fm_r

  
addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise

  
addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key)

  
addToFM_C3 combiner (Branch key elt size fm_l fm_rnew_key new_elt addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key)

  
addToFM_C4 combiner EmptyFM key elt unitFM key elt
addToFM_C4 wuu wuv wuw wux addToFM_C3 wuu wuv wuw wux

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vuv vuw EmptyFM(key,elt)
findMax (Branch key elt vux vuy fm_rfindMax fm_r

  findMin :: FiniteMap b a  ->  (b,a)
findMin (Branch key elt wz EmptyFM xu(key,elt)
findMin (Branch key elt xv fm_l xwfindMin fm_l

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

  
fmToList0 key elt rest (key,elt: rest

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

  mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkBalBranch key elt fm_L fm_R mkBalBranch6 key elt fm_L fm_R

  
mkBalBranch6 key elt fm_L fm_R mkBalBranch6MkBalBranch5 key elt fm_L fm_R key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_L fm_R + mkBalBranch6Size_r key elt fm_L fm_R < Pos (Succ (Succ Zero)))

  
mkBalBranch6Double_L wyx wyy wyz wzu fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlr) fm_rrmkBranch (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) key_rl elt_rl (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) wyx wyy fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R wyx wyy wyz wzu (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) key_lr elt_lr (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) key_l elt_l fm_ll fm_lrl) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) wyx wyy fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rrmkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr True mkBalBranch6Double_L wyx wyy wyz wzu fm_L fm_R

  
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr True mkBalBranch6Single_L wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr False mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rrmkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr True mkBalBranch6Double_R wyx wyy wyz wzu fm_L fm_R

  
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr True mkBalBranch6Single_R wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr False mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 wyx wyy wyz wzu key elt fm_L fm_R True mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R True mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R False mkBalBranch6MkBalBranch2 wyx wyy wyz wzu key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R True mkBalBranch6MkBalBranch0 wyx wyy wyz wzu fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R False mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R (mkBalBranch6Size_l wyx wyy wyz wzu > sIZE_RATIO * mkBalBranch6Size_r wyx wyy wyz wzu)

  
mkBalBranch6MkBalBranch5 wyx wyy wyz wzu key elt fm_L fm_R True mkBranch (Pos (Succ Zero)) key elt fm_L fm_R
mkBalBranch6MkBalBranch5 wyx wyy wyz wzu key elt fm_L fm_R False mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R (mkBalBranch6Size_r wyx wyy wyz wzu > sIZE_RATIO * mkBalBranch6Size_l wyx wyy wyz wzu)

  
mkBalBranch6Single_L wyx wyy wyz wzu fm_l (Branch key_r elt_r vuu fm_rl fm_rrmkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) wyx wyy fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R wyx wyy wyz wzu (Branch key_l elt_l yv fm_ll fm_lrfm_r mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))) key_l elt_l fm_ll (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) wyx wyy fm_lr fm_r)

  
mkBalBranch6Size_l wyx wyy wyz wzu sizeFM wyz

  
mkBalBranch6Size_r wyx wyy wyz wzu sizeFM wzu

  mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBranch which key elt fm_l fm_r mkBranchResult key elt fm_r fm_l

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxy wxx wxy

  
mkBranchLeft_ok0 wxw wxx wxy fm_l key EmptyFM True
mkBranchLeft_ok0 wxw wxx wxy fm_l key (Branch left_key vw vx vy vzmkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key wzw fst (findMax wzw)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxy

  
mkBranchResult wxz wyu wyv wyw Branch wxz wyu (mkBranchUnbox wyv wxz wyw (Pos (Succ Zero+ mkBranchLeft_size wyv wxz wyw + mkBranchRight_size wyv wxz wyw)) wyw wyv

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxw wxx wxw

  
mkBranchRight_ok0 wxw wxx wxy fm_r key EmptyFM True
mkBranchRight_ok0 wxw wxx wxy fm_r key (Branch right_key wu wv ww wxkey < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key wzx fst (findMin wzx)

  
mkBranchRight_size wxw wxx wxy sizeFM wxw

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)))
mkBranchUnbox wxw wxx wxy x x

  sIZE_RATIO :: Int
sIZE_RATIO Pos (Succ (Succ (Succ (Succ (Succ Zero)))))

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM Pos Zero
sizeFM (Branch xx xy size xz yusize

  unitFM :: a  ->  b  ->  FiniteMap a b
unitFM key elt Branch key elt (Pos (Succ Zero)) emptyFM emptyFM


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
                                  ↳ QDP
                                  ↳ QDP

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

new_primEqNat(Succ(xuu400000), Succ(xuu30000)) → new_primEqNat(xuu400000, xuu30000)

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

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



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

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

new_primCmpNat(Succ(xuu30000), Succ(xuu31000)) → new_primCmpNat(xuu30000, xuu31000)

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

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



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

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

new_primMinusNat(Succ(xuu25200), Succ(xuu9400)) → new_primMinusNat(xuu25200, xuu9400)

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
                                  ↳ QDP
                                  ↳ QDP

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

new_primPlusNat(Succ(xuu25200), Succ(xuu9400)) → new_primPlusNat(xuu25200, xuu9400)

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

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



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

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

new_primMulNat(Succ(xuu4000000), Succ(xuu300000)) → new_primMulNat(xuu4000000, Succ(xuu300000))

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

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



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

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

new_esEs1(Right(xuu40000), Right(xuu3000), hd, app(ty_Maybe, bae)) → new_esEs3(xuu40000, xuu3000, bae)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), cb, cc, app(app(ty_Either, da), db)) → new_esEs1(xuu40002, xuu3002, da, db)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), app(ty_Maybe, ga), cc, dg) → new_esEs3(xuu40000, xuu3000, ga)
new_esEs1(Left(xuu40000), Left(xuu3000), app(app(app(ty_@3, gd), ge), gf), gc) → new_esEs0(xuu40000, xuu3000, gd, ge, gf)
new_esEs2(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), baf, app(app(ty_@2, bbe), bbf)) → new_esEs2(xuu40001, xuu3001, bbe, bbf)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), app(app(ty_Either, fd), ff), cc, dg) → new_esEs1(xuu40000, xuu3000, fd, ff)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), cb, app(app(ty_@2, ee), ef), dg) → new_esEs2(xuu40001, xuu3001, ee, ef)
new_esEs2(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), app(ty_Maybe, bda), bca) → new_esEs3(xuu40000, xuu3000, bda)
new_esEs1(Right(xuu40000), Right(xuu3000), hd, app(app(app(ty_@3, hf), hg), hh)) → new_esEs0(xuu40000, xuu3000, hf, hg, hh)
new_esEs(:(xuu40000, xuu40001), :(xuu3000, xuu3001), app(app(ty_@2, bg), bh)) → new_esEs2(xuu40000, xuu3000, bg, bh)
new_esEs2(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), baf, app(ty_Maybe, bbg)) → new_esEs3(xuu40001, xuu3001, bbg)
new_esEs2(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), app(app(ty_@2, bcg), bch), bca) → new_esEs2(xuu40000, xuu3000, bcg, bch)
new_esEs1(Left(xuu40000), Left(xuu3000), app(app(ty_Either, gg), gh), gc) → new_esEs1(xuu40000, xuu3000, gg, gh)
new_esEs1(Right(xuu40000), Right(xuu3000), hd, app(app(ty_Either, baa), bab)) → new_esEs1(xuu40000, xuu3000, baa, bab)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), cb, app(app(app(ty_@3, dh), ea), eb), dg) → new_esEs0(xuu40001, xuu3001, dh, ea, eb)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), cb, cc, app(ty_[], cd)) → new_esEs(xuu40002, xuu3002, cd)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), app(app(ty_@2, fg), fh), cc, dg) → new_esEs2(xuu40000, xuu3000, fg, fh)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), cb, app(app(ty_Either, ec), ed), dg) → new_esEs1(xuu40001, xuu3001, ec, ed)
new_esEs1(Left(xuu40000), Left(xuu3000), app(app(ty_@2, ha), hb), gc) → new_esEs2(xuu40000, xuu3000, ha, hb)
new_esEs3(Just(xuu40000), Just(xuu3000), app(app(ty_@2, bdh), bea)) → new_esEs2(xuu40000, xuu3000, bdh, bea)
new_esEs3(Just(xuu40000), Just(xuu3000), app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs0(xuu40000, xuu3000, bdc, bdd, bde)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), cb, app(ty_Maybe, eg), dg) → new_esEs3(xuu40001, xuu3001, eg)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), cb, cc, app(ty_Maybe, de)) → new_esEs3(xuu40002, xuu3002, de)
new_esEs2(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), baf, app(app(ty_Either, bbc), bbd)) → new_esEs1(xuu40001, xuu3001, bbc, bbd)
new_esEs3(Just(xuu40000), Just(xuu3000), app(ty_[], bdb)) → new_esEs(xuu40000, xuu3000, bdb)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), cb, cc, app(app(ty_@2, dc), dd)) → new_esEs2(xuu40002, xuu3002, dc, dd)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), app(ty_[], eh), cc, dg) → new_esEs(xuu40000, xuu3000, eh)
new_esEs2(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), baf, app(app(app(ty_@3, bah), bba), bbb)) → new_esEs0(xuu40001, xuu3001, bah, bba, bbb)
new_esEs(:(xuu40000, xuu40001), :(xuu3000, xuu3001), h) → new_esEs(xuu40001, xuu3001, h)
new_esEs2(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), baf, app(ty_[], bag)) → new_esEs(xuu40001, xuu3001, bag)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), cb, cc, app(app(app(ty_@3, ce), cf), cg)) → new_esEs0(xuu40002, xuu3002, ce, cf, cg)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), cb, app(ty_[], df), dg) → new_esEs(xuu40001, xuu3001, df)
new_esEs1(Right(xuu40000), Right(xuu3000), hd, app(app(ty_@2, bac), bad)) → new_esEs2(xuu40000, xuu3000, bac, bad)
new_esEs2(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), app(app(app(ty_@3, bcb), bcc), bcd), bca) → new_esEs0(xuu40000, xuu3000, bcb, bcc, bcd)
new_esEs3(Just(xuu40000), Just(xuu3000), app(ty_Maybe, beb)) → new_esEs3(xuu40000, xuu3000, beb)
new_esEs(:(xuu40000, xuu40001), :(xuu3000, xuu3001), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(xuu40000, xuu3000, bb, bc, bd)
new_esEs(:(xuu40000, xuu40001), :(xuu3000, xuu3001), app(ty_Maybe, ca)) → new_esEs3(xuu40000, xuu3000, ca)
new_esEs1(Left(xuu40000), Left(xuu3000), app(ty_Maybe, hc), gc) → new_esEs3(xuu40000, xuu3000, hc)
new_esEs2(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), app(ty_[], bbh), bca) → new_esEs(xuu40000, xuu3000, bbh)
new_esEs(:(xuu40000, xuu40001), :(xuu3000, xuu3001), app(app(ty_Either, be), bf)) → new_esEs1(xuu40000, xuu3000, be, bf)
new_esEs1(Right(xuu40000), Right(xuu3000), hd, app(ty_[], he)) → new_esEs(xuu40000, xuu3000, he)
new_esEs1(Left(xuu40000), Left(xuu3000), app(ty_[], gb), gc) → new_esEs(xuu40000, xuu3000, gb)
new_esEs3(Just(xuu40000), Just(xuu3000), app(app(ty_Either, bdf), bdg)) → new_esEs1(xuu40000, xuu3000, bdf, bdg)
new_esEs2(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), app(app(ty_Either, bce), bcf), bca) → new_esEs1(xuu40000, xuu3000, bce, bcf)
new_esEs(:(xuu40000, xuu40001), :(xuu3000, xuu3001), app(ty_[], ba)) → new_esEs(xuu40000, xuu3000, ba)
new_esEs0(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), app(app(app(ty_@3, fa), fb), fc), cc, dg) → new_esEs0(xuu40000, xuu3000, fa, fb, fc)

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

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



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

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

new_ltEs1(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), gb, app(app(ty_@2, gg), gh)) → new_ltEs1(xuu30001, xuu31001, gg, gh)
new_ltEs3(Left(xuu30000), Left(xuu31000), app(app(ty_Either, bcg), bch), bcb) → new_ltEs3(xuu30000, xuu31000, bcg, bch)
new_compare21(Just(@2(xuu30000, xuu30001)), Just(@2(xuu31000, xuu31001)), False, app(app(ty_@2, gb), app(app(app(ty_@3, gc), gd), ge))) → new_ltEs(xuu30001, xuu31001, gc, gd, ge)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), bc, bd, app(ty_Maybe, cc)) → new_ltEs2(xuu30002, xuu31002, cc)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, app(ty_Maybe, ed)), bd), db)) → new_compare21(xuu30000, xuu31000, new_esEs6(xuu30000, xuu31000, ed), ed)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, bc), app(ty_Maybe, df)), db)) → new_lt2(xuu30001, xuu31001, df)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, app(ty_[], ea)), bd), db)) → new_compare(xuu30000, xuu31000, ea)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, app(app(app(ty_@3, h), ba), bb)), bd), db)) → new_compare2(xuu30000, xuu31000, new_esEs4(xuu30000, xuu31000, h, ba, bb), h, ba, bb)
new_compare20(xuu30000, xuu31000, False, eb, ec) → new_ltEs1(xuu30000, xuu31000, eb, ec)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), app(ty_Maybe, ed), bd, db) → new_compare21(xuu30000, xuu31000, new_esEs6(xuu30000, xuu31000, ed), ed)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), bc, bd, app(ty_[], bh)) → new_ltEs0(xuu30002, xuu31002, bh)
new_ltEs1(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), gb, app(ty_Maybe, ha)) → new_ltEs2(xuu30001, xuu31001, ha)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), bc, bd, app(app(ty_@2, ca), cb)) → new_ltEs1(xuu30002, xuu31002, ca, cb)
new_lt3(xuu30000, xuu31000, ee, ef) → new_compare22(xuu30000, xuu31000, new_esEs7(xuu30000, xuu31000, ee, ef), ee, ef)
new_primCompAux(xuu30000, xuu31000, xuu174, app(ty_[], fc)) → new_compare(xuu30000, xuu31000, fc)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, bc), app(ty_[], dc)), db)) → new_lt0(xuu30001, xuu31001, dc)
new_lt0(xuu30000, xuu31000, ea) → new_compare(xuu30000, xuu31000, ea)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, bc), app(app(ty_@2, dd), de)), db)) → new_lt1(xuu30001, xuu31001, dd, de)
new_compare21(Just(Left(xuu30000)), Just(Left(xuu31000)), False, app(app(ty_Either, app(app(ty_Either, bcg), bch)), bcb)) → new_ltEs3(xuu30000, xuu31000, bcg, bch)
new_primCompAux(xuu30000, xuu31000, xuu174, app(app(ty_Either, fh), ga)) → new_compare5(xuu30000, xuu31000, fh, ga)
new_lt2(xuu30000, xuu31000, ed) → new_compare21(xuu30000, xuu31000, new_esEs6(xuu30000, xuu31000, ed), ed)
new_ltEs3(Right(xuu30000), Right(xuu31000), bda, app(app(ty_Either, bea), beb)) → new_ltEs3(xuu30000, xuu31000, bea, beb)
new_compare21(Just(@2(xuu30000, xuu30001)), Just(@2(xuu31000, xuu31001)), False, app(app(ty_@2, gb), app(app(ty_@2, gg), gh))) → new_ltEs1(xuu30001, xuu31001, gg, gh)
new_compare21(Just(Right(xuu30000)), Just(Right(xuu31000)), False, app(app(ty_Either, bda), app(ty_Maybe, bdh))) → new_ltEs2(xuu30000, xuu31000, bdh)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, bc), bd), app(app(ty_@2, ca), cb))) → new_ltEs1(xuu30002, xuu31002, ca, cb)
new_ltEs3(Left(xuu30000), Left(xuu31000), app(app(app(ty_@3, bbg), bbh), bca), bcb) → new_ltEs(xuu30000, xuu31000, bbg, bbh, bca)
new_compare21(Just(:(xuu30000, xuu30001)), Just(:(xuu31000, xuu31001)), False, app(ty_[], eg)) → new_primCompAux(xuu30000, xuu31000, new_compare0(xuu30001, xuu31001, eg), eg)
new_ltEs1(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), gb, app(app(app(ty_@3, gc), gd), ge)) → new_ltEs(xuu30001, xuu31001, gc, gd, ge)
new_ltEs3(Right(xuu30000), Right(xuu31000), bda, app(ty_[], bde)) → new_ltEs0(xuu30000, xuu31000, bde)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), bc, app(ty_[], dc), db) → new_lt0(xuu30001, xuu31001, dc)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), bc, app(app(ty_@2, dd), de), db) → new_lt1(xuu30001, xuu31001, dd, de)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), bc, app(app(app(ty_@3, cf), cg), da), db) → new_lt(xuu30001, xuu31001, cf, cg, da)
new_compare21(Just(Just(xuu30000)), Just(Just(xuu31000)), False, app(ty_Maybe, app(app(ty_@2, bbb), bbc))) → new_ltEs1(xuu30000, xuu31000, bbb, bbc)
new_compare21(Just(Right(xuu30000)), Just(Right(xuu31000)), False, app(app(ty_Either, bda), app(app(app(ty_@3, bdb), bdc), bdd))) → new_ltEs(xuu30000, xuu31000, bdb, bdc, bdd)
new_compare2(xuu30000, xuu31000, False, h, ba, bb) → new_ltEs(xuu30000, xuu31000, h, ba, bb)
new_compare21(Just(Left(xuu30000)), Just(Left(xuu31000)), False, app(app(ty_Either, app(app(app(ty_@3, bbg), bbh), bca)), bcb)) → new_ltEs(xuu30000, xuu31000, bbg, bbh, bca)
new_compare4(xuu30000, xuu31000, ed) → new_compare21(xuu30000, xuu31000, new_esEs6(xuu30000, xuu31000, ed), ed)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), app(ty_[], ea), bd, db) → new_compare(xuu30000, xuu31000, ea)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), app(app(app(ty_@3, h), ba), bb), bd, db) → new_compare2(xuu30000, xuu31000, new_esEs4(xuu30000, xuu31000, h, ba, bb), h, ba, bb)
new_ltEs2(Just(xuu30000), Just(xuu31000), app(ty_[], bba)) → new_ltEs0(xuu30000, xuu31000, bba)
new_compare21(Just(Just(xuu30000)), Just(Just(xuu31000)), False, app(ty_Maybe, app(ty_Maybe, bbd))) → new_ltEs2(xuu30000, xuu31000, bbd)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), bc, bd, app(app(app(ty_@3, be), bf), bg)) → new_ltEs(xuu30002, xuu31002, be, bf, bg)
new_compare21(Just(@2(xuu30000, xuu30001)), Just(@2(xuu31000, xuu31001)), False, app(app(ty_@2, app(ty_[], hh)), hg)) → new_lt0(xuu30000, xuu31000, hh)
new_compare21(Just(@2(xuu30000, xuu30001)), Just(@2(xuu31000, xuu31001)), False, app(app(ty_@2, app(app(ty_Either, bad), bae)), hg)) → new_lt3(xuu30000, xuu31000, bad, bae)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), bc, app(ty_Maybe, df), db) → new_lt2(xuu30001, xuu31001, df)
new_ltEs3(Left(xuu30000), Left(xuu31000), app(app(ty_@2, bcd), bce), bcb) → new_ltEs1(xuu30000, xuu31000, bcd, bce)
new_compare21(Just(Left(xuu30000)), Just(Left(xuu31000)), False, app(app(ty_Either, app(app(ty_@2, bcd), bce)), bcb)) → new_ltEs1(xuu30000, xuu31000, bcd, bce)
new_compare21(Just(Just(xuu30000)), Just(Just(xuu31000)), False, app(ty_Maybe, app(app(app(ty_@3, baf), bag), bah))) → new_ltEs(xuu30000, xuu31000, baf, bag, bah)
new_compare21(Just(@2(xuu30000, xuu30001)), Just(@2(xuu31000, xuu31001)), False, app(app(ty_@2, gb), app(app(ty_Either, hb), hc))) → new_ltEs3(xuu30001, xuu31001, hb, hc)
new_compare21(Just(@2(xuu30000, xuu30001)), Just(@2(xuu31000, xuu31001)), False, app(app(ty_@2, app(app(ty_@2, baa), bab)), hg)) → new_lt1(xuu30000, xuu31000, baa, bab)
new_compare21(Just(@2(xuu30000, xuu30001)), Just(@2(xuu31000, xuu31001)), False, app(app(ty_@2, app(app(app(ty_@3, hd), he), hf)), hg)) → new_lt(xuu30000, xuu31000, hd, he, hf)
new_ltEs2(Just(xuu30000), Just(xuu31000), app(app(ty_@2, bbb), bbc)) → new_ltEs1(xuu30000, xuu31000, bbb, bbc)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, bc), bd), app(app(ty_Either, cd), ce))) → new_ltEs3(xuu30002, xuu31002, cd, ce)
new_ltEs0(:(xuu30000, xuu30001), :(xuu31000, xuu31001), eg) → new_compare(xuu30001, xuu31001, eg)
new_compare22(xuu30000, xuu31000, False, ee, ef) → new_ltEs3(xuu30000, xuu31000, ee, ef)
new_ltEs1(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), app(ty_[], hh), hg) → new_lt0(xuu30000, xuu31000, hh)
new_lt1(xuu30000, xuu31000, eb, ec) → new_compare20(xuu30000, xuu31000, new_esEs5(xuu30000, xuu31000, eb, ec), eb, ec)
new_primCompAux(xuu30000, xuu31000, xuu174, app(app(app(ty_@3, eh), fa), fb)) → new_compare1(xuu30000, xuu31000, eh, fa, fb)
new_primCompAux(xuu30000, xuu31000, xuu174, app(app(ty_@2, fd), ff)) → new_compare3(xuu30000, xuu31000, fd, ff)
new_ltEs3(Left(xuu30000), Left(xuu31000), app(ty_[], bcc), bcb) → new_ltEs0(xuu30000, xuu31000, bcc)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), app(app(ty_@2, eb), ec), bd, db) → new_compare20(xuu30000, xuu31000, new_esEs5(xuu30000, xuu31000, eb, ec), eb, ec)
new_compare21(Just(@2(xuu30000, xuu30001)), Just(@2(xuu31000, xuu31001)), False, app(app(ty_@2, app(ty_Maybe, bac)), hg)) → new_lt2(xuu30000, xuu31000, bac)
new_compare3(xuu30000, xuu31000, eb, ec) → new_compare20(xuu30000, xuu31000, new_esEs5(xuu30000, xuu31000, eb, ec), eb, ec)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, app(app(ty_@2, eb), ec)), bd), db)) → new_compare20(xuu30000, xuu31000, new_esEs5(xuu30000, xuu31000, eb, ec), eb, ec)
new_ltEs2(Just(xuu30000), Just(xuu31000), app(app(ty_Either, bbe), bbf)) → new_ltEs3(xuu30000, xuu31000, bbe, bbf)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, bc), app(app(ty_Either, dg), dh)), db)) → new_lt3(xuu30001, xuu31001, dg, dh)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, bc), bd), app(ty_[], bh))) → new_ltEs0(xuu30002, xuu31002, bh)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, bc), app(app(app(ty_@3, cf), cg), da)), db)) → new_lt(xuu30001, xuu31001, cf, cg, da)
new_lt(xuu30000, xuu31000, h, ba, bb) → new_compare2(xuu30000, xuu31000, new_esEs4(xuu30000, xuu31000, h, ba, bb), h, ba, bb)
new_compare21(Just(:(xuu30000, xuu30001)), Just(:(xuu31000, xuu31001)), False, app(ty_[], eg)) → new_compare(xuu30001, xuu31001, eg)
new_compare1(xuu30000, xuu31000, h, ba, bb) → new_compare2(xuu30000, xuu31000, new_esEs4(xuu30000, xuu31000, h, ba, bb), h, ba, bb)
new_compare21(Just(Right(xuu30000)), Just(Right(xuu31000)), False, app(app(ty_Either, bda), app(app(ty_Either, bea), beb))) → new_ltEs3(xuu30000, xuu31000, bea, beb)
new_ltEs1(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), gb, app(ty_[], gf)) → new_ltEs0(xuu30001, xuu31001, gf)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), bc, bd, app(app(ty_Either, cd), ce)) → new_ltEs3(xuu30002, xuu31002, cd, ce)
new_ltEs0(:(xuu30000, xuu30001), :(xuu31000, xuu31001), eg) → new_primCompAux(xuu30000, xuu31000, new_compare0(xuu30001, xuu31001, eg), eg)
new_ltEs1(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), app(app(ty_Either, bad), bae), hg) → new_lt3(xuu30000, xuu31000, bad, bae)
new_ltEs3(Right(xuu30000), Right(xuu31000), bda, app(ty_Maybe, bdh)) → new_ltEs2(xuu30000, xuu31000, bdh)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, bc), bd), app(app(app(ty_@3, be), bf), bg))) → new_ltEs(xuu30002, xuu31002, be, bf, bg)
new_compare21(Just(@2(xuu30000, xuu30001)), Just(@2(xuu31000, xuu31001)), False, app(app(ty_@2, gb), app(ty_Maybe, ha))) → new_ltEs2(xuu30001, xuu31001, ha)
new_ltEs1(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), app(app(ty_@2, baa), bab), hg) → new_lt1(xuu30000, xuu31000, baa, bab)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), bc, app(app(ty_Either, dg), dh), db) → new_lt3(xuu30001, xuu31001, dg, dh)
new_compare21(Just(Right(xuu30000)), Just(Right(xuu31000)), False, app(app(ty_Either, bda), app(ty_[], bde))) → new_ltEs0(xuu30000, xuu31000, bde)
new_compare21(Just(Left(xuu30000)), Just(Left(xuu31000)), False, app(app(ty_Either, app(ty_Maybe, bcf)), bcb)) → new_ltEs2(xuu30000, xuu31000, bcf)
new_ltEs3(Right(xuu30000), Right(xuu31000), bda, app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs(xuu30000, xuu31000, bdb, bdc, bdd)
new_ltEs2(Just(xuu30000), Just(xuu31000), app(ty_Maybe, bbd)) → new_ltEs2(xuu30000, xuu31000, bbd)
new_compare(:(xuu30000, xuu30001), :(xuu31000, xuu31001), eg) → new_compare(xuu30001, xuu31001, eg)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, bc), bd), app(ty_Maybe, cc))) → new_ltEs2(xuu30002, xuu31002, cc)
new_ltEs2(Just(xuu30000), Just(xuu31000), app(app(app(ty_@3, baf), bag), bah)) → new_ltEs(xuu30000, xuu31000, baf, bag, bah)
new_compare21(Just(Just(xuu30000)), Just(Just(xuu31000)), False, app(ty_Maybe, app(ty_[], bba))) → new_ltEs0(xuu30000, xuu31000, bba)
new_compare21(Just(Left(xuu30000)), Just(Left(xuu31000)), False, app(app(ty_Either, app(ty_[], bcc)), bcb)) → new_ltEs0(xuu30000, xuu31000, bcc)
new_compare5(xuu30000, xuu31000, ee, ef) → new_compare22(xuu30000, xuu31000, new_esEs7(xuu30000, xuu31000, ee, ef), ee, ef)
new_compare(:(xuu30000, xuu30001), :(xuu31000, xuu31001), eg) → new_primCompAux(xuu30000, xuu31000, new_compare0(xuu30001, xuu31001, eg), eg)
new_compare21(Just(Just(xuu30000)), Just(Just(xuu31000)), False, app(ty_Maybe, app(app(ty_Either, bbe), bbf))) → new_ltEs3(xuu30000, xuu31000, bbe, bbf)
new_compare21(Just(@3(xuu30000, xuu30001, xuu30002)), Just(@3(xuu31000, xuu31001, xuu31002)), False, app(app(app(ty_@3, app(app(ty_Either, ee), ef)), bd), db)) → new_compare22(xuu30000, xuu31000, new_esEs7(xuu30000, xuu31000, ee, ef), ee, ef)
new_ltEs1(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), app(app(app(ty_@3, hd), he), hf), hg) → new_lt(xuu30000, xuu31000, hd, he, hf)
new_ltEs1(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), gb, app(app(ty_Either, hb), hc)) → new_ltEs3(xuu30001, xuu31001, hb, hc)
new_ltEs3(Right(xuu30000), Right(xuu31000), bda, app(app(ty_@2, bdf), bdg)) → new_ltEs1(xuu30000, xuu31000, bdf, bdg)
new_primCompAux(xuu30000, xuu31000, xuu174, app(ty_Maybe, fg)) → new_compare4(xuu30000, xuu31000, fg)
new_compare21(Just(Right(xuu30000)), Just(Right(xuu31000)), False, app(app(ty_Either, bda), app(app(ty_@2, bdf), bdg))) → new_ltEs1(xuu30000, xuu31000, bdf, bdg)
new_ltEs(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), app(app(ty_Either, ee), ef), bd, db) → new_compare22(xuu30000, xuu31000, new_esEs7(xuu30000, xuu31000, ee, ef), ee, ef)
new_ltEs1(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), app(ty_Maybe, bac), hg) → new_lt2(xuu30000, xuu31000, bac)
new_ltEs3(Left(xuu30000), Left(xuu31000), app(ty_Maybe, bcf), bcb) → new_ltEs2(xuu30000, xuu31000, bcf)
new_compare21(Just(@2(xuu30000, xuu30001)), Just(@2(xuu31000, xuu31001)), False, app(app(ty_@2, gb), app(ty_[], gf))) → new_ltEs0(xuu30001, xuu31001, gf)

The TRS R consists of the following rules:

new_esEs25(xuu40001, xuu3001, ty_Char) → new_esEs19(xuu40001, xuu3001)
new_primCmpNat0(xuu3000, Succ(xuu3100)) → new_primCmpNat2(xuu3000, xuu3100)
new_ltEs6(xuu30002, xuu31002, app(app(ty_@2, ca), cb)) → new_ltEs15(xuu30002, xuu31002, ca, cb)
new_ltEs19(xuu30001, xuu31001, ty_Ordering) → new_ltEs12(xuu30001, xuu31001)
new_esEs28(xuu40000, xuu3000, app(ty_[], dbc)) → new_esEs13(xuu40000, xuu3000, dbc)
new_esEs23(xuu40000, xuu3000, app(app(ty_Either, ccd), cce)) → new_esEs7(xuu40000, xuu3000, ccd, cce)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(ty_@2, cbc), cbd)) → new_esEs5(xuu40000, xuu3000, cbc, cbd)
new_compare112(xuu130, xuu131, True, cab) → LT
new_ltEs20(xuu3000, xuu3100, ty_Char) → new_ltEs18(xuu3000, xuu3100)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(ty_Either, bfd), bfe), beg) → new_esEs7(xuu40000, xuu3000, bfd, bfe)
new_ltEs8(False, True) → True
new_esEs7(Right(xuu40000), Right(xuu3000), bga, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_esEs10(xuu30000, xuu31000, app(app(app(ty_@3, h), ba), bb)) → new_esEs4(xuu30000, xuu31000, h, ba, bb)
new_esEs27(xuu40001, xuu3001, ty_Char) → new_esEs19(xuu40001, xuu3001)
new_compare13(xuu30000, xuu31000, app(app(app(ty_@3, eh), fa), fb)) → new_compare14(xuu30000, xuu31000, eh, fa, fb)
new_ltEs10(xuu3000, xuu3100) → new_fsEs(new_compare16(xuu3000, xuu3100))
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Ordering) → new_ltEs12(xuu30000, xuu31000)
new_esEs13([], [], cbf) → True
new_ltEs12(LT, GT) → True
new_ltEs19(xuu30001, xuu31001, app(ty_[], gf)) → new_ltEs9(xuu30001, xuu31001, gf)
new_lt20(xuu30000, xuu31000, app(ty_Ratio, caa)) → new_lt16(xuu30000, xuu31000, caa)
new_lt7(xuu30001, xuu31001, ty_Bool) → new_lt11(xuu30001, xuu31001)
new_lt16(xuu30000, xuu31000, bee) → new_esEs8(new_compare8(xuu30000, xuu31000, bee), LT)
new_esEs4(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), cda, cdb, cdc) → new_asAs(new_esEs26(xuu40000, xuu3000, cda), new_asAs(new_esEs25(xuu40001, xuu3001, cdb), new_esEs24(xuu40002, xuu3002, cdc)))
new_esEs11(Integer(xuu40000), Integer(xuu3000)) → new_primEqInt(xuu40000, xuu3000)
new_esEs15(Double(xuu40000, xuu40001), Double(xuu3000, xuu3001)) → new_esEs16(new_sr0(xuu40000, xuu3000), new_sr0(xuu40001, xuu3001))
new_compare13(xuu30000, xuu31000, app(ty_Maybe, fg)) → new_compare7(xuu30000, xuu31000, fg)
new_esEs28(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs26(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_compare19(xuu30000, xuu31000, ee, ef) → new_compare23(xuu30000, xuu31000, new_esEs7(xuu30000, xuu31000, ee, ef), ee, ef)
new_ltEs19(xuu30001, xuu31001, ty_Double) → new_ltEs11(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(ty_@2, bcd), bce), bcb) → new_ltEs15(xuu30000, xuu31000, bcd, bce)
new_primMulNat0(Zero, Zero) → Zero
new_esEs27(xuu40001, xuu3001, app(app(app(ty_@3, dab), dac), dad)) → new_esEs4(xuu40001, xuu3001, dab, dac, dad)
new_ltEs12(LT, LT) → True
new_compare29(xuu30000, xuu31000, True) → EQ
new_sr(Integer(xuu300000), Integer(xuu310010)) → Integer(new_primMulInt(xuu300000, xuu310010))
new_esEs12(True, True) → True
new_ltEs6(xuu30002, xuu31002, app(app(app(ty_@3, be), bf), bg)) → new_ltEs5(xuu30002, xuu31002, be, bf, bg)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_@0) → new_ltEs10(xuu30000, xuu31000)
new_ltEs15(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), gb, hg) → new_pePe(new_lt20(xuu30000, xuu31000, gb), new_asAs(new_esEs22(xuu30000, xuu31000, gb), new_ltEs19(xuu30001, xuu31001, hg)))
new_esEs23(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_esEs7(Right(xuu40000), Right(xuu3000), bga, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Integer) → new_ltEs7(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, ty_Double) → new_ltEs11(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), bga, app(ty_Ratio, bgb)) → new_esEs17(xuu40000, xuu3000, bgb)
new_lt12(xuu30000, xuu31000, ea) → new_esEs8(new_compare0(xuu30000, xuu31000, ea), LT)
new_esEs24(xuu40002, xuu3002, ty_@0) → new_esEs14(xuu40002, xuu3002)
new_lt8(xuu30000, xuu31000, app(ty_[], ea)) → new_lt12(xuu30000, xuu31000, ea)
new_compare16(@0, @0) → EQ
new_compare8(:%(xuu30000, xuu30001), :%(xuu31000, xuu31001), ty_Integer) → new_compare9(new_sr(xuu30000, xuu31001), new_sr(xuu31000, xuu30001))
new_lt20(xuu30000, xuu31000, ty_Double) → new_lt14(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Integer) → new_lt9(xuu30000, xuu31000)
new_ltEs12(LT, EQ) → True
new_ltEs20(xuu3000, xuu3100, app(ty_[], eg)) → new_ltEs9(xuu3000, xuu3100, eg)
new_lt8(xuu30000, xuu31000, app(ty_Ratio, bee)) → new_lt16(xuu30000, xuu31000, bee)
new_ltEs11(xuu3000, xuu3100) → new_fsEs(new_compare17(xuu3000, xuu3100))
new_esEs22(xuu30000, xuu31000, app(app(ty_@2, baa), bab)) → new_esEs5(xuu30000, xuu31000, baa, bab)
new_compare0(:(xuu30000, xuu30001), :(xuu31000, xuu31001), eg) → new_primCompAux0(xuu30000, xuu31000, new_compare0(xuu30001, xuu31001, eg), eg)
new_compare210(Nothing, Nothing, False, chc) → LT
new_esEs24(xuu40002, xuu3002, app(app(ty_@2, cec), ced)) → new_esEs5(xuu40002, xuu3002, cec, ced)
new_esEs22(xuu30000, xuu31000, app(ty_Maybe, bac)) → new_esEs6(xuu30000, xuu31000, bac)
new_ltEs20(xuu3000, xuu3100, app(ty_Ratio, chb)) → new_ltEs14(xuu3000, xuu3100, chb)
new_esEs27(xuu40001, xuu3001, app(ty_Maybe, dba)) → new_esEs6(xuu40001, xuu3001, dba)
new_esEs26(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_esEs25(xuu40001, xuu3001, ty_Double) → new_esEs15(xuu40001, xuu3001)
new_compare15(xuu30000, xuu31000) → new_compare29(xuu30000, xuu31000, new_esEs12(xuu30000, xuu31000))
new_lt20(xuu30000, xuu31000, ty_Ordering) → new_lt15(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, ty_Char) → new_ltEs18(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, app(app(ty_Either, bad), bae)) → new_esEs7(xuu30000, xuu31000, bad, bae)
new_lt18(xuu30000, xuu31000) → new_esEs8(new_compare25(xuu30000, xuu31000), LT)
new_ltEs19(xuu30001, xuu31001, ty_Char) → new_ltEs18(xuu30001, xuu31001)
new_esEs7(Right(xuu40000), Right(xuu3000), bga, app(ty_Maybe, bhc)) → new_esEs6(xuu40000, xuu3000, bhc)
new_ltEs19(xuu30001, xuu31001, app(app(ty_Either, hb), hc)) → new_ltEs4(xuu30001, xuu31001, hb, hc)
new_pePe(False, xuu163) → xuu163
new_esEs7(Right(xuu40000), Right(xuu3000), bga, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_esEs7(Left(xuu40000), Right(xuu3000), bga, beg) → False
new_esEs7(Right(xuu40000), Left(xuu3000), bga, beg) → False
new_lt20(xuu30000, xuu31000, ty_Bool) → new_lt11(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, ty_Bool) → new_esEs12(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Double, bcb) → new_ltEs11(xuu30000, xuu31000)
new_compare6(xuu30000, xuu31000, eb, ec) → new_compare24(xuu30000, xuu31000, new_esEs5(xuu30000, xuu31000, eb, ec), eb, ec)
new_esEs28(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, app(app(ty_Either, dae), daf)) → new_esEs7(xuu40001, xuu3001, dae, daf)
new_esEs20(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_ltEs20(xuu3000, xuu3100, ty_@0) → new_ltEs10(xuu3000, xuu3100)
new_compare13(xuu30000, xuu31000, ty_Int) → new_compare10(xuu30000, xuu31000)
new_esEs26(xuu40000, xuu3000, app(ty_Ratio, cfh)) → new_esEs17(xuu40000, xuu3000, cfh)
new_esEs22(xuu30000, xuu31000, ty_Double) → new_esEs15(xuu30000, xuu31000)
new_esEs26(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_ltEs20(xuu3000, xuu3100, app(app(ty_Either, bda), bcb)) → new_ltEs4(xuu3000, xuu3100, bda, bcb)
new_lt20(xuu30000, xuu31000, app(app(app(ty_@3, hd), he), hf)) → new_lt10(xuu30000, xuu31000, hd, he, hf)
new_esEs28(xuu40000, xuu3000, app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs4(xuu40000, xuu3000, dbd, dbe, dbf)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Double) → new_ltEs11(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, app(app(ty_Either, bea), beb)) → new_ltEs4(xuu30000, xuu31000, bea, beb)
new_esEs22(xuu30000, xuu31000, ty_Ordering) → new_esEs8(xuu30000, xuu31000)
new_compare111(xuu30000, xuu31000, False) → GT
new_compare111(xuu30000, xuu31000, True) → LT
new_esEs26(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_ltEs4(Left(xuu30000), Right(xuu31000), bda, bcb) → True
new_esEs7(Right(xuu40000), Right(xuu3000), bga, app(app(ty_@2, bha), bhb)) → new_esEs5(xuu40000, xuu3000, bha, bhb)
new_ltEs20(xuu3000, xuu3100, ty_Ordering) → new_ltEs12(xuu3000, xuu3100)
new_primCmpInt(Neg(Succ(xuu3000)), Neg(xuu310)) → new_primCmpNat1(xuu310, xuu3000)
new_lt6(xuu300, xuu310) → new_esEs8(new_compare10(xuu300, xuu310), LT)
new_ltEs20(xuu3000, xuu3100, ty_Bool) → new_ltEs8(xuu3000, xuu3100)
new_esEs8(LT, LT) → True
new_ltEs16(Nothing, Nothing, bhe) → True
new_lt20(xuu30000, xuu31000, ty_Char) → new_lt19(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Integer, beg) → new_esEs11(xuu40000, xuu3000)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_Maybe, bcf), bcb) → new_ltEs16(xuu30000, xuu31000, bcf)
new_esEs25(xuu40001, xuu3001, ty_Ordering) → new_esEs8(xuu40001, xuu3001)
new_esEs20(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_esEs28(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_compare210(Nothing, Just(xuu3100), False, chc) → LT
new_esEs24(xuu40002, xuu3002, app(app(ty_Either, cea), ceb)) → new_esEs7(xuu40002, xuu3002, cea, ceb)
new_ltEs6(xuu30002, xuu31002, ty_Double) → new_ltEs11(xuu30002, xuu31002)
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, ty_@0) → new_ltEs10(xuu30000, xuu31000)
new_pePe(True, xuu163) → True
new_compare0([], [], eg) → EQ
new_esEs24(xuu40002, xuu3002, ty_Int) → new_esEs16(xuu40002, xuu3002)
new_primEqNat0(Zero, Zero) → True
new_ltEs19(xuu30001, xuu31001, ty_Int) → new_ltEs13(xuu30001, xuu31001)
new_compare210(Just(xuu3000), Just(xuu3100), False, chc) → new_compare112(xuu3000, xuu3100, new_ltEs20(xuu3000, xuu3100, chc), chc)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(ty_@2, bff), bfg), beg) → new_esEs5(xuu40000, xuu3000, bff, bfg)
new_esEs26(xuu40000, xuu3000, app(ty_Maybe, cha)) → new_esEs6(xuu40000, xuu3000, cha)
new_esEs14(@0, @0) → True
new_esEs9(xuu30001, xuu31001, app(app(app(ty_@3, cf), cg), da)) → new_esEs4(xuu30001, xuu31001, cf, cg, da)
new_ltEs6(xuu30002, xuu31002, ty_@0) → new_ltEs10(xuu30002, xuu31002)
new_esEs9(xuu30001, xuu31001, app(ty_Maybe, df)) → new_esEs6(xuu30001, xuu31001, df)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Float, bcb) → new_ltEs17(xuu30000, xuu31000)
new_esEs9(xuu30001, xuu31001, ty_@0) → new_esEs14(xuu30001, xuu31001)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Ordering, beg) → new_esEs8(xuu40000, xuu3000)
new_esEs24(xuu40002, xuu3002, app(ty_Ratio, cdd)) → new_esEs17(xuu40002, xuu3002, cdd)
new_compare13(xuu30000, xuu31000, ty_Integer) → new_compare9(xuu30000, xuu31000)
new_compare12(xuu30000, xuu31000, False, eb, ec) → GT
new_compare13(xuu30000, xuu31000, ty_Ordering) → new_compare18(xuu30000, xuu31000)
new_lt7(xuu30001, xuu31001, ty_Double) → new_lt14(xuu30001, xuu31001)
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, ty_Ordering) → new_ltEs12(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Int, bcb) → new_ltEs13(xuu30000, xuu31000)
new_esEs26(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3100))) → new_primCmpNat0(xuu3100, Zero)
new_esEs24(xuu40002, xuu3002, ty_Char) → new_esEs19(xuu40002, xuu3002)
new_esEs8(GT, GT) → True
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_[], bba)) → new_ltEs9(xuu30000, xuu31000, bba)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3100))) → new_primCmpNat1(Zero, xuu3100)
new_esEs7(Right(xuu40000), Right(xuu3000), bga, app(app(ty_Either, bgg), bgh)) → new_esEs7(xuu40000, xuu3000, bgg, bgh)
new_compare13(xuu30000, xuu31000, app(ty_[], fc)) → new_compare0(xuu30000, xuu31000, fc)
new_esEs12(False, False) → True
new_lt15(xuu30000, xuu31000) → new_esEs8(new_compare18(xuu30000, xuu31000), LT)
new_esEs26(xuu40000, xuu3000, app(app(app(ty_@3, cgb), cgc), cgd)) → new_esEs4(xuu40000, xuu3000, cgb, cgc, cgd)
new_ltEs20(xuu3000, xuu3100, app(app(ty_@2, gb), hg)) → new_ltEs15(xuu3000, xuu3100, gb, hg)
new_esEs7(Right(xuu40000), Right(xuu3000), bga, app(ty_[], bgc)) → new_esEs13(xuu40000, xuu3000, bgc)
new_ltEs19(xuu30001, xuu31001, app(ty_Ratio, bhh)) → new_ltEs14(xuu30001, xuu31001, bhh)
new_lt10(xuu30000, xuu31000, h, ba, bb) → new_esEs8(new_compare14(xuu30000, xuu31000, h, ba, bb), LT)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_esEs28(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_lt20(xuu30000, xuu31000, app(app(ty_Either, bad), bae)) → new_lt17(xuu30000, xuu31000, bad, bae)
new_esEs9(xuu30001, xuu31001, ty_Integer) → new_esEs11(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_@0, bcb) → new_ltEs10(xuu30000, xuu31000)
new_ltEs20(xuu3000, xuu3100, app(app(app(ty_@3, bc), bd), db)) → new_ltEs5(xuu3000, xuu3100, bc, bd, db)
new_lt8(xuu30000, xuu31000, ty_Double) → new_lt14(xuu30000, xuu31000)
new_ltEs16(Nothing, Just(xuu31000), bhe) → True
new_primEqInt(Neg(Succ(xuu400000)), Neg(Succ(xuu30000))) → new_primEqNat0(xuu400000, xuu30000)
new_esEs26(xuu40000, xuu3000, app(ty_[], cga)) → new_esEs13(xuu40000, xuu3000, cga)
new_esEs23(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs13(:(xuu40000, xuu40001), :(xuu3000, xuu3001), cbf) → new_asAs(new_esEs23(xuu40000, xuu3000, cbf), new_esEs13(xuu40001, xuu3001, cbf))
new_primPlusNat1(Succ(xuu25200), Zero) → Succ(xuu25200)
new_primPlusNat1(Zero, Succ(xuu9400)) → Succ(xuu9400)
new_ltEs6(xuu30002, xuu31002, ty_Char) → new_ltEs18(xuu30002, xuu31002)
new_lt8(xuu30000, xuu31000, app(ty_Maybe, ed)) → new_lt5(xuu30000, xuu31000, ed)
new_ltEs8(True, True) → True
new_esEs16(xuu4000, xuu300) → new_primEqInt(xuu4000, xuu300)
new_primCmpNat1(Zero, xuu3000) → LT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_Maybe, bbd)) → new_ltEs16(xuu30000, xuu31000, bbd)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Char, bcb) → new_ltEs18(xuu30000, xuu31000)
new_ltEs12(EQ, EQ) → True
new_compare13(xuu30000, xuu31000, ty_Float) → new_compare25(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, ty_Integer) → new_ltEs7(xuu30000, xuu31000)
new_lt8(xuu30000, xuu31000, ty_Integer) → new_lt9(xuu30000, xuu31000)
new_esEs21(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs28(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_primEqInt(Neg(Zero), Neg(Succ(xuu30000))) → False
new_primEqInt(Neg(Succ(xuu400000)), Neg(Zero)) → False
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(ty_Either, bcg), bch), bcb) → new_ltEs4(xuu30000, xuu31000, bcg, bch)
new_esEs8(EQ, EQ) → True
new_esEs6(Just(xuu40000), Just(xuu3000), ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs17(:%(xuu40000, xuu40001), :%(xuu3000, xuu3001), bhg) → new_asAs(new_esEs21(xuu40000, xuu3000, bhg), new_esEs20(xuu40001, xuu3001, bhg))
new_esEs23(xuu40000, xuu3000, app(app(app(ty_@3, cca), ccb), ccc)) → new_esEs4(xuu40000, xuu3000, cca, ccb, ccc)
new_compare24(xuu30000, xuu31000, True, eb, ec) → EQ
new_esEs5(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), chf, chg) → new_asAs(new_esEs28(xuu40000, xuu3000, chf), new_esEs27(xuu40001, xuu3001, chg))
new_lt20(xuu30000, xuu31000, app(ty_Maybe, bac)) → new_lt5(xuu30000, xuu31000, bac)
new_ltEs7(xuu3000, xuu3100) → new_fsEs(new_compare9(xuu3000, xuu3100))
new_ltEs13(xuu3000, xuu3100) → new_fsEs(new_compare10(xuu3000, xuu3100))
new_esEs7(Right(xuu40000), Right(xuu3000), bga, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_ltEs19(xuu30001, xuu31001, app(ty_Maybe, ha)) → new_ltEs16(xuu30001, xuu31001, ha)
new_esEs26(xuu40000, xuu3000, app(app(ty_Either, cge), cgf)) → new_esEs7(xuu40000, xuu3000, cge, cgf)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs9(xuu30001, xuu31001, ty_Float) → new_esEs18(xuu30001, xuu31001)
new_ltEs14(xuu3000, xuu3100, chb) → new_fsEs(new_compare8(xuu3000, xuu3100, chb))
new_compare23(xuu30000, xuu31000, False, ee, ef) → new_compare11(xuu30000, xuu31000, new_ltEs4(xuu30000, xuu31000, ee, ef), ee, ef)
new_compare113(xuu30000, xuu31000, False, h, ba, bb) → GT
new_esEs6(Nothing, Nothing, cac) → True
new_ltEs6(xuu30002, xuu31002, app(ty_Maybe, cc)) → new_ltEs16(xuu30002, xuu31002, cc)
new_ltEs20(xuu3000, xuu3100, app(ty_Maybe, bhe)) → new_ltEs16(xuu3000, xuu3100, bhe)
new_primEqInt(Pos(Succ(xuu400000)), Pos(Succ(xuu30000))) → new_primEqNat0(xuu400000, xuu30000)
new_lt20(xuu30000, xuu31000, app(ty_[], hh)) → new_lt12(xuu30000, xuu31000, hh)
new_lt5(xuu30000, xuu31000, ed) → new_esEs8(new_compare7(xuu30000, xuu31000, ed), LT)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_compare24(xuu30000, xuu31000, False, eb, ec) → new_compare12(xuu30000, xuu31000, new_ltEs15(xuu30000, xuu31000, eb, ec), eb, ec)
new_compare12(xuu30000, xuu31000, True, eb, ec) → LT
new_compare8(:%(xuu30000, xuu30001), :%(xuu31000, xuu31001), ty_Int) → new_compare10(new_sr0(xuu30000, xuu31001), new_sr0(xuu31000, xuu30001))
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_Ratio, cad)) → new_esEs17(xuu40000, xuu3000, cad)
new_esEs7(Right(xuu40000), Right(xuu3000), bga, app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs4(xuu40000, xuu3000, bgd, bge, bgf)
new_esEs6(Just(xuu40000), Nothing, cac) → False
new_esEs6(Nothing, Just(xuu3000), cac) → False
new_primEqNat0(Succ(xuu400000), Succ(xuu30000)) → new_primEqNat0(xuu400000, xuu30000)
new_esEs23(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, ty_Ordering) → new_esEs8(xuu40001, xuu3001)
new_lt13(xuu30000, xuu31000) → new_esEs8(new_compare16(xuu30000, xuu31000), LT)
new_lt8(xuu30000, xuu31000, ty_Bool) → new_lt11(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, ty_Double) → new_esEs15(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, ty_Bool) → new_esEs12(xuu30000, xuu31000)
new_lt14(xuu30000, xuu31000) → new_esEs8(new_compare17(xuu30000, xuu31000), LT)
new_lt7(xuu30001, xuu31001, ty_Float) → new_lt18(xuu30001, xuu31001)
new_primCompAux00(xuu180, LT) → LT
new_lt11(xuu30000, xuu31000) → new_esEs8(new_compare15(xuu30000, xuu31000), LT)
new_esEs24(xuu40002, xuu3002, ty_Ordering) → new_esEs8(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, app(ty_Ratio, bec)) → new_ltEs14(xuu30002, xuu31002, bec)
new_esEs23(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_ltEs19(xuu30001, xuu31001, ty_Bool) → new_ltEs8(xuu30001, xuu31001)
new_esEs28(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Int, beg) → new_esEs16(xuu40000, xuu3000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu30000))) → False
new_primEqInt(Pos(Succ(xuu400000)), Pos(Zero)) → False
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Float) → new_ltEs17(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, app(app(ty_Either, ee), ef)) → new_esEs7(xuu30000, xuu31000, ee, ef)
new_compare14(xuu30000, xuu31000, h, ba, bb) → new_compare28(xuu30000, xuu31000, new_esEs4(xuu30000, xuu31000, h, ba, bb), h, ba, bb)
new_ltEs19(xuu30001, xuu31001, ty_Float) → new_ltEs17(xuu30001, xuu31001)
new_lt20(xuu30000, xuu31000, app(app(ty_@2, baa), bab)) → new_lt4(xuu30000, xuu31000, baa, bab)
new_esEs23(xuu40000, xuu3000, app(app(ty_@2, ccf), ccg)) → new_esEs5(xuu40000, xuu3000, ccf, ccg)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3100))) → LT
new_compare11(xuu30000, xuu31000, True, ee, ef) → LT
new_esEs9(xuu30001, xuu31001, app(ty_[], dc)) → new_esEs13(xuu30001, xuu31001, dc)
new_primPlusNat1(Succ(xuu25200), Succ(xuu9400)) → Succ(Succ(new_primPlusNat1(xuu25200, xuu9400)))
new_primEqInt(Neg(Succ(xuu400000)), Pos(xuu3000)) → False
new_primEqInt(Pos(Succ(xuu400000)), Neg(xuu3000)) → False
new_ltEs6(xuu30002, xuu31002, ty_Ordering) → new_ltEs12(xuu30002, xuu31002)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_Ratio, bef), beg) → new_esEs17(xuu40000, xuu3000, bef)
new_compare210(xuu300, xuu310, True, chc) → EQ
new_ltEs12(GT, EQ) → False
new_esEs24(xuu40002, xuu3002, app(ty_[], cde)) → new_esEs13(xuu40002, xuu3002, cde)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_[], bcc), bcb) → new_ltEs9(xuu30000, xuu31000, bcc)
new_primCmpNat2(Zero, Succ(xuu31000)) → LT
new_lt19(xuu30000, xuu31000) → new_esEs8(new_compare26(xuu30000, xuu31000), LT)
new_esEs28(xuu40000, xuu3000, app(ty_Maybe, dcc)) → new_esEs6(xuu40000, xuu3000, dcc)
new_primEqInt(Neg(Zero), Pos(Succ(xuu30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu30000))) → False
new_primCompAux00(xuu180, EQ) → xuu180
new_esEs28(xuu40000, xuu3000, app(app(ty_Either, dbg), dbh)) → new_esEs7(xuu40000, xuu3000, dbg, dbh)
new_esEs10(xuu30000, xuu31000, ty_Int) → new_esEs16(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, app(app(ty_@2, bdf), bdg)) → new_ltEs15(xuu30000, xuu31000, bdf, bdg)
new_compare18(xuu30000, xuu31000) → new_compare27(xuu30000, xuu31000, new_esEs8(xuu30000, xuu31000))
new_esEs25(xuu40001, xuu3001, ty_@0) → new_esEs14(xuu40001, xuu3001)
new_compare13(xuu30000, xuu31000, app(app(ty_@2, fd), ff)) → new_compare6(xuu30000, xuu31000, fd, ff)
new_ltEs20(xuu3000, xuu3100, ty_Int) → new_ltEs13(xuu3000, xuu3100)
new_esEs10(xuu30000, xuu31000, ty_Char) → new_esEs19(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), bga, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_lt8(xuu30000, xuu31000, app(app(app(ty_@3, h), ba), bb)) → new_lt10(xuu30000, xuu31000, h, ba, bb)
new_compare28(xuu30000, xuu31000, False, h, ba, bb) → new_compare113(xuu30000, xuu31000, new_ltEs5(xuu30000, xuu31000, h, ba, bb), h, ba, bb)
new_esEs26(xuu40000, xuu3000, app(app(ty_@2, cgg), cgh)) → new_esEs5(xuu40000, xuu3000, cgg, cgh)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(app(ty_@3, bfa), bfb), bfc), beg) → new_esEs4(xuu40000, xuu3000, bfa, bfb, bfc)
new_esEs22(xuu30000, xuu31000, ty_Float) → new_esEs18(xuu30000, xuu31000)
new_ltEs16(Just(xuu30000), Nothing, bhe) → False
new_esEs9(xuu30001, xuu31001, ty_Ordering) → new_esEs8(xuu30001, xuu31001)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs4(Right(xuu30000), Left(xuu31000), bda, bcb) → False
new_esEs7(Right(xuu40000), Right(xuu3000), bga, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs10(xuu30000, xuu31000, ty_@0) → new_esEs14(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_Maybe, bfh), beg) → new_esEs6(xuu40000, xuu3000, bfh)
new_esEs23(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_lt8(xuu30000, xuu31000, app(app(ty_@2, eb), ec)) → new_lt4(xuu30000, xuu31000, eb, ec)
new_esEs7(Right(xuu40000), Right(xuu3000), bga, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs9(xuu30001, xuu31001, ty_Int) → new_esEs16(xuu30001, xuu31001)
new_esEs25(xuu40001, xuu3001, ty_Float) → new_esEs18(xuu40001, xuu3001)
new_esEs25(xuu40001, xuu3001, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs4(xuu40001, xuu3001, ceh, cfa, cfb)
new_esEs27(xuu40001, xuu3001, ty_@0) → new_esEs14(xuu40001, xuu3001)
new_esEs28(xuu40000, xuu3000, app(app(ty_@2, dca), dcb)) → new_esEs5(xuu40000, xuu3000, dca, dcb)
new_esEs22(xuu30000, xuu31000, ty_Integer) → new_esEs11(xuu30000, xuu31000)
new_compare0(:(xuu30000, xuu30001), [], eg) → GT
new_lt8(xuu30000, xuu31000, ty_Ordering) → new_lt15(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Int) → new_lt6(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, app(app(app(ty_@3, hd), he), hf)) → new_esEs4(xuu30000, xuu31000, hd, he, hf)
new_esEs22(xuu30000, xuu31000, app(ty_[], hh)) → new_esEs13(xuu30000, xuu31000, hh)
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, app(ty_Maybe, bdh)) → new_ltEs16(xuu30000, xuu31000, bdh)
new_lt8(xuu30000, xuu31000, ty_Int) → new_lt6(xuu30000, xuu31000)
new_lt7(xuu30001, xuu31001, ty_@0) → new_lt13(xuu30001, xuu31001)
new_compare11(xuu30000, xuu31000, False, ee, ef) → GT
new_esEs25(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_primCmpInt(Pos(Succ(xuu3000)), Neg(xuu310)) → GT
new_lt7(xuu30001, xuu31001, ty_Int) → new_lt6(xuu30001, xuu31001)
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, ty_Bool) → new_ltEs8(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, ty_Float) → new_esEs18(xuu40002, xuu3002)
new_esEs24(xuu40002, xuu3002, ty_Double) → new_esEs15(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, ty_Integer) → new_ltEs7(xuu30002, xuu31002)
new_primMulInt(Pos(xuu400000), Pos(xuu30000)) → Pos(new_primMulNat0(xuu400000, xuu30000))
new_esEs24(xuu40002, xuu3002, ty_Integer) → new_esEs11(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, app(app(ty_Either, cd), ce)) → new_ltEs4(xuu30002, xuu31002, cd, ce)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_@0, beg) → new_esEs14(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, ty_Double) → new_esEs15(xuu40001, xuu3001)
new_primMulInt(Neg(xuu400000), Neg(xuu30000)) → Pos(new_primMulNat0(xuu400000, xuu30000))
new_primCmpNat2(Zero, Zero) → EQ
new_compare110(xuu30000, xuu31000, True) → LT
new_ltEs12(EQ, GT) → True
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(ty_Either, bbe), bbf)) → new_ltEs4(xuu30000, xuu31000, bbe, bbf)
new_compare13(xuu30000, xuu31000, ty_@0) → new_compare16(xuu30000, xuu31000)
new_ltEs20(xuu3000, xuu3100, ty_Float) → new_ltEs17(xuu3000, xuu3100)
new_primEqNat0(Zero, Succ(xuu30000)) → False
new_primEqNat0(Succ(xuu400000), Zero) → False
new_ltEs8(False, False) → True
new_esEs25(xuu40001, xuu3001, app(ty_Ratio, cef)) → new_esEs17(xuu40001, xuu3001, cef)
new_esEs25(xuu40001, xuu3001, app(ty_Maybe, cfg)) → new_esEs6(xuu40001, xuu3001, cfg)
new_compare110(xuu30000, xuu31000, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare113(xuu30000, xuu31000, True, h, ba, bb) → LT
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Float) → new_esEs18(xuu40000, xuu3000)
new_lt9(xuu30000, xuu31000) → new_esEs8(new_compare9(xuu30000, xuu31000), LT)
new_primPlusNat0(xuu104, xuu300000) → new_primPlusNat1(xuu104, Succ(xuu300000))
new_esEs10(xuu30000, xuu31000, app(ty_[], ea)) → new_esEs13(xuu30000, xuu31000, ea)
new_primCmpNat2(Succ(xuu30000), Succ(xuu31000)) → new_primCmpNat2(xuu30000, xuu31000)
new_primCmpInt(Pos(Succ(xuu3000)), Pos(xuu310)) → new_primCmpNat0(xuu3000, xuu310)
new_lt7(xuu30001, xuu31001, app(app(ty_@2, dd), de)) → new_lt4(xuu30001, xuu31001, dd, de)
new_compare13(xuu30000, xuu31000, ty_Char) → new_compare26(xuu30000, xuu31000)
new_esEs27(xuu40001, xuu3001, app(app(ty_@2, dag), dah)) → new_esEs5(xuu40001, xuu3001, dag, dah)
new_compare28(xuu30000, xuu31000, True, h, ba, bb) → EQ
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Double) → new_esEs15(xuu40000, xuu3000)
new_primCmpNat0(xuu3000, Zero) → GT
new_compare13(xuu30000, xuu31000, app(ty_Ratio, bhd)) → new_compare8(xuu30000, xuu31000, bhd)
new_esEs10(xuu30000, xuu31000, ty_Integer) → new_esEs11(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Float) → new_lt18(xuu30000, xuu31000)
new_esEs26(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_esEs10(xuu30000, xuu31000, app(app(ty_@2, eb), ec)) → new_esEs5(xuu30000, xuu31000, eb, ec)
new_compare25(Float(xuu30000, xuu30001), Float(xuu31000, xuu31001)) → new_compare10(new_sr0(xuu30000, xuu31000), new_sr0(xuu30001, xuu31001))
new_esEs28(xuu40000, xuu3000, app(ty_Ratio, dbb)) → new_esEs17(xuu40000, xuu3000, dbb)
new_esEs23(xuu40000, xuu3000, app(ty_Ratio, cbg)) → new_esEs17(xuu40000, xuu3000, cbg)
new_esEs9(xuu30001, xuu31001, app(ty_Ratio, bed)) → new_esEs17(xuu30001, xuu31001, bed)
new_compare23(xuu30000, xuu31000, True, ee, ef) → EQ
new_esEs25(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3100))) → GT
new_lt7(xuu30001, xuu31001, ty_Ordering) → new_lt15(xuu30001, xuu31001)
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, app(ty_[], bde)) → new_ltEs9(xuu30000, xuu31000, bde)
new_sr0(xuu40000, xuu3000) → new_primMulInt(xuu40000, xuu3000)
new_esEs26(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(app(ty_@3, caf), cag), cah)) → new_esEs4(xuu40000, xuu3000, caf, cag, cah)
new_lt8(xuu30000, xuu31000, app(app(ty_Either, ee), ef)) → new_lt17(xuu30000, xuu31000, ee, ef)
new_compare13(xuu30000, xuu31000, ty_Bool) → new_compare15(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Integer, bcb) → new_ltEs7(xuu30000, xuu31000)
new_esEs19(Char(xuu40000), Char(xuu3000)) → new_primEqNat0(xuu40000, xuu3000)
new_esEs22(xuu30000, xuu31000, ty_Char) → new_esEs19(xuu30000, xuu31000)
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_Ratio, bhf)) → new_ltEs14(xuu30000, xuu31000, bhf)
new_esEs23(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs9(xuu30001, xuu31001, app(app(ty_@2, dd), de)) → new_esEs5(xuu30001, xuu31001, dd, de)
new_ltEs17(xuu3000, xuu3100) → new_fsEs(new_compare25(xuu3000, xuu3100))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs25(xuu40001, xuu3001, ty_Bool) → new_esEs12(xuu40001, xuu3001)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Char) → new_ltEs18(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_@0) → new_lt13(xuu30000, xuu31000)
new_esEs27(xuu40001, xuu3001, ty_Float) → new_esEs18(xuu40001, xuu3001)
new_compare9(Integer(xuu30000), Integer(xuu31000)) → new_primCmpInt(xuu30000, xuu31000)
new_asAs(False, xuu137) → False
new_primMulInt(Pos(xuu400000), Neg(xuu30000)) → Neg(new_primMulNat0(xuu400000, xuu30000))
new_primMulInt(Neg(xuu400000), Pos(xuu30000)) → Neg(new_primMulNat0(xuu400000, xuu30000))
new_esEs13([], :(xuu3000, xuu3001), cbf) → False
new_esEs13(:(xuu40000, xuu40001), [], cbf) → False
new_primMulNat0(Succ(xuu4000000), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu300000)) → Zero
new_lt7(xuu30001, xuu31001, app(app(ty_Either, dg), dh)) → new_lt17(xuu30001, xuu31001, dg, dh)
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_Maybe, cbe)) → new_esEs6(xuu40000, xuu3000, cbe)
new_compare26(Char(xuu30000), Char(xuu31000)) → new_primCmpNat2(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_Ratio, chd), bcb) → new_ltEs14(xuu30000, xuu31000, chd)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Double, beg) → new_esEs15(xuu40000, xuu3000)
new_ltEs20(xuu3000, xuu3100, ty_Integer) → new_ltEs7(xuu3000, xuu3100)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_[], beh), beg) → new_esEs13(xuu40000, xuu3000, beh)
new_esEs21(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_ltEs12(GT, GT) → True
new_ltEs20(xuu3000, xuu3100, ty_Double) → new_ltEs11(xuu3000, xuu3100)
new_esEs9(xuu30001, xuu31001, ty_Bool) → new_esEs12(xuu30001, xuu31001)
new_esEs10(xuu30000, xuu31000, app(ty_Maybe, ed)) → new_esEs6(xuu30000, xuu31000, ed)
new_ltEs19(xuu30001, xuu31001, ty_@0) → new_ltEs10(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Ordering, bcb) → new_ltEs12(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Float, beg) → new_esEs18(xuu40000, xuu3000)
new_primCmpNat1(Succ(xuu3100), xuu3000) → new_primCmpNat2(xuu3100, xuu3000)
new_esEs23(xuu40000, xuu3000, app(ty_Maybe, cch)) → new_esEs6(xuu40000, xuu3000, cch)
new_primCmpNat2(Succ(xuu30000), Zero) → GT
new_lt7(xuu30001, xuu31001, app(ty_Ratio, bed)) → new_lt16(xuu30001, xuu31001, bed)
new_compare210(Just(xuu3000), Nothing, False, chc) → GT
new_lt7(xuu30001, xuu31001, app(ty_Maybe, df)) → new_lt5(xuu30001, xuu31001, df)
new_lt8(xuu30000, xuu31000, ty_Float) → new_lt18(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, ty_Bool) → new_esEs12(xuu40002, xuu3002)
new_esEs25(xuu40001, xuu3001, app(ty_[], ceg)) → new_esEs13(xuu40001, xuu3001, ceg)
new_esEs23(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare27(xuu30000, xuu31000, True) → EQ
new_esEs10(xuu30000, xuu31000, ty_Float) → new_esEs18(xuu30000, xuu31000)
new_ltEs6(xuu30002, xuu31002, ty_Bool) → new_ltEs8(xuu30002, xuu31002)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Bool) → new_ltEs8(xuu30000, xuu31000)
new_compare17(Double(xuu30000, xuu30001), Double(xuu31000, xuu31001)) → new_compare10(new_sr0(xuu30000, xuu31000), new_sr0(xuu30001, xuu31001))
new_esEs12(True, False) → False
new_esEs12(False, True) → False
new_esEs28(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, ty_Int) → new_ltEs13(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Bool, beg) → new_esEs12(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_ltEs9(xuu3000, xuu3100, eg) → new_fsEs(new_compare0(xuu3000, xuu3100, eg))
new_esEs27(xuu40001, xuu3001, ty_Bool) → new_esEs12(xuu40001, xuu3001)
new_lt8(xuu30000, xuu31000, ty_Char) → new_lt19(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, ty_Float) → new_ltEs17(xuu30000, xuu31000)
new_ltEs19(xuu30001, xuu31001, app(app(app(ty_@3, gc), gd), ge)) → new_ltEs5(xuu30001, xuu31001, gc, gd, ge)
new_compare13(xuu30000, xuu31000, ty_Double) → new_compare17(xuu30000, xuu31000)
new_ltEs18(xuu3000, xuu3100) → new_fsEs(new_compare26(xuu3000, xuu3100))
new_esEs7(Right(xuu40000), Right(xuu3000), bga, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare10(xuu30, xuu31) → new_primCmpInt(xuu30, xuu31)
new_esEs10(xuu30000, xuu31000, app(ty_Ratio, bee)) → new_esEs17(xuu30000, xuu31000, bee)
new_lt7(xuu30001, xuu31001, app(app(app(ty_@3, cf), cg), da)) → new_lt10(xuu30001, xuu31001, cf, cg, da)
new_ltEs12(EQ, LT) → False
new_esEs25(xuu40001, xuu3001, app(app(ty_@2, cfe), cff)) → new_esEs5(xuu40001, xuu3001, cfe, cff)
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_[], cae)) → new_esEs13(xuu40000, xuu3000, cae)
new_lt8(xuu30000, xuu31000, ty_@0) → new_lt13(xuu30000, xuu31000)
new_ltEs19(xuu30001, xuu31001, app(app(ty_@2, gg), gh)) → new_ltEs15(xuu30001, xuu31001, gg, gh)
new_compare13(xuu30000, xuu31000, app(app(ty_Either, fh), ga)) → new_compare19(xuu30000, xuu31000, fh, ga)
new_lt7(xuu30001, xuu31001, app(ty_[], dc)) → new_lt12(xuu30001, xuu31001, dc)
new_esEs22(xuu30000, xuu31000, ty_@0) → new_esEs14(xuu30000, xuu31000)
new_esEs23(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_compare112(xuu130, xuu131, False, cab) → GT
new_compare29(xuu30000, xuu31000, False) → new_compare111(xuu30000, xuu31000, new_ltEs8(xuu30000, xuu31000))
new_esEs22(xuu30000, xuu31000, app(ty_Ratio, caa)) → new_esEs17(xuu30000, xuu31000, caa)
new_ltEs19(xuu30001, xuu31001, ty_Integer) → new_ltEs7(xuu30001, xuu31001)
new_esEs10(xuu30000, xuu31000, ty_Ordering) → new_esEs8(xuu30000, xuu31000)
new_lt4(xuu30000, xuu31000, eb, ec) → new_esEs8(new_compare6(xuu30000, xuu31000, eb, ec), LT)
new_lt7(xuu30001, xuu31001, ty_Char) → new_lt19(xuu30001, xuu31001)
new_compare0([], :(xuu31000, xuu31001), eg) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs9(xuu30001, xuu31001, ty_Char) → new_esEs19(xuu30001, xuu31001)
new_primCompAux0(xuu30000, xuu31000, xuu174, eg) → new_primCompAux00(xuu174, new_compare13(xuu30000, xuu31000, eg))
new_esEs9(xuu30001, xuu31001, ty_Double) → new_esEs15(xuu30001, xuu31001)
new_asAs(True, xuu137) → xuu137
new_primMulNat0(Succ(xuu4000000), Succ(xuu300000)) → new_primPlusNat0(new_primMulNat0(xuu4000000, Succ(xuu300000)), xuu300000)
new_esEs27(xuu40001, xuu3001, app(ty_[], daa)) → new_esEs13(xuu40001, xuu3001, daa)
new_esEs27(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_esEs26(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(ty_Either, cba), cbb)) → new_esEs7(xuu40000, xuu3000, cba, cbb)
new_ltEs6(xuu30002, xuu31002, ty_Int) → new_ltEs13(xuu30002, xuu31002)
new_esEs9(xuu30001, xuu31001, app(app(ty_Either, dg), dh)) → new_esEs7(xuu30001, xuu31001, dg, dh)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Int) → new_ltEs13(xuu30000, xuu31000)
new_lt17(xuu30000, xuu31000, ee, ef) → new_esEs8(new_compare19(xuu30000, xuu31000, ee, ef), LT)
new_fsEs(xuu147) → new_not(new_esEs8(xuu147, GT))
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare27(xuu30000, xuu31000, False) → new_compare110(xuu30000, xuu31000, new_ltEs12(xuu30000, xuu31000))
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(ty_@2, bbb), bbc)) → new_ltEs15(xuu30000, xuu31000, bbb, bbc)
new_ltEs6(xuu30002, xuu31002, ty_Float) → new_ltEs17(xuu30002, xuu31002)
new_ltEs6(xuu30002, xuu31002, app(ty_[], bh)) → new_ltEs9(xuu30002, xuu31002, bh)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Bool, bcb) → new_ltEs8(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, app(ty_Maybe, cee)) → new_esEs6(xuu40002, xuu3002, cee)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Char, beg) → new_esEs19(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, app(ty_Ratio, chh)) → new_esEs17(xuu40001, xuu3001, chh)
new_compare7(xuu30000, xuu31000, ed) → new_compare210(xuu30000, xuu31000, new_esEs6(xuu30000, xuu31000, ed), ed)
new_esEs24(xuu40002, xuu3002, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs4(xuu40002, xuu3002, cdf, cdg, cdh)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_primCompAux00(xuu180, GT) → GT
new_esEs25(xuu40001, xuu3001, app(app(ty_Either, cfc), cfd)) → new_esEs7(xuu40001, xuu3001, cfc, cfd)
new_esEs18(Float(xuu40000, xuu40001), Float(xuu3000, xuu3001)) → new_esEs16(new_sr0(xuu40000, xuu3000), new_sr0(xuu40001, xuu3001))
new_ltEs12(GT, LT) → False
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(app(ty_@3, bbg), bbh), bca), bcb) → new_ltEs5(xuu30000, xuu31000, bbg, bbh, bca)
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, app(ty_Ratio, che)) → new_ltEs14(xuu30000, xuu31000, che)
new_lt7(xuu30001, xuu31001, ty_Integer) → new_lt9(xuu30001, xuu31001)
new_esEs28(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs5(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), bc, bd, db) → new_pePe(new_lt8(xuu30000, xuu31000, bc), new_asAs(new_esEs10(xuu30000, xuu31000, bc), new_pePe(new_lt7(xuu30001, xuu31001, bd), new_asAs(new_esEs9(xuu30001, xuu31001, bd), new_ltEs6(xuu30002, xuu31002, db)))))
new_primCmpInt(Neg(Succ(xuu3000)), Pos(xuu310)) → LT
new_esEs23(xuu40000, xuu3000, app(ty_[], cbh)) → new_esEs13(xuu40000, xuu3000, cbh)
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(app(ty_@3, baf), bag), bah)) → new_ltEs5(xuu30000, xuu31000, baf, bag, bah)
new_esEs22(xuu30000, xuu31000, ty_Int) → new_esEs16(xuu30000, xuu31000)
new_not(True) → False
new_ltEs4(Right(xuu30000), Right(xuu31000), bda, app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs5(xuu30000, xuu31000, bdb, bdc, bdd)

The set Q consists of the following terms:

new_primCompAux00(x0, EQ)
new_esEs9(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_@0)
new_compare113(x0, x1, False, x2, x3, x4)
new_esEs9(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Double)
new_pePe(True, x0)
new_ltEs12(LT, LT)
new_lt10(x0, x1, x2, x3, x4)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, ty_Integer)
new_lt8(x0, x1, ty_@0)
new_compare13(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_Integer)
new_primCmpNat0(x0, Succ(x1))
new_compare13(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, ty_Float)
new_lt7(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_esEs12(False, False)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, ty_Char)
new_ltEs6(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Bool)
new_esEs16(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt8(x0, x1, ty_Integer)
new_lt16(x0, x1, x2)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs20(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Ordering)
new_compare26(Char(x0), Char(x1))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primPlusNat0(x0, x1)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs8(GT, GT)
new_esEs27(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primCompAux00(x0, LT)
new_lt7(x0, x1, ty_Float)
new_ltEs14(x0, x1, x2)
new_esEs22(x0, x1, ty_Float)
new_ltEs12(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1)
new_ltEs8(True, True)
new_lt7(x0, x1, app(ty_[], x2))
new_compare13(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs8(LT, LT)
new_primCompAux00(x0, GT)
new_esEs21(x0, x1, ty_Int)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_compare28(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, ty_Int)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare0(:(x0, x1), [], x2)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs15(Double(x0, x1), Double(x2, x3))
new_primCompAux0(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Bool)
new_esEs9(x0, x1, ty_Char)
new_esEs6(Nothing, Nothing, x0)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True, x2)
new_esEs21(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_@0)
new_lt20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(x0, x1, ty_Bool)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs23(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs26(x0, x1, ty_Int)
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False, x2, x3)
new_ltEs16(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_lt8(x0, x1, ty_Char)
new_primCmpNat2(Succ(x0), Succ(x1))
new_ltEs18(x0, x1)
new_ltEs6(x0, x1, ty_Double)
new_ltEs10(x0, x1)
new_primEqNat0(Zero, Zero)
new_ltEs9(x0, x1, x2)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Just(x0), Just(x1), ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, ty_Int)
new_lt4(x0, x1, x2, x3)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs7(x0, x1)
new_compare13(x0, x1, ty_@0)
new_lt15(x0, x1)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt7(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Zero)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_lt8(x0, x1, ty_Float)
new_compare7(x0, x1, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, True, x2, x3)
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs27(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Ordering)
new_lt8(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Float)
new_lt6(x0, x1)
new_compare13(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1)
new_ltEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Char)
new_ltEs6(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_primCmpNat1(Zero, x0)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare112(x0, x1, True, x2)
new_esEs14(@0, @0)
new_esEs13([], [], x0)
new_ltEs19(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt7(x0, x1, ty_Double)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs6(Nothing, Just(x0), x1)
new_compare13(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare112(x0, x1, False, x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_compare16(@0, @0)
new_compare111(x0, x1, True)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_lt8(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Float)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare24(x0, x1, True, x2, x3)
new_lt7(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, False, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt18(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs24(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Integer)
new_lt5(x0, x1, x2)
new_ltEs6(x0, x1, ty_Bool)
new_primCmpNat1(Succ(x0), x1)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpNat2(Zero, Zero)
new_ltEs16(Just(x0), Just(x1), ty_Double)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs9(x0, x1, ty_@0)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare25(Float(x0, x1), Float(x2, x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs6(x0, x1, app(ty_[], x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat1(Succ(x0), Zero)
new_lt12(x0, x1, x2)
new_esEs23(x0, x1, ty_@0)
new_compare10(x0, x1)
new_compare0([], :(x0, x1), x2)
new_compare210(Just(x0), Nothing, False, x1)
new_ltEs16(Just(x0), Just(x1), ty_Bool)
new_ltEs11(x0, x1)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare28(x0, x1, True, x2, x3, x4)
new_compare19(x0, x1, x2, x3)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Integer)
new_ltEs12(GT, EQ)
new_ltEs12(EQ, GT)
new_ltEs16(Just(x0), Just(x1), ty_Char)
new_compare13(x0, x1, app(ty_[], x2))
new_sr(Integer(x0), Integer(x1))
new_esEs11(Integer(x0), Integer(x1))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt7(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_compare13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare11(x0, x1, True, x2, x3)
new_esEs12(True, True)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs8(False, False)
new_esEs9(x0, x1, ty_Double)
new_ltEs16(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs24(x0, x1, ty_Int)
new_compare27(x0, x1, False)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(x0, Zero)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_pePe(False, x0)
new_lt20(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_ltEs12(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, ty_Double)
new_compare29(x0, x1, True)
new_compare210(Nothing, Nothing, False, x0)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Integer)
new_compare9(Integer(x0), Integer(x1))
new_ltEs13(x0, x1)
new_lt14(x0, x1)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare17(Double(x0, x1), Double(x2, x3))
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs17(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs13([], :(x0, x1), x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare110(x0, x1, False)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare14(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, ty_Char)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare29(x0, x1, False)
new_fsEs(x0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_lt8(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt17(x0, x1, x2, x3)
new_ltEs16(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs19(Char(x0), Char(x1))
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_primCmpNat2(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt7(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs22(x0, x1, ty_Integer)
new_compare111(x0, x1, False)
new_esEs9(x0, x1, ty_Integer)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1)
new_asAs(True, x0)
new_ltEs19(x0, x1, ty_Float)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare6(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs10(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_esEs28(x0, x1, ty_Integer)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(Just(x0), Just(x1), app(ty_[], x2))
new_compare0([], [], x0)
new_compare12(x0, x1, True, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt11(x0, x1)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs12(True, False)
new_esEs12(False, True)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt20(x0, x1, ty_Ordering)
new_compare23(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_Double)
new_primCmpNat2(Zero, Succ(x0))
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs22(x0, x1, ty_Ordering)
new_compare12(x0, x1, False, x2, x3)
new_esEs20(x0, x1, ty_Integer)
new_asAs(False, x0)
new_esEs25(x0, x1, ty_Float)
new_not(True)
new_ltEs6(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs6(x0, x1, ty_Integer)
new_compare13(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_esEs13(:(x0, x1), [], x2)
new_not(False)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_lt8(x0, x1, ty_Double)
new_compare18(x0, x1)
new_compare13(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Just(x0), Just(x1), ty_Float)
new_esEs25(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_compare15(x0, x1)
new_ltEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Float)
new_compare13(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Int)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt8(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Zero)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_sr0(x0, x1)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs24(x0, x1, ty_Char)
new_ltEs16(Nothing, Nothing, x0)
new_lt7(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs12(EQ, LT)
new_ltEs12(LT, EQ)
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs10(x0, x1, ty_Double)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_compare113(x0, x1, True, x2, x3, x4)
new_ltEs16(Nothing, Just(x0), x1)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Just(x0), Nothing, x1)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt7(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs12(GT, LT)
new_ltEs12(LT, GT)
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare27(x0, x1, True)
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs26(x0, x1, ty_Double)
new_lt8(x0, x1, ty_Int)
new_ltEs16(Just(x0), Just(x1), ty_Ordering)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs16(Just(x0), Nothing, x1)
new_compare210(Just(x0), Just(x1), False, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_ltEs16(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Char)
new_compare210(Nothing, Just(x0), False, x1)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs25(x0, x1, ty_Int)

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

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



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

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

new_addToFM_C1(xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_addToFM_C(xuu34, Nothing, xuu401, h, ba)
new_addToFM_C20(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, False, h, ba) → new_addToFM_C11(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, new_esEs8(new_compare210(Just(xuu4000), Nothing, False, h), GT), h, ba)
new_addToFM_C21(xuu14, xuu15, xuu16, xuu17, xuu18, xuu19, xuu20, True, bb, bc) → new_addToFM_C(xuu17, Just(xuu19), xuu20, bb, bc)
new_addToFM_C2(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_addToFM_C(xuu33, Nothing, xuu401, h, ba)
new_addToFM_C20(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, True, h, ba) → new_addToFM_C(xuu33, Just(xuu4000), xuu401, h, ba)
new_addToFM_C(Branch(Just(xuu300), xuu31, xuu32, xuu33, xuu34), Nothing, xuu401, h, ba) → new_addToFM_C2(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Just(xuu300), False, h), LT), h, ba)
new_addToFM_C(Branch(Just(xuu300), xuu31, xuu32, xuu33, xuu34), Just(xuu4000), xuu401, h, ba) → new_addToFM_C21(xuu300, xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, new_esEs8(new_compare210(Just(xuu4000), Just(xuu300), new_esEs29(xuu4000, xuu300, h), h), LT), h, ba)
new_addToFM_C21(xuu14, xuu15, xuu16, xuu17, xuu18, xuu19, xuu20, False, bb, bc) → new_addToFM_C12(xuu14, xuu15, xuu16, xuu17, xuu18, xuu19, xuu20, new_esEs8(new_compare210(Just(xuu19), Just(xuu14), new_esEs30(xuu19, xuu14, bb), bb), GT), bb, bc)
new_addToFM_C(Branch(Nothing, xuu31, xuu32, xuu33, xuu34), Nothing, xuu401, h, ba) → new_addToFM_C1(xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C11(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, True, h, ba) → new_addToFM_C(xuu34, Just(xuu4000), xuu401, h, ba)
new_addToFM_C2(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, False, h, ba) → new_addToFM_C10(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Just(xuu300), False, h), GT), h, ba)
new_addToFM_C(Branch(Nothing, xuu31, xuu32, xuu33, xuu34), Just(xuu4000), xuu401, h, ba) → new_addToFM_C20(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, new_esEs8(new_compare210(Just(xuu4000), Nothing, False, h), LT), h, ba)
new_addToFM_C10(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_addToFM_C(xuu34, Nothing, xuu401, h, ba)
new_addToFM_C12(xuu14, xuu15, xuu16, xuu17, xuu18, xuu19, xuu20, True, bb, bc) → new_addToFM_C(xuu18, Just(xuu19), xuu20, bb, bc)

The TRS R consists of the following rules:

new_esEs30(xuu19, xuu14, app(ty_Maybe, bee)) → new_esEs6(xuu19, xuu14, bee)
new_esEs25(xuu40001, xuu3001, ty_Char) → new_esEs19(xuu40001, xuu3001)
new_primCmpNat0(xuu3000, Succ(xuu3100)) → new_primCmpNat2(xuu3000, xuu3100)
new_ltEs19(xuu30001, xuu31001, ty_Ordering) → new_ltEs12(xuu30001, xuu31001)
new_ltEs6(xuu30002, xuu31002, app(app(ty_@2, db), dc)) → new_ltEs15(xuu30002, xuu31002, db, dc)
new_esEs28(xuu40000, xuu3000, app(ty_[], dda)) → new_esEs13(xuu40000, xuu3000, dda)
new_esEs23(xuu40000, xuu3000, app(app(ty_Either, ccc), ccd)) → new_esEs7(xuu40000, xuu3000, ccc, ccd)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(ty_@2, cbc), cbd)) → new_esEs5(xuu40000, xuu3000, cbc, cbd)
new_compare112(xuu130, xuu131, True, cac) → LT
new_esEs29(xuu4000, xuu300, ty_Int) → new_esEs16(xuu4000, xuu300)
new_ltEs20(xuu3000, xuu3100, ty_Char) → new_ltEs18(xuu3000, xuu3100)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(ty_Either, ge), gf), fh) → new_esEs7(xuu40000, xuu3000, ge, gf)
new_ltEs8(False, True) → True
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_esEs10(xuu30000, xuu31000, app(app(app(ty_@3, fa), fb), fc)) → new_esEs4(xuu30000, xuu31000, fa, fb, fc)
new_esEs27(xuu40001, xuu3001, ty_Char) → new_esEs19(xuu40001, xuu3001)
new_compare13(xuu30000, xuu31000, app(app(app(ty_@3, baf), bag), bah)) → new_compare14(xuu30000, xuu31000, baf, bag, bah)
new_ltEs10(xuu3000, xuu3100) → new_fsEs(new_compare16(xuu3000, xuu3100))
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Ordering) → new_ltEs12(xuu30000, xuu31000)
new_esEs13([], [], bhd) → True
new_ltEs12(LT, GT) → True
new_ltEs19(xuu30001, xuu31001, app(ty_[], bfc)) → new_ltEs9(xuu30001, xuu31001, bfc)
new_lt20(xuu30000, xuu31000, app(ty_Ratio, bgf)) → new_lt16(xuu30000, xuu31000, bgf)
new_lt7(xuu30001, xuu31001, ty_Bool) → new_lt11(xuu30001, xuu31001)
new_lt16(xuu30000, xuu31000, ff) → new_esEs8(new_compare8(xuu30000, xuu31000, ff), LT)
new_esEs4(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), bhe, bhf, bhg) → new_asAs(new_esEs26(xuu40000, xuu3000, bhe), new_asAs(new_esEs25(xuu40001, xuu3001, bhf), new_esEs24(xuu40002, xuu3002, bhg)))
new_esEs11(Integer(xuu40000), Integer(xuu3000)) → new_primEqInt(xuu40000, xuu3000)
new_esEs30(xuu19, xuu14, app(ty_[], bde)) → new_esEs13(xuu19, xuu14, bde)
new_esEs15(Double(xuu40000, xuu40001), Double(xuu3000, xuu3001)) → new_esEs16(new_sr0(xuu40000, xuu3000), new_sr0(xuu40001, xuu3001))
new_compare13(xuu30000, xuu31000, app(ty_Maybe, bbe)) → new_compare7(xuu30000, xuu31000, bbe)
new_esEs28(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs26(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_compare19(xuu30000, xuu31000, bg, bh) → new_compare23(xuu30000, xuu31000, new_esEs7(xuu30000, xuu31000, bg, bh), bg, bh)
new_ltEs19(xuu30001, xuu31001, ty_Double) → new_ltEs11(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(ty_@2, chg), chh), cha) → new_ltEs15(xuu30000, xuu31000, chg, chh)
new_primMulNat0(Zero, Zero) → Zero
new_esEs27(xuu40001, xuu3001, app(app(app(ty_@3, dbh), dca), dcb)) → new_esEs4(xuu40001, xuu3001, dbh, dca, dcb)
new_ltEs12(LT, LT) → True
new_compare29(xuu30000, xuu31000, True) → EQ
new_sr(Integer(xuu300000), Integer(xuu310010)) → Integer(new_primMulInt(xuu300000, xuu310010))
new_esEs12(True, True) → True
new_ltEs6(xuu30002, xuu31002, app(app(app(ty_@3, cd), ce), cf)) → new_ltEs5(xuu30002, xuu31002, cd, ce, cf)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_@0) → new_ltEs10(xuu30000, xuu31000)
new_ltEs15(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), bef, beg) → new_pePe(new_lt20(xuu30000, xuu31000, bef), new_asAs(new_esEs22(xuu30000, xuu31000, bef), new_ltEs19(xuu30001, xuu31001, beg)))
new_esEs23(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Integer) → new_ltEs7(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Double) → new_ltEs11(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(ty_Ratio, hc)) → new_esEs17(xuu40000, xuu3000, hc)
new_lt12(xuu30000, xuu31000, fd) → new_esEs8(new_compare0(xuu30000, xuu31000, fd), LT)
new_esEs24(xuu40002, xuu3002, ty_@0) → new_esEs14(xuu40002, xuu3002)
new_lt8(xuu30000, xuu31000, app(ty_[], fd)) → new_lt12(xuu30000, xuu31000, fd)
new_compare16(@0, @0) → EQ
new_esEs30(xuu19, xuu14, app(app(ty_Either, bea), beb)) → new_esEs7(xuu19, xuu14, bea, beb)
new_compare8(:%(xuu30000, xuu30001), :%(xuu31000, xuu31001), ty_Integer) → new_compare9(new_sr(xuu30000, xuu31001), new_sr(xuu31000, xuu30001))
new_lt20(xuu30000, xuu31000, ty_Double) → new_lt14(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Integer) → new_lt9(xuu30000, xuu31000)
new_ltEs12(LT, EQ) → True
new_ltEs20(xuu3000, xuu3100, app(ty_[], bae)) → new_ltEs9(xuu3000, xuu3100, bae)
new_lt8(xuu30000, xuu31000, app(ty_Ratio, ff)) → new_lt16(xuu30000, xuu31000, ff)
new_ltEs11(xuu3000, xuu3100) → new_fsEs(new_compare17(xuu3000, xuu3100))
new_esEs22(xuu30000, xuu31000, app(app(ty_@2, bgg), bgh)) → new_esEs5(xuu30000, xuu31000, bgg, bgh)
new_compare0(:(xuu30000, xuu30001), :(xuu31000, xuu31001), bae) → new_primCompAux0(xuu30000, xuu31000, new_compare0(xuu30001, xuu31001, bae), bae)
new_compare210(Nothing, Nothing, False, cgg) → LT
new_esEs24(xuu40002, xuu3002, app(app(ty_@2, cdg), cdh)) → new_esEs5(xuu40002, xuu3002, cdg, cdh)
new_esEs22(xuu30000, xuu31000, app(ty_Maybe, bha)) → new_esEs6(xuu30000, xuu31000, bha)
new_ltEs20(xuu3000, xuu3100, app(ty_Ratio, cgf)) → new_ltEs14(xuu3000, xuu3100, cgf)
new_esEs27(xuu40001, xuu3001, app(ty_Maybe, dcg)) → new_esEs6(xuu40001, xuu3001, dcg)
new_esEs26(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_esEs25(xuu40001, xuu3001, ty_Double) → new_esEs15(xuu40001, xuu3001)
new_compare15(xuu30000, xuu31000) → new_compare29(xuu30000, xuu31000, new_esEs12(xuu30000, xuu31000))
new_esEs29(xuu4000, xuu300, ty_Float) → new_esEs18(xuu4000, xuu300)
new_lt20(xuu30000, xuu31000, ty_Ordering) → new_lt15(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Char) → new_ltEs18(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, app(app(ty_Either, bhb), bhc)) → new_esEs7(xuu30000, xuu31000, bhb, bhc)
new_lt18(xuu30000, xuu31000) → new_esEs8(new_compare25(xuu30000, xuu31000), LT)
new_ltEs19(xuu30001, xuu31001, ty_Char) → new_ltEs18(xuu30001, xuu31001)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(ty_Maybe, bad)) → new_esEs6(xuu40000, xuu3000, bad)
new_ltEs19(xuu30001, xuu31001, app(app(ty_Either, bfh), bga)) → new_ltEs4(xuu30001, xuu31001, bfh, bga)
new_pePe(False, xuu163) → xuu163
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_esEs7(Left(xuu40000), Right(xuu3000), hb, fh) → False
new_esEs7(Right(xuu40000), Left(xuu3000), hb, fh) → False
new_lt20(xuu30000, xuu31000, ty_Bool) → new_lt11(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, ty_Bool) → new_esEs12(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Double, cha) → new_ltEs11(xuu30000, xuu31000)
new_compare6(xuu30000, xuu31000, bd, be) → new_compare24(xuu30000, xuu31000, new_esEs5(xuu30000, xuu31000, bd, be), bd, be)
new_esEs28(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, app(app(ty_Either, dcc), dcd)) → new_esEs7(xuu40001, xuu3001, dcc, dcd)
new_esEs20(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_ltEs20(xuu3000, xuu3100, ty_@0) → new_ltEs10(xuu3000, xuu3100)
new_compare13(xuu30000, xuu31000, ty_Int) → new_compare10(xuu30000, xuu31000)
new_esEs26(xuu40000, xuu3000, app(ty_Ratio, cfd)) → new_esEs17(xuu40000, xuu3000, cfd)
new_esEs22(xuu30000, xuu31000, ty_Double) → new_esEs15(xuu30000, xuu31000)
new_esEs26(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_ltEs20(xuu3000, xuu3100, app(app(ty_Either, cgh), cha)) → new_ltEs4(xuu3000, xuu3100, cgh, cha)
new_lt20(xuu30000, xuu31000, app(app(app(ty_@3, bgb), bgc), bgd)) → new_lt10(xuu30000, xuu31000, bgb, bgc, bgd)
new_esEs28(xuu40000, xuu3000, app(app(app(ty_@3, ddb), ddc), ddd)) → new_esEs4(xuu40000, xuu3000, ddb, ddc, ddd)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Double) → new_ltEs11(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(app(ty_Either, dbd), dbe)) → new_ltEs4(xuu30000, xuu31000, dbd, dbe)
new_esEs22(xuu30000, xuu31000, ty_Ordering) → new_esEs8(xuu30000, xuu31000)
new_compare111(xuu30000, xuu31000, False) → GT
new_compare111(xuu30000, xuu31000, True) → LT
new_esEs26(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_ltEs4(Left(xuu30000), Right(xuu31000), cgh, cha) → True
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(app(ty_@2, bab), bac)) → new_esEs5(xuu40000, xuu3000, bab, bac)
new_ltEs20(xuu3000, xuu3100, ty_Ordering) → new_ltEs12(xuu3000, xuu3100)
new_primCmpInt(Neg(Succ(xuu3000)), Neg(xuu310)) → new_primCmpNat1(xuu310, xuu3000)
new_lt6(xuu300, xuu310) → new_esEs8(new_compare10(xuu300, xuu310), LT)
new_ltEs20(xuu3000, xuu3100, ty_Bool) → new_ltEs8(xuu3000, xuu3100)
new_esEs8(LT, LT) → True
new_esEs30(xuu19, xuu14, ty_Float) → new_esEs18(xuu19, xuu14)
new_ltEs16(Nothing, Nothing, bbh) → True
new_lt20(xuu30000, xuu31000, ty_Char) → new_lt19(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Integer, fh) → new_esEs11(xuu40000, xuu3000)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_Maybe, daa), cha) → new_ltEs16(xuu30000, xuu31000, daa)
new_esEs25(xuu40001, xuu3001, ty_Ordering) → new_esEs8(xuu40001, xuu3001)
new_esEs20(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_esEs28(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_compare210(Nothing, Just(xuu3100), False, cgg) → LT
new_esEs24(xuu40002, xuu3002, app(app(ty_Either, cde), cdf)) → new_esEs7(xuu40002, xuu3002, cde, cdf)
new_ltEs6(xuu30002, xuu31002, ty_Double) → new_ltEs11(xuu30002, xuu31002)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_@0) → new_ltEs10(xuu30000, xuu31000)
new_pePe(True, xuu163) → True
new_compare0([], [], bae) → EQ
new_esEs24(xuu40002, xuu3002, ty_Int) → new_esEs16(xuu40002, xuu3002)
new_primEqNat0(Zero, Zero) → True
new_ltEs19(xuu30001, xuu31001, ty_Int) → new_ltEs13(xuu30001, xuu31001)
new_esEs29(xuu4000, xuu300, app(ty_Maybe, cab)) → new_esEs6(xuu4000, xuu300, cab)
new_compare210(Just(xuu3000), Just(xuu3100), False, cgg) → new_compare112(xuu3000, xuu3100, new_ltEs20(xuu3000, xuu3100, cgg), cgg)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(ty_@2, gg), gh), fh) → new_esEs5(xuu40000, xuu3000, gg, gh)
new_esEs26(xuu40000, xuu3000, app(ty_Maybe, cge)) → new_esEs6(xuu40000, xuu3000, cge)
new_esEs14(@0, @0) → True
new_esEs30(xuu19, xuu14, ty_Double) → new_esEs15(xuu19, xuu14)
new_esEs9(xuu30001, xuu31001, app(app(app(ty_@3, dg), dh), ea)) → new_esEs4(xuu30001, xuu31001, dg, dh, ea)
new_ltEs6(xuu30002, xuu31002, ty_@0) → new_ltEs10(xuu30002, xuu31002)
new_esEs29(xuu4000, xuu300, app(ty_[], bhd)) → new_esEs13(xuu4000, xuu300, bhd)
new_esEs9(xuu30001, xuu31001, app(ty_Maybe, ef)) → new_esEs6(xuu30001, xuu31001, ef)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Float, cha) → new_ltEs17(xuu30000, xuu31000)
new_esEs9(xuu30001, xuu31001, ty_@0) → new_esEs14(xuu30001, xuu31001)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Ordering, fh) → new_esEs8(xuu40000, xuu3000)
new_esEs24(xuu40002, xuu3002, app(ty_Ratio, cch)) → new_esEs17(xuu40002, xuu3002, cch)
new_compare13(xuu30000, xuu31000, ty_Integer) → new_compare9(xuu30000, xuu31000)
new_compare12(xuu30000, xuu31000, False, bd, be) → GT
new_esEs30(xuu19, xuu14, ty_Char) → new_esEs19(xuu19, xuu14)
new_compare13(xuu30000, xuu31000, ty_Ordering) → new_compare18(xuu30000, xuu31000)
new_lt7(xuu30001, xuu31001, ty_Double) → new_lt14(xuu30001, xuu31001)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Ordering) → new_ltEs12(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Int, cha) → new_ltEs13(xuu30000, xuu31000)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3100))) → new_primCmpNat0(xuu3100, Zero)
new_esEs26(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs24(xuu40002, xuu3002, ty_Char) → new_esEs19(xuu40002, xuu3002)
new_esEs8(GT, GT) → True
new_esEs30(xuu19, xuu14, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs4(xuu19, xuu14, bdf, bdg, bdh)
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_[], bcd)) → new_ltEs9(xuu30000, xuu31000, bcd)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3100))) → new_primCmpNat1(Zero, xuu3100)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(app(ty_Either, hh), baa)) → new_esEs7(xuu40000, xuu3000, hh, baa)
new_compare13(xuu30000, xuu31000, app(ty_[], bba)) → new_compare0(xuu30000, xuu31000, bba)
new_lt15(xuu30000, xuu31000) → new_esEs8(new_compare18(xuu30000, xuu31000), LT)
new_esEs12(False, False) → True
new_esEs26(xuu40000, xuu3000, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs4(xuu40000, xuu3000, cff, cfg, cfh)
new_ltEs20(xuu3000, xuu3100, app(app(ty_@2, bef), beg)) → new_ltEs15(xuu3000, xuu3100, bef, beg)
new_ltEs19(xuu30001, xuu31001, app(ty_Ratio, bfd)) → new_ltEs14(xuu30001, xuu31001, bfd)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(ty_[], hd)) → new_esEs13(xuu40000, xuu3000, hd)
new_lt10(xuu30000, xuu31000, fa, fb, fc) → new_esEs8(new_compare14(xuu30000, xuu31000, fa, fb, fc), LT)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_esEs28(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_lt20(xuu30000, xuu31000, app(app(ty_Either, bhb), bhc)) → new_lt17(xuu30000, xuu31000, bhb, bhc)
new_esEs9(xuu30001, xuu31001, ty_Integer) → new_esEs11(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_@0, cha) → new_ltEs10(xuu30000, xuu31000)
new_ltEs20(xuu3000, xuu3100, app(app(app(ty_@3, ca), cb), cc)) → new_ltEs5(xuu3000, xuu3100, ca, cb, cc)
new_lt8(xuu30000, xuu31000, ty_Double) → new_lt14(xuu30000, xuu31000)
new_ltEs16(Nothing, Just(xuu31000), bbh) → True
new_primEqInt(Neg(Succ(xuu400000)), Neg(Succ(xuu30000))) → new_primEqNat0(xuu400000, xuu30000)
new_esEs23(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs13(:(xuu40000, xuu40001), :(xuu3000, xuu3001), bhd) → new_asAs(new_esEs23(xuu40000, xuu3000, bhd), new_esEs13(xuu40001, xuu3001, bhd))
new_esEs26(xuu40000, xuu3000, app(ty_[], cfe)) → new_esEs13(xuu40000, xuu3000, cfe)
new_primPlusNat1(Succ(xuu25200), Zero) → Succ(xuu25200)
new_primPlusNat1(Zero, Succ(xuu9400)) → Succ(xuu9400)
new_ltEs6(xuu30002, xuu31002, ty_Char) → new_ltEs18(xuu30002, xuu31002)
new_lt8(xuu30000, xuu31000, app(ty_Maybe, bf)) → new_lt5(xuu30000, xuu31000, bf)
new_ltEs8(True, True) → True
new_esEs16(xuu4000, xuu300) → new_primEqInt(xuu4000, xuu300)
new_primCmpNat1(Zero, xuu3000) → LT
new_esEs30(xuu19, xuu14, ty_Integer) → new_esEs11(xuu19, xuu14)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_Maybe, bch)) → new_ltEs16(xuu30000, xuu31000, bch)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Char, cha) → new_ltEs18(xuu30000, xuu31000)
new_ltEs12(EQ, EQ) → True
new_compare13(xuu30000, xuu31000, ty_Float) → new_compare25(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Integer) → new_ltEs7(xuu30000, xuu31000)
new_lt8(xuu30000, xuu31000, ty_Integer) → new_lt9(xuu30000, xuu31000)
new_esEs21(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs28(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_primEqInt(Neg(Zero), Neg(Succ(xuu30000))) → False
new_primEqInt(Neg(Succ(xuu400000)), Neg(Zero)) → False
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(ty_Either, dab), dac), cha) → new_ltEs4(xuu30000, xuu31000, dab, dac)
new_esEs8(EQ, EQ) → True
new_esEs6(Just(xuu40000), Just(xuu3000), ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs17(:%(xuu40000, xuu40001), :%(xuu3000, xuu3001), bdc) → new_asAs(new_esEs21(xuu40000, xuu3000, bdc), new_esEs20(xuu40001, xuu3001, bdc))
new_esEs23(xuu40000, xuu3000, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs4(xuu40000, xuu3000, cbh, cca, ccb)
new_compare24(xuu30000, xuu31000, True, bd, be) → EQ
new_esEs5(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), bhh, caa) → new_asAs(new_esEs28(xuu40000, xuu3000, bhh), new_esEs27(xuu40001, xuu3001, caa))
new_lt20(xuu30000, xuu31000, app(ty_Maybe, bha)) → new_lt5(xuu30000, xuu31000, bha)
new_ltEs7(xuu3000, xuu3100) → new_fsEs(new_compare9(xuu3000, xuu3100))
new_ltEs13(xuu3000, xuu3100) → new_fsEs(new_compare10(xuu3000, xuu3100))
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_ltEs19(xuu30001, xuu31001, app(ty_Maybe, bfg)) → new_ltEs16(xuu30001, xuu31001, bfg)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs26(xuu40000, xuu3000, app(app(ty_Either, cga), cgb)) → new_esEs7(xuu40000, xuu3000, cga, cgb)
new_esEs9(xuu30001, xuu31001, ty_Float) → new_esEs18(xuu30001, xuu31001)
new_ltEs14(xuu3000, xuu3100, cgf) → new_fsEs(new_compare8(xuu3000, xuu3100, cgf))
new_compare23(xuu30000, xuu31000, False, bg, bh) → new_compare11(xuu30000, xuu31000, new_ltEs4(xuu30000, xuu31000, bg, bh), bg, bh)
new_esEs6(Nothing, Nothing, cab) → True
new_ltEs6(xuu30002, xuu31002, app(ty_Maybe, dd)) → new_ltEs16(xuu30002, xuu31002, dd)
new_compare113(xuu30000, xuu31000, False, fa, fb, fc) → GT
new_ltEs20(xuu3000, xuu3100, app(ty_Maybe, bbh)) → new_ltEs16(xuu3000, xuu3100, bbh)
new_primEqInt(Pos(Succ(xuu400000)), Pos(Succ(xuu30000))) → new_primEqNat0(xuu400000, xuu30000)
new_lt20(xuu30000, xuu31000, app(ty_[], bge)) → new_lt12(xuu30000, xuu31000, bge)
new_lt5(xuu30000, xuu31000, bf) → new_esEs8(new_compare7(xuu30000, xuu31000, bf), LT)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_compare24(xuu30000, xuu31000, False, bd, be) → new_compare12(xuu30000, xuu31000, new_ltEs15(xuu30000, xuu31000, bd, be), bd, be)
new_compare12(xuu30000, xuu31000, True, bd, be) → LT
new_esEs30(xuu19, xuu14, ty_Int) → new_esEs16(xuu19, xuu14)
new_compare8(:%(xuu30000, xuu30001), :%(xuu31000, xuu31001), ty_Int) → new_compare10(new_sr0(xuu30000, xuu31001), new_sr0(xuu31000, xuu30001))
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_Ratio, cad)) → new_esEs17(xuu40000, xuu3000, cad)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(app(app(ty_@3, he), hf), hg)) → new_esEs4(xuu40000, xuu3000, he, hf, hg)
new_esEs6(Just(xuu40000), Nothing, cab) → False
new_esEs6(Nothing, Just(xuu3000), cab) → False
new_primEqNat0(Succ(xuu400000), Succ(xuu30000)) → new_primEqNat0(xuu400000, xuu30000)
new_esEs23(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, ty_Ordering) → new_esEs8(xuu40001, xuu3001)
new_lt13(xuu30000, xuu31000) → new_esEs8(new_compare16(xuu30000, xuu31000), LT)
new_lt8(xuu30000, xuu31000, ty_Bool) → new_lt11(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, ty_Double) → new_esEs15(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, ty_Bool) → new_esEs12(xuu30000, xuu31000)
new_lt14(xuu30000, xuu31000) → new_esEs8(new_compare17(xuu30000, xuu31000), LT)
new_lt7(xuu30001, xuu31001, ty_Float) → new_lt18(xuu30001, xuu31001)
new_primCompAux00(xuu180, LT) → LT
new_lt11(xuu30000, xuu31000) → new_esEs8(new_compare15(xuu30000, xuu31000), LT)
new_esEs24(xuu40002, xuu3002, ty_Ordering) → new_esEs8(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, app(ty_Ratio, da)) → new_ltEs14(xuu30002, xuu31002, da)
new_esEs23(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_ltEs19(xuu30001, xuu31001, ty_Bool) → new_ltEs8(xuu30001, xuu31001)
new_esEs28(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Int, fh) → new_esEs16(xuu40000, xuu3000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu30000))) → False
new_primEqInt(Pos(Succ(xuu400000)), Pos(Zero)) → False
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Float) → new_ltEs17(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, app(app(ty_Either, bg), bh)) → new_esEs7(xuu30000, xuu31000, bg, bh)
new_compare14(xuu30000, xuu31000, fa, fb, fc) → new_compare28(xuu30000, xuu31000, new_esEs4(xuu30000, xuu31000, fa, fb, fc), fa, fb, fc)
new_ltEs19(xuu30001, xuu31001, ty_Float) → new_ltEs17(xuu30001, xuu31001)
new_lt20(xuu30000, xuu31000, app(app(ty_@2, bgg), bgh)) → new_lt4(xuu30000, xuu31000, bgg, bgh)
new_esEs23(xuu40000, xuu3000, app(app(ty_@2, cce), ccf)) → new_esEs5(xuu40000, xuu3000, cce, ccf)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3100))) → LT
new_esEs29(xuu4000, xuu300, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs4(xuu4000, xuu300, bhe, bhf, bhg)
new_compare11(xuu30000, xuu31000, True, bg, bh) → LT
new_esEs9(xuu30001, xuu31001, app(ty_[], eb)) → new_esEs13(xuu30001, xuu31001, eb)
new_primPlusNat1(Succ(xuu25200), Succ(xuu9400)) → Succ(Succ(new_primPlusNat1(xuu25200, xuu9400)))
new_primEqInt(Neg(Succ(xuu400000)), Pos(xuu3000)) → False
new_primEqInt(Pos(Succ(xuu400000)), Neg(xuu3000)) → False
new_ltEs6(xuu30002, xuu31002, ty_Ordering) → new_ltEs12(xuu30002, xuu31002)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_Ratio, fg), fh) → new_esEs17(xuu40000, xuu3000, fg)
new_esEs29(xuu4000, xuu300, ty_Char) → new_esEs19(xuu4000, xuu300)
new_compare210(xuu300, xuu310, True, cgg) → EQ
new_ltEs12(GT, EQ) → False
new_esEs29(xuu4000, xuu300, app(app(ty_@2, bhh), caa)) → new_esEs5(xuu4000, xuu300, bhh, caa)
new_esEs24(xuu40002, xuu3002, app(ty_[], cda)) → new_esEs13(xuu40002, xuu3002, cda)
new_esEs29(xuu4000, xuu300, ty_@0) → new_esEs14(xuu4000, xuu300)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_[], che), cha) → new_ltEs9(xuu30000, xuu31000, che)
new_primCmpNat2(Zero, Succ(xuu31000)) → LT
new_lt19(xuu30000, xuu31000) → new_esEs8(new_compare26(xuu30000, xuu31000), LT)
new_esEs28(xuu40000, xuu3000, app(ty_Maybe, dea)) → new_esEs6(xuu40000, xuu3000, dea)
new_primEqInt(Neg(Zero), Pos(Succ(xuu30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu30000))) → False
new_esEs29(xuu4000, xuu300, ty_Integer) → new_esEs11(xuu4000, xuu300)
new_esEs30(xuu19, xuu14, app(ty_Ratio, bdd)) → new_esEs17(xuu19, xuu14, bdd)
new_primCompAux00(xuu180, EQ) → xuu180
new_esEs28(xuu40000, xuu3000, app(app(ty_Either, dde), ddf)) → new_esEs7(xuu40000, xuu3000, dde, ddf)
new_esEs10(xuu30000, xuu31000, ty_Int) → new_esEs16(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(app(ty_@2, dba), dbb)) → new_ltEs15(xuu30000, xuu31000, dba, dbb)
new_esEs25(xuu40001, xuu3001, ty_@0) → new_esEs14(xuu40001, xuu3001)
new_compare18(xuu30000, xuu31000) → new_compare27(xuu30000, xuu31000, new_esEs8(xuu30000, xuu31000))
new_compare13(xuu30000, xuu31000, app(app(ty_@2, bbc), bbd)) → new_compare6(xuu30000, xuu31000, bbc, bbd)
new_ltEs20(xuu3000, xuu3100, ty_Int) → new_ltEs13(xuu3000, xuu3100)
new_esEs10(xuu30000, xuu31000, ty_Char) → new_esEs19(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs30(xuu19, xuu14, ty_Bool) → new_esEs12(xuu19, xuu14)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_lt8(xuu30000, xuu31000, app(app(app(ty_@3, fa), fb), fc)) → new_lt10(xuu30000, xuu31000, fa, fb, fc)
new_compare28(xuu30000, xuu31000, False, fa, fb, fc) → new_compare113(xuu30000, xuu31000, new_ltEs5(xuu30000, xuu31000, fa, fb, fc), fa, fb, fc)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(app(ty_@3, gb), gc), gd), fh) → new_esEs4(xuu40000, xuu3000, gb, gc, gd)
new_esEs26(xuu40000, xuu3000, app(app(ty_@2, cgc), cgd)) → new_esEs5(xuu40000, xuu3000, cgc, cgd)
new_esEs22(xuu30000, xuu31000, ty_Float) → new_esEs18(xuu30000, xuu31000)
new_ltEs16(Just(xuu30000), Nothing, bbh) → False
new_esEs9(xuu30001, xuu31001, ty_Ordering) → new_esEs8(xuu30001, xuu31001)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs4(Right(xuu30000), Left(xuu31000), cgh, cha) → False
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs30(xuu19, xuu14, ty_@0) → new_esEs14(xuu19, xuu14)
new_esEs10(xuu30000, xuu31000, ty_@0) → new_esEs14(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_Maybe, ha), fh) → new_esEs6(xuu40000, xuu3000, ha)
new_esEs23(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_lt8(xuu30000, xuu31000, app(app(ty_@2, bd), be)) → new_lt4(xuu30000, xuu31000, bd, be)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs9(xuu30001, xuu31001, ty_Int) → new_esEs16(xuu30001, xuu31001)
new_esEs25(xuu40001, xuu3001, ty_Float) → new_esEs18(xuu40001, xuu3001)
new_esEs25(xuu40001, xuu3001, app(app(app(ty_@3, ced), cee), cef)) → new_esEs4(xuu40001, xuu3001, ced, cee, cef)
new_esEs27(xuu40001, xuu3001, ty_@0) → new_esEs14(xuu40001, xuu3001)
new_esEs28(xuu40000, xuu3000, app(app(ty_@2, ddg), ddh)) → new_esEs5(xuu40000, xuu3000, ddg, ddh)
new_esEs22(xuu30000, xuu31000, ty_Integer) → new_esEs11(xuu30000, xuu31000)
new_compare0(:(xuu30000, xuu30001), [], bae) → GT
new_lt8(xuu30000, xuu31000, ty_Ordering) → new_lt15(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Int) → new_lt6(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs4(xuu30000, xuu31000, bgb, bgc, bgd)
new_esEs22(xuu30000, xuu31000, app(ty_[], bge)) → new_esEs13(xuu30000, xuu31000, bge)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(ty_Maybe, dbc)) → new_ltEs16(xuu30000, xuu31000, dbc)
new_lt8(xuu30000, xuu31000, ty_Int) → new_lt6(xuu30000, xuu31000)
new_lt7(xuu30001, xuu31001, ty_@0) → new_lt13(xuu30001, xuu31001)
new_compare11(xuu30000, xuu31000, False, bg, bh) → GT
new_esEs25(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_primCmpInt(Pos(Succ(xuu3000)), Neg(xuu310)) → GT
new_lt7(xuu30001, xuu31001, ty_Int) → new_lt6(xuu30001, xuu31001)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Bool) → new_ltEs8(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, ty_Float) → new_esEs18(xuu40002, xuu3002)
new_esEs24(xuu40002, xuu3002, ty_Double) → new_esEs15(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, ty_Integer) → new_ltEs7(xuu30002, xuu31002)
new_primMulInt(Pos(xuu400000), Pos(xuu30000)) → Pos(new_primMulNat0(xuu400000, xuu30000))
new_esEs30(xuu19, xuu14, app(app(ty_@2, bec), bed)) → new_esEs5(xuu19, xuu14, bec, bed)
new_esEs24(xuu40002, xuu3002, ty_Integer) → new_esEs11(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, app(app(ty_Either, de), df)) → new_ltEs4(xuu30002, xuu31002, de, df)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_@0, fh) → new_esEs14(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, ty_Double) → new_esEs15(xuu40001, xuu3001)
new_primMulInt(Neg(xuu400000), Neg(xuu30000)) → Pos(new_primMulNat0(xuu400000, xuu30000))
new_primCmpNat2(Zero, Zero) → EQ
new_compare110(xuu30000, xuu31000, True) → LT
new_ltEs12(EQ, GT) → True
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(ty_Either, bda), bdb)) → new_ltEs4(xuu30000, xuu31000, bda, bdb)
new_compare13(xuu30000, xuu31000, ty_@0) → new_compare16(xuu30000, xuu31000)
new_ltEs20(xuu3000, xuu3100, ty_Float) → new_ltEs17(xuu3000, xuu3100)
new_esEs29(xuu4000, xuu300, app(ty_Ratio, bdc)) → new_esEs17(xuu4000, xuu300, bdc)
new_primEqNat0(Zero, Succ(xuu30000)) → False
new_primEqNat0(Succ(xuu400000), Zero) → False
new_ltEs8(False, False) → True
new_esEs25(xuu40001, xuu3001, app(ty_Ratio, ceb)) → new_esEs17(xuu40001, xuu3001, ceb)
new_esEs25(xuu40001, xuu3001, app(ty_Maybe, cfc)) → new_esEs6(xuu40001, xuu3001, cfc)
new_compare110(xuu30000, xuu31000, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Float) → new_esEs18(xuu40000, xuu3000)
new_compare113(xuu30000, xuu31000, True, fa, fb, fc) → LT
new_lt9(xuu30000, xuu31000) → new_esEs8(new_compare9(xuu30000, xuu31000), LT)
new_primPlusNat0(xuu104, xuu300000) → new_primPlusNat1(xuu104, Succ(xuu300000))
new_esEs10(xuu30000, xuu31000, app(ty_[], fd)) → new_esEs13(xuu30000, xuu31000, fd)
new_primCmpNat2(Succ(xuu30000), Succ(xuu31000)) → new_primCmpNat2(xuu30000, xuu31000)
new_primCmpInt(Pos(Succ(xuu3000)), Pos(xuu310)) → new_primCmpNat0(xuu3000, xuu310)
new_lt7(xuu30001, xuu31001, app(app(ty_@2, ed), ee)) → new_lt4(xuu30001, xuu31001, ed, ee)
new_compare13(xuu30000, xuu31000, ty_Char) → new_compare26(xuu30000, xuu31000)
new_esEs27(xuu40001, xuu3001, app(app(ty_@2, dce), dcf)) → new_esEs5(xuu40001, xuu3001, dce, dcf)
new_compare28(xuu30000, xuu31000, True, fa, fb, fc) → EQ
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Double) → new_esEs15(xuu40000, xuu3000)
new_primCmpNat0(xuu3000, Zero) → GT
new_compare13(xuu30000, xuu31000, app(ty_Ratio, bbb)) → new_compare8(xuu30000, xuu31000, bbb)
new_esEs10(xuu30000, xuu31000, ty_Integer) → new_esEs11(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Float) → new_lt18(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, app(app(ty_@2, bd), be)) → new_esEs5(xuu30000, xuu31000, bd, be)
new_esEs26(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare25(Float(xuu30000, xuu30001), Float(xuu31000, xuu31001)) → new_compare10(new_sr0(xuu30000, xuu31000), new_sr0(xuu30001, xuu31001))
new_esEs28(xuu40000, xuu3000, app(ty_Ratio, dch)) → new_esEs17(xuu40000, xuu3000, dch)
new_esEs23(xuu40000, xuu3000, app(ty_Ratio, cbf)) → new_esEs17(xuu40000, xuu3000, cbf)
new_esEs9(xuu30001, xuu31001, app(ty_Ratio, ec)) → new_esEs17(xuu30001, xuu31001, ec)
new_compare23(xuu30000, xuu31000, True, bg, bh) → EQ
new_esEs25(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3100))) → GT
new_lt7(xuu30001, xuu31001, ty_Ordering) → new_lt15(xuu30001, xuu31001)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(ty_[], dag)) → new_ltEs9(xuu30000, xuu31000, dag)
new_sr0(xuu40000, xuu3000) → new_primMulInt(xuu40000, xuu3000)
new_esEs26(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(app(ty_@3, caf), cag), cah)) → new_esEs4(xuu40000, xuu3000, caf, cag, cah)
new_lt8(xuu30000, xuu31000, app(app(ty_Either, bg), bh)) → new_lt17(xuu30000, xuu31000, bg, bh)
new_compare13(xuu30000, xuu31000, ty_Bool) → new_compare15(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Integer, cha) → new_ltEs7(xuu30000, xuu31000)
new_esEs19(Char(xuu40000), Char(xuu3000)) → new_primEqNat0(xuu40000, xuu3000)
new_esEs22(xuu30000, xuu31000, ty_Char) → new_esEs19(xuu30000, xuu31000)
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_Ratio, bce)) → new_ltEs14(xuu30000, xuu31000, bce)
new_esEs23(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs9(xuu30001, xuu31001, app(app(ty_@2, ed), ee)) → new_esEs5(xuu30001, xuu31001, ed, ee)
new_ltEs17(xuu3000, xuu3100) → new_fsEs(new_compare25(xuu3000, xuu3100))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs25(xuu40001, xuu3001, ty_Bool) → new_esEs12(xuu40001, xuu3001)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Char) → new_ltEs18(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_@0) → new_lt13(xuu30000, xuu31000)
new_esEs27(xuu40001, xuu3001, ty_Float) → new_esEs18(xuu40001, xuu3001)
new_compare9(Integer(xuu30000), Integer(xuu31000)) → new_primCmpInt(xuu30000, xuu31000)
new_asAs(False, xuu137) → False
new_esEs29(xuu4000, xuu300, ty_Bool) → new_esEs12(xuu4000, xuu300)
new_primMulInt(Pos(xuu400000), Neg(xuu30000)) → Neg(new_primMulNat0(xuu400000, xuu30000))
new_primMulInt(Neg(xuu400000), Pos(xuu30000)) → Neg(new_primMulNat0(xuu400000, xuu30000))
new_esEs13([], :(xuu3000, xuu3001), bhd) → False
new_esEs13(:(xuu40000, xuu40001), [], bhd) → False
new_primMulNat0(Succ(xuu4000000), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu300000)) → Zero
new_lt7(xuu30001, xuu31001, app(app(ty_Either, eg), eh)) → new_lt17(xuu30001, xuu31001, eg, eh)
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_Maybe, cbe)) → new_esEs6(xuu40000, xuu3000, cbe)
new_compare26(Char(xuu30000), Char(xuu31000)) → new_primCmpNat2(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_Ratio, chf), cha) → new_ltEs14(xuu30000, xuu31000, chf)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Double, fh) → new_esEs15(xuu40000, xuu3000)
new_ltEs20(xuu3000, xuu3100, ty_Integer) → new_ltEs7(xuu3000, xuu3100)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_[], ga), fh) → new_esEs13(xuu40000, xuu3000, ga)
new_esEs21(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_ltEs12(GT, GT) → True
new_ltEs20(xuu3000, xuu3100, ty_Double) → new_ltEs11(xuu3000, xuu3100)
new_esEs9(xuu30001, xuu31001, ty_Bool) → new_esEs12(xuu30001, xuu31001)
new_esEs10(xuu30000, xuu31000, app(ty_Maybe, bf)) → new_esEs6(xuu30000, xuu31000, bf)
new_ltEs19(xuu30001, xuu31001, ty_@0) → new_ltEs10(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Ordering, cha) → new_ltEs12(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Float, fh) → new_esEs18(xuu40000, xuu3000)
new_primCmpNat1(Succ(xuu3100), xuu3000) → new_primCmpNat2(xuu3100, xuu3000)
new_esEs23(xuu40000, xuu3000, app(ty_Maybe, ccg)) → new_esEs6(xuu40000, xuu3000, ccg)
new_primCmpNat2(Succ(xuu30000), Zero) → GT
new_lt7(xuu30001, xuu31001, app(ty_Ratio, ec)) → new_lt16(xuu30001, xuu31001, ec)
new_compare210(Just(xuu3000), Nothing, False, cgg) → GT
new_lt7(xuu30001, xuu31001, app(ty_Maybe, ef)) → new_lt5(xuu30001, xuu31001, ef)
new_lt8(xuu30000, xuu31000, ty_Float) → new_lt18(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, ty_Bool) → new_esEs12(xuu40002, xuu3002)
new_esEs25(xuu40001, xuu3001, app(ty_[], cec)) → new_esEs13(xuu40001, xuu3001, cec)
new_esEs23(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare27(xuu30000, xuu31000, True) → EQ
new_esEs10(xuu30000, xuu31000, ty_Float) → new_esEs18(xuu30000, xuu31000)
new_ltEs6(xuu30002, xuu31002, ty_Bool) → new_ltEs8(xuu30002, xuu31002)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Bool) → new_ltEs8(xuu30000, xuu31000)
new_compare17(Double(xuu30000, xuu30001), Double(xuu31000, xuu31001)) → new_compare10(new_sr0(xuu30000, xuu31000), new_sr0(xuu30001, xuu31001))
new_esEs12(False, True) → False
new_esEs12(True, False) → False
new_esEs28(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Int) → new_ltEs13(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Bool, fh) → new_esEs12(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_esEs29(xuu4000, xuu300, ty_Double) → new_esEs15(xuu4000, xuu300)
new_ltEs9(xuu3000, xuu3100, bae) → new_fsEs(new_compare0(xuu3000, xuu3100, bae))
new_esEs27(xuu40001, xuu3001, ty_Bool) → new_esEs12(xuu40001, xuu3001)
new_lt8(xuu30000, xuu31000, ty_Char) → new_lt19(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Float) → new_ltEs17(xuu30000, xuu31000)
new_ltEs19(xuu30001, xuu31001, app(app(app(ty_@3, beh), bfa), bfb)) → new_ltEs5(xuu30001, xuu31001, beh, bfa, bfb)
new_compare13(xuu30000, xuu31000, ty_Double) → new_compare17(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_ltEs18(xuu3000, xuu3100) → new_fsEs(new_compare26(xuu3000, xuu3100))
new_compare10(xuu30, xuu31) → new_primCmpInt(xuu30, xuu31)
new_esEs10(xuu30000, xuu31000, app(ty_Ratio, ff)) → new_esEs17(xuu30000, xuu31000, ff)
new_lt7(xuu30001, xuu31001, app(app(app(ty_@3, dg), dh), ea)) → new_lt10(xuu30001, xuu31001, dg, dh, ea)
new_ltEs12(EQ, LT) → False
new_esEs25(xuu40001, xuu3001, app(app(ty_@2, cfa), cfb)) → new_esEs5(xuu40001, xuu3001, cfa, cfb)
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_[], cae)) → new_esEs13(xuu40000, xuu3000, cae)
new_lt8(xuu30000, xuu31000, ty_@0) → new_lt13(xuu30000, xuu31000)
new_ltEs19(xuu30001, xuu31001, app(app(ty_@2, bfe), bff)) → new_ltEs15(xuu30001, xuu31001, bfe, bff)
new_compare13(xuu30000, xuu31000, app(app(ty_Either, bbf), bbg)) → new_compare19(xuu30000, xuu31000, bbf, bbg)
new_lt7(xuu30001, xuu31001, app(ty_[], eb)) → new_lt12(xuu30001, xuu31001, eb)
new_esEs22(xuu30000, xuu31000, ty_@0) → new_esEs14(xuu30000, xuu31000)
new_esEs23(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs29(xuu4000, xuu300, app(app(ty_Either, hb), fh)) → new_esEs7(xuu4000, xuu300, hb, fh)
new_compare112(xuu130, xuu131, False, cac) → GT
new_compare29(xuu30000, xuu31000, False) → new_compare111(xuu30000, xuu31000, new_ltEs8(xuu30000, xuu31000))
new_esEs22(xuu30000, xuu31000, app(ty_Ratio, bgf)) → new_esEs17(xuu30000, xuu31000, bgf)
new_ltEs19(xuu30001, xuu31001, ty_Integer) → new_ltEs7(xuu30001, xuu31001)
new_esEs30(xuu19, xuu14, ty_Ordering) → new_esEs8(xuu19, xuu14)
new_esEs10(xuu30000, xuu31000, ty_Ordering) → new_esEs8(xuu30000, xuu31000)
new_lt4(xuu30000, xuu31000, bd, be) → new_esEs8(new_compare6(xuu30000, xuu31000, bd, be), LT)
new_lt7(xuu30001, xuu31001, ty_Char) → new_lt19(xuu30001, xuu31001)
new_compare0([], :(xuu31000, xuu31001), bae) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs9(xuu30001, xuu31001, ty_Char) → new_esEs19(xuu30001, xuu31001)
new_primCompAux0(xuu30000, xuu31000, xuu174, bae) → new_primCompAux00(xuu174, new_compare13(xuu30000, xuu31000, bae))
new_esEs9(xuu30001, xuu31001, ty_Double) → new_esEs15(xuu30001, xuu31001)
new_asAs(True, xuu137) → xuu137
new_primMulNat0(Succ(xuu4000000), Succ(xuu300000)) → new_primPlusNat0(new_primMulNat0(xuu4000000, Succ(xuu300000)), xuu300000)
new_esEs27(xuu40001, xuu3001, app(ty_[], dbg)) → new_esEs13(xuu40001, xuu3001, dbg)
new_esEs27(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(ty_Either, cba), cbb)) → new_esEs7(xuu40000, xuu3000, cba, cbb)
new_esEs26(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_ltEs6(xuu30002, xuu31002, ty_Int) → new_ltEs13(xuu30002, xuu31002)
new_esEs9(xuu30001, xuu31001, app(app(ty_Either, eg), eh)) → new_esEs7(xuu30001, xuu31001, eg, eh)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Int) → new_ltEs13(xuu30000, xuu31000)
new_lt17(xuu30000, xuu31000, bg, bh) → new_esEs8(new_compare19(xuu30000, xuu31000, bg, bh), LT)
new_fsEs(xuu147) → new_not(new_esEs8(xuu147, GT))
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare27(xuu30000, xuu31000, False) → new_compare110(xuu30000, xuu31000, new_ltEs12(xuu30000, xuu31000))
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(ty_@2, bcf), bcg)) → new_ltEs15(xuu30000, xuu31000, bcf, bcg)
new_ltEs6(xuu30002, xuu31002, ty_Float) → new_ltEs17(xuu30002, xuu31002)
new_ltEs6(xuu30002, xuu31002, app(ty_[], cg)) → new_ltEs9(xuu30002, xuu31002, cg)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Bool, cha) → new_ltEs8(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, app(ty_Maybe, cea)) → new_esEs6(xuu40002, xuu3002, cea)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Char, fh) → new_esEs19(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, app(ty_Ratio, dbf)) → new_esEs17(xuu40001, xuu3001, dbf)
new_compare7(xuu30000, xuu31000, bf) → new_compare210(xuu30000, xuu31000, new_esEs6(xuu30000, xuu31000, bf), bf)
new_esEs24(xuu40002, xuu3002, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs4(xuu40002, xuu3002, cdb, cdc, cdd)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_primCompAux00(xuu180, GT) → GT
new_esEs25(xuu40001, xuu3001, app(app(ty_Either, ceg), ceh)) → new_esEs7(xuu40001, xuu3001, ceg, ceh)
new_esEs18(Float(xuu40000, xuu40001), Float(xuu3000, xuu3001)) → new_esEs16(new_sr0(xuu40000, xuu3000), new_sr0(xuu40001, xuu3001))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs12(GT, LT) → False
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(app(ty_@3, chb), chc), chd), cha) → new_ltEs5(xuu30000, xuu31000, chb, chc, chd)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(ty_Ratio, dah)) → new_ltEs14(xuu30000, xuu31000, dah)
new_esEs29(xuu4000, xuu300, ty_Ordering) → new_esEs8(xuu4000, xuu300)
new_lt7(xuu30001, xuu31001, ty_Integer) → new_lt9(xuu30001, xuu31001)
new_esEs28(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs5(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), ca, cb, cc) → new_pePe(new_lt8(xuu30000, xuu31000, ca), new_asAs(new_esEs10(xuu30000, xuu31000, ca), new_pePe(new_lt7(xuu30001, xuu31001, cb), new_asAs(new_esEs9(xuu30001, xuu31001, cb), new_ltEs6(xuu30002, xuu31002, cc)))))
new_primCmpInt(Neg(Succ(xuu3000)), Pos(xuu310)) → LT
new_esEs23(xuu40000, xuu3000, app(ty_[], cbg)) → new_esEs13(xuu40000, xuu3000, cbg)
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs5(xuu30000, xuu31000, bca, bcb, bcc)
new_esEs22(xuu30000, xuu31000, ty_Int) → new_esEs16(xuu30000, xuu31000)
new_not(True) → False
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(app(app(ty_@3, dad), dae), daf)) → new_ltEs5(xuu30000, xuu31000, dad, dae, daf)

The set Q consists of the following terms:

new_primCompAux00(x0, EQ)
new_esEs9(x0, x1, ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs14(x0, x1, x2)
new_esEs9(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Double)
new_pePe(True, x0)
new_ltEs12(LT, LT)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, ty_Integer)
new_lt8(x0, x1, ty_@0)
new_compare13(x0, x1, ty_Char)
new_compare11(x0, x1, False, x2, x3)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs10(x0, x1, ty_Integer)
new_primCmpNat0(x0, Succ(x1))
new_compare13(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, ty_Float)
new_lt7(x0, x1, ty_Ordering)
new_compare28(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, ty_@0)
new_esEs12(False, False)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs6(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs16(x0, x1)
new_lt8(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, x2, x3, x4)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Ordering)
new_compare26(Char(x0), Char(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs30(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare210(Just(x0), Nothing, False, x1)
new_primPlusNat0(x0, x1)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs8(GT, GT)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_primCompAux00(x0, LT)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Float)
new_ltEs12(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_lt9(x0, x1)
new_ltEs8(True, True)
new_compare13(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs8(LT, LT)
new_primCompAux00(x0, GT)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs15(Double(x0, x1), Double(x2, x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Bool)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_lt7(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_Bool)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs23(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primMulNat0(Succ(x0), Zero)
new_ltEs16(Just(x0), Just(x1), ty_@0)
new_compare113(x0, x1, True, x2, x3, x4)
new_lt8(x0, x1, ty_Char)
new_compare13(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), Succ(x1))
new_ltEs18(x0, x1)
new_ltEs6(x0, x1, ty_Double)
new_ltEs10(x0, x1)
new_primEqNat0(Zero, Zero)
new_compare24(x0, x1, False, x2, x3)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Just(x0), Nothing, x1)
new_ltEs16(Just(x0), Just(x1), ty_Integer)
new_ltEs16(Nothing, Nothing, x0)
new_compare13(x0, x1, ty_Int)
new_ltEs7(x0, x1)
new_compare13(x0, x1, ty_@0)
new_lt15(x0, x1)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primMulNat0(Zero, Zero)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt8(x0, x1, ty_Float)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Ordering)
new_lt8(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt13(x0, x1)
new_lt16(x0, x1, x2)
new_esEs25(x0, x1, ty_Char)
new_compare6(x0, x1, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_primCmpNat1(Zero, x0)
new_compare13(x0, x1, app(ty_[], x2))
new_esEs14(@0, @0)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Double)
new_lt8(x0, x1, app(ty_[], x2))
new_ltEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare13(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs16(Nothing, Just(x0), x1)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare16(@0, @0)
new_compare111(x0, x1, True)
new_esEs25(x0, x1, ty_Bool)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs28(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt18(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare210(Nothing, Just(x0), False, x1)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Integer)
new_ltEs6(x0, x1, ty_Bool)
new_primCmpNat1(Succ(x0), x1)
new_lt5(x0, x1, x2)
new_primPlusNat1(Zero, Zero)
new_compare210(Just(x0), Just(x1), False, x2)
new_esEs24(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpNat2(Zero, Zero)
new_ltEs16(Just(x0), Just(x1), ty_Double)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs9(x0, x1, x2)
new_esEs9(x0, x1, ty_@0)
new_compare25(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat1(Succ(x0), Zero)
new_esEs23(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare10(x0, x1)
new_esEs30(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), ty_Bool)
new_ltEs11(x0, x1)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare7(x0, x1, x2)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs12(GT, EQ)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(EQ, GT)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs16(Just(x0), Just(x1), ty_Char)
new_sr(Integer(x0), Integer(x1))
new_esEs11(Integer(x0), Integer(x1))
new_compare12(x0, x1, False, x2, x3)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt7(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs12(True, True)
new_ltEs8(False, False)
new_esEs29(x0, x1, ty_Char)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Double)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Ordering)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs24(x0, x1, ty_Int)
new_compare27(x0, x1, False)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs20(x0, x1, ty_Ordering)
new_lt4(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primCmpNat0(x0, Zero)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, x2)
new_pePe(False, x0)
new_lt20(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs12(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, ty_Double)
new_compare29(x0, x1, True)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_compare9(Integer(x0), Integer(x1))
new_ltEs13(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt14(x0, x1)
new_esEs30(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare17(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs13([], :(x0, x1), x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs17(x0, x1)
new_compare14(x0, x1, x2, x3, x4)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare23(x0, x1, True, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_compare110(x0, x1, False)
new_esEs29(x0, x1, ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_fsEs(x0)
new_ltEs16(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_lt8(x0, x1, app(ty_Maybe, x2))
new_esEs19(Char(x0), Char(x1))
new_esEs30(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs20(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primCmpNat2(Succ(x0), Zero)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Ordering)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_lt7(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs6(Nothing, Just(x0), x1)
new_esEs29(x0, x1, ty_Ordering)
new_compare111(x0, x1, False)
new_esEs9(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_asAs(True, x0)
new_ltEs19(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_compare210(Nothing, Nothing, False, x0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs10(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs28(x0, x1, ty_Integer)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(False, True)
new_esEs12(True, False)
new_ltEs16(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2, x3)
new_compare13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_primCmpNat2(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare28(x0, x1, False, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Integer)
new_asAs(False, x0)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs16(Just(x0), Nothing, x1)
new_lt17(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_not(True)
new_ltEs6(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Integer)
new_compare23(x0, x1, False, x2, x3)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_not(False)
new_primPlusNat1(Zero, Succ(x0))
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt8(x0, x1, ty_Double)
new_compare18(x0, x1)
new_ltEs16(Just(x0), Just(x1), ty_Float)
new_esEs25(x0, x1, ty_@0)
new_esEs13(:(x0, x1), [], x2)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, ty_Double)
new_ltEs16(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(x0, x1)
new_compare210(x0, x1, True, x2)
new_esEs27(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, ty_Int)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt8(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Zero)
new_sr0(x0, x1)
new_esEs13([], [], x0)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs24(x0, x1, ty_Char)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Float)
new_compare11(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Bool)
new_ltEs12(EQ, LT)
new_ltEs12(LT, EQ)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_compare112(x0, x1, False, x2)
new_esEs10(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_compare12(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_compare112(x0, x1, True, x2)
new_lt7(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs12(GT, LT)
new_ltEs12(LT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare113(x0, x1, False, x2, x3, x4)
new_compare27(x0, x1, True)
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt8(x0, x1, ty_Int)
new_ltEs16(Just(x0), Just(x1), ty_Ordering)
new_compare0([], [], x0)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_ltEs16(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs.

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

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

new_addToFM_C20(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, False, h, ba) → new_addToFM_C11(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, new_esEs8(new_compare210(Just(xuu4000), Nothing, False, h), GT), h, ba)
new_addToFM_C21(xuu14, xuu15, xuu16, xuu17, xuu18, xuu19, xuu20, False, bb, bc) → new_addToFM_C12(xuu14, xuu15, xuu16, xuu17, xuu18, xuu19, xuu20, new_esEs8(new_compare210(Just(xuu19), Just(xuu14), new_esEs30(xuu19, xuu14, bb), bb), GT), bb, bc)
new_addToFM_C21(xuu14, xuu15, xuu16, xuu17, xuu18, xuu19, xuu20, True, bb, bc) → new_addToFM_C(xuu17, Just(xuu19), xuu20, bb, bc)
new_addToFM_C11(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, True, h, ba) → new_addToFM_C(xuu34, Just(xuu4000), xuu401, h, ba)
new_addToFM_C(Branch(Nothing, xuu31, xuu32, xuu33, xuu34), Just(xuu4000), xuu401, h, ba) → new_addToFM_C20(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, new_esEs8(new_compare210(Just(xuu4000), Nothing, False, h), LT), h, ba)
new_addToFM_C12(xuu14, xuu15, xuu16, xuu17, xuu18, xuu19, xuu20, True, bb, bc) → new_addToFM_C(xuu18, Just(xuu19), xuu20, bb, bc)
new_addToFM_C20(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, True, h, ba) → new_addToFM_C(xuu33, Just(xuu4000), xuu401, h, ba)
new_addToFM_C(Branch(Just(xuu300), xuu31, xuu32, xuu33, xuu34), Just(xuu4000), xuu401, h, ba) → new_addToFM_C21(xuu300, xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, new_esEs8(new_compare210(Just(xuu4000), Just(xuu300), new_esEs29(xuu4000, xuu300, h), h), LT), h, ba)

The TRS R consists of the following rules:

new_esEs30(xuu19, xuu14, app(ty_Maybe, bee)) → new_esEs6(xuu19, xuu14, bee)
new_esEs25(xuu40001, xuu3001, ty_Char) → new_esEs19(xuu40001, xuu3001)
new_primCmpNat0(xuu3000, Succ(xuu3100)) → new_primCmpNat2(xuu3000, xuu3100)
new_ltEs19(xuu30001, xuu31001, ty_Ordering) → new_ltEs12(xuu30001, xuu31001)
new_ltEs6(xuu30002, xuu31002, app(app(ty_@2, db), dc)) → new_ltEs15(xuu30002, xuu31002, db, dc)
new_esEs28(xuu40000, xuu3000, app(ty_[], dda)) → new_esEs13(xuu40000, xuu3000, dda)
new_esEs23(xuu40000, xuu3000, app(app(ty_Either, ccc), ccd)) → new_esEs7(xuu40000, xuu3000, ccc, ccd)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(ty_@2, cbc), cbd)) → new_esEs5(xuu40000, xuu3000, cbc, cbd)
new_compare112(xuu130, xuu131, True, cac) → LT
new_esEs29(xuu4000, xuu300, ty_Int) → new_esEs16(xuu4000, xuu300)
new_ltEs20(xuu3000, xuu3100, ty_Char) → new_ltEs18(xuu3000, xuu3100)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(ty_Either, ge), gf), fh) → new_esEs7(xuu40000, xuu3000, ge, gf)
new_ltEs8(False, True) → True
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_esEs10(xuu30000, xuu31000, app(app(app(ty_@3, fa), fb), fc)) → new_esEs4(xuu30000, xuu31000, fa, fb, fc)
new_esEs27(xuu40001, xuu3001, ty_Char) → new_esEs19(xuu40001, xuu3001)
new_compare13(xuu30000, xuu31000, app(app(app(ty_@3, baf), bag), bah)) → new_compare14(xuu30000, xuu31000, baf, bag, bah)
new_ltEs10(xuu3000, xuu3100) → new_fsEs(new_compare16(xuu3000, xuu3100))
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Ordering) → new_ltEs12(xuu30000, xuu31000)
new_esEs13([], [], bhd) → True
new_ltEs12(LT, GT) → True
new_ltEs19(xuu30001, xuu31001, app(ty_[], bfc)) → new_ltEs9(xuu30001, xuu31001, bfc)
new_lt20(xuu30000, xuu31000, app(ty_Ratio, bgf)) → new_lt16(xuu30000, xuu31000, bgf)
new_lt7(xuu30001, xuu31001, ty_Bool) → new_lt11(xuu30001, xuu31001)
new_lt16(xuu30000, xuu31000, ff) → new_esEs8(new_compare8(xuu30000, xuu31000, ff), LT)
new_esEs4(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), bhe, bhf, bhg) → new_asAs(new_esEs26(xuu40000, xuu3000, bhe), new_asAs(new_esEs25(xuu40001, xuu3001, bhf), new_esEs24(xuu40002, xuu3002, bhg)))
new_esEs11(Integer(xuu40000), Integer(xuu3000)) → new_primEqInt(xuu40000, xuu3000)
new_esEs30(xuu19, xuu14, app(ty_[], bde)) → new_esEs13(xuu19, xuu14, bde)
new_esEs15(Double(xuu40000, xuu40001), Double(xuu3000, xuu3001)) → new_esEs16(new_sr0(xuu40000, xuu3000), new_sr0(xuu40001, xuu3001))
new_compare13(xuu30000, xuu31000, app(ty_Maybe, bbe)) → new_compare7(xuu30000, xuu31000, bbe)
new_esEs28(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs26(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_compare19(xuu30000, xuu31000, bg, bh) → new_compare23(xuu30000, xuu31000, new_esEs7(xuu30000, xuu31000, bg, bh), bg, bh)
new_ltEs19(xuu30001, xuu31001, ty_Double) → new_ltEs11(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(ty_@2, chg), chh), cha) → new_ltEs15(xuu30000, xuu31000, chg, chh)
new_primMulNat0(Zero, Zero) → Zero
new_esEs27(xuu40001, xuu3001, app(app(app(ty_@3, dbh), dca), dcb)) → new_esEs4(xuu40001, xuu3001, dbh, dca, dcb)
new_ltEs12(LT, LT) → True
new_compare29(xuu30000, xuu31000, True) → EQ
new_sr(Integer(xuu300000), Integer(xuu310010)) → Integer(new_primMulInt(xuu300000, xuu310010))
new_esEs12(True, True) → True
new_ltEs6(xuu30002, xuu31002, app(app(app(ty_@3, cd), ce), cf)) → new_ltEs5(xuu30002, xuu31002, cd, ce, cf)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_@0) → new_ltEs10(xuu30000, xuu31000)
new_ltEs15(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), bef, beg) → new_pePe(new_lt20(xuu30000, xuu31000, bef), new_asAs(new_esEs22(xuu30000, xuu31000, bef), new_ltEs19(xuu30001, xuu31001, beg)))
new_esEs23(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Integer) → new_ltEs7(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Double) → new_ltEs11(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(ty_Ratio, hc)) → new_esEs17(xuu40000, xuu3000, hc)
new_lt12(xuu30000, xuu31000, fd) → new_esEs8(new_compare0(xuu30000, xuu31000, fd), LT)
new_esEs24(xuu40002, xuu3002, ty_@0) → new_esEs14(xuu40002, xuu3002)
new_lt8(xuu30000, xuu31000, app(ty_[], fd)) → new_lt12(xuu30000, xuu31000, fd)
new_compare16(@0, @0) → EQ
new_esEs30(xuu19, xuu14, app(app(ty_Either, bea), beb)) → new_esEs7(xuu19, xuu14, bea, beb)
new_compare8(:%(xuu30000, xuu30001), :%(xuu31000, xuu31001), ty_Integer) → new_compare9(new_sr(xuu30000, xuu31001), new_sr(xuu31000, xuu30001))
new_lt20(xuu30000, xuu31000, ty_Double) → new_lt14(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Integer) → new_lt9(xuu30000, xuu31000)
new_ltEs12(LT, EQ) → True
new_ltEs20(xuu3000, xuu3100, app(ty_[], bae)) → new_ltEs9(xuu3000, xuu3100, bae)
new_lt8(xuu30000, xuu31000, app(ty_Ratio, ff)) → new_lt16(xuu30000, xuu31000, ff)
new_ltEs11(xuu3000, xuu3100) → new_fsEs(new_compare17(xuu3000, xuu3100))
new_esEs22(xuu30000, xuu31000, app(app(ty_@2, bgg), bgh)) → new_esEs5(xuu30000, xuu31000, bgg, bgh)
new_compare0(:(xuu30000, xuu30001), :(xuu31000, xuu31001), bae) → new_primCompAux0(xuu30000, xuu31000, new_compare0(xuu30001, xuu31001, bae), bae)
new_compare210(Nothing, Nothing, False, cgg) → LT
new_esEs24(xuu40002, xuu3002, app(app(ty_@2, cdg), cdh)) → new_esEs5(xuu40002, xuu3002, cdg, cdh)
new_esEs22(xuu30000, xuu31000, app(ty_Maybe, bha)) → new_esEs6(xuu30000, xuu31000, bha)
new_ltEs20(xuu3000, xuu3100, app(ty_Ratio, cgf)) → new_ltEs14(xuu3000, xuu3100, cgf)
new_esEs27(xuu40001, xuu3001, app(ty_Maybe, dcg)) → new_esEs6(xuu40001, xuu3001, dcg)
new_esEs26(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_esEs25(xuu40001, xuu3001, ty_Double) → new_esEs15(xuu40001, xuu3001)
new_compare15(xuu30000, xuu31000) → new_compare29(xuu30000, xuu31000, new_esEs12(xuu30000, xuu31000))
new_esEs29(xuu4000, xuu300, ty_Float) → new_esEs18(xuu4000, xuu300)
new_lt20(xuu30000, xuu31000, ty_Ordering) → new_lt15(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Char) → new_ltEs18(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, app(app(ty_Either, bhb), bhc)) → new_esEs7(xuu30000, xuu31000, bhb, bhc)
new_lt18(xuu30000, xuu31000) → new_esEs8(new_compare25(xuu30000, xuu31000), LT)
new_ltEs19(xuu30001, xuu31001, ty_Char) → new_ltEs18(xuu30001, xuu31001)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(ty_Maybe, bad)) → new_esEs6(xuu40000, xuu3000, bad)
new_ltEs19(xuu30001, xuu31001, app(app(ty_Either, bfh), bga)) → new_ltEs4(xuu30001, xuu31001, bfh, bga)
new_pePe(False, xuu163) → xuu163
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_esEs7(Left(xuu40000), Right(xuu3000), hb, fh) → False
new_esEs7(Right(xuu40000), Left(xuu3000), hb, fh) → False
new_lt20(xuu30000, xuu31000, ty_Bool) → new_lt11(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, ty_Bool) → new_esEs12(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Double, cha) → new_ltEs11(xuu30000, xuu31000)
new_compare6(xuu30000, xuu31000, bd, be) → new_compare24(xuu30000, xuu31000, new_esEs5(xuu30000, xuu31000, bd, be), bd, be)
new_esEs28(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, app(app(ty_Either, dcc), dcd)) → new_esEs7(xuu40001, xuu3001, dcc, dcd)
new_esEs20(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_ltEs20(xuu3000, xuu3100, ty_@0) → new_ltEs10(xuu3000, xuu3100)
new_compare13(xuu30000, xuu31000, ty_Int) → new_compare10(xuu30000, xuu31000)
new_esEs26(xuu40000, xuu3000, app(ty_Ratio, cfd)) → new_esEs17(xuu40000, xuu3000, cfd)
new_esEs22(xuu30000, xuu31000, ty_Double) → new_esEs15(xuu30000, xuu31000)
new_esEs26(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_ltEs20(xuu3000, xuu3100, app(app(ty_Either, cgh), cha)) → new_ltEs4(xuu3000, xuu3100, cgh, cha)
new_lt20(xuu30000, xuu31000, app(app(app(ty_@3, bgb), bgc), bgd)) → new_lt10(xuu30000, xuu31000, bgb, bgc, bgd)
new_esEs28(xuu40000, xuu3000, app(app(app(ty_@3, ddb), ddc), ddd)) → new_esEs4(xuu40000, xuu3000, ddb, ddc, ddd)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Double) → new_ltEs11(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(app(ty_Either, dbd), dbe)) → new_ltEs4(xuu30000, xuu31000, dbd, dbe)
new_esEs22(xuu30000, xuu31000, ty_Ordering) → new_esEs8(xuu30000, xuu31000)
new_compare111(xuu30000, xuu31000, False) → GT
new_compare111(xuu30000, xuu31000, True) → LT
new_esEs26(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_ltEs4(Left(xuu30000), Right(xuu31000), cgh, cha) → True
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(app(ty_@2, bab), bac)) → new_esEs5(xuu40000, xuu3000, bab, bac)
new_ltEs20(xuu3000, xuu3100, ty_Ordering) → new_ltEs12(xuu3000, xuu3100)
new_primCmpInt(Neg(Succ(xuu3000)), Neg(xuu310)) → new_primCmpNat1(xuu310, xuu3000)
new_lt6(xuu300, xuu310) → new_esEs8(new_compare10(xuu300, xuu310), LT)
new_ltEs20(xuu3000, xuu3100, ty_Bool) → new_ltEs8(xuu3000, xuu3100)
new_esEs8(LT, LT) → True
new_esEs30(xuu19, xuu14, ty_Float) → new_esEs18(xuu19, xuu14)
new_ltEs16(Nothing, Nothing, bbh) → True
new_lt20(xuu30000, xuu31000, ty_Char) → new_lt19(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Integer, fh) → new_esEs11(xuu40000, xuu3000)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_Maybe, daa), cha) → new_ltEs16(xuu30000, xuu31000, daa)
new_esEs25(xuu40001, xuu3001, ty_Ordering) → new_esEs8(xuu40001, xuu3001)
new_esEs20(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_esEs28(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_compare210(Nothing, Just(xuu3100), False, cgg) → LT
new_esEs24(xuu40002, xuu3002, app(app(ty_Either, cde), cdf)) → new_esEs7(xuu40002, xuu3002, cde, cdf)
new_ltEs6(xuu30002, xuu31002, ty_Double) → new_ltEs11(xuu30002, xuu31002)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_@0) → new_ltEs10(xuu30000, xuu31000)
new_pePe(True, xuu163) → True
new_compare0([], [], bae) → EQ
new_esEs24(xuu40002, xuu3002, ty_Int) → new_esEs16(xuu40002, xuu3002)
new_primEqNat0(Zero, Zero) → True
new_ltEs19(xuu30001, xuu31001, ty_Int) → new_ltEs13(xuu30001, xuu31001)
new_esEs29(xuu4000, xuu300, app(ty_Maybe, cab)) → new_esEs6(xuu4000, xuu300, cab)
new_compare210(Just(xuu3000), Just(xuu3100), False, cgg) → new_compare112(xuu3000, xuu3100, new_ltEs20(xuu3000, xuu3100, cgg), cgg)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(ty_@2, gg), gh), fh) → new_esEs5(xuu40000, xuu3000, gg, gh)
new_esEs26(xuu40000, xuu3000, app(ty_Maybe, cge)) → new_esEs6(xuu40000, xuu3000, cge)
new_esEs14(@0, @0) → True
new_esEs30(xuu19, xuu14, ty_Double) → new_esEs15(xuu19, xuu14)
new_esEs9(xuu30001, xuu31001, app(app(app(ty_@3, dg), dh), ea)) → new_esEs4(xuu30001, xuu31001, dg, dh, ea)
new_ltEs6(xuu30002, xuu31002, ty_@0) → new_ltEs10(xuu30002, xuu31002)
new_esEs29(xuu4000, xuu300, app(ty_[], bhd)) → new_esEs13(xuu4000, xuu300, bhd)
new_esEs9(xuu30001, xuu31001, app(ty_Maybe, ef)) → new_esEs6(xuu30001, xuu31001, ef)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Float, cha) → new_ltEs17(xuu30000, xuu31000)
new_esEs9(xuu30001, xuu31001, ty_@0) → new_esEs14(xuu30001, xuu31001)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Ordering, fh) → new_esEs8(xuu40000, xuu3000)
new_esEs24(xuu40002, xuu3002, app(ty_Ratio, cch)) → new_esEs17(xuu40002, xuu3002, cch)
new_compare13(xuu30000, xuu31000, ty_Integer) → new_compare9(xuu30000, xuu31000)
new_compare12(xuu30000, xuu31000, False, bd, be) → GT
new_esEs30(xuu19, xuu14, ty_Char) → new_esEs19(xuu19, xuu14)
new_compare13(xuu30000, xuu31000, ty_Ordering) → new_compare18(xuu30000, xuu31000)
new_lt7(xuu30001, xuu31001, ty_Double) → new_lt14(xuu30001, xuu31001)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Ordering) → new_ltEs12(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Int, cha) → new_ltEs13(xuu30000, xuu31000)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3100))) → new_primCmpNat0(xuu3100, Zero)
new_esEs26(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs24(xuu40002, xuu3002, ty_Char) → new_esEs19(xuu40002, xuu3002)
new_esEs8(GT, GT) → True
new_esEs30(xuu19, xuu14, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs4(xuu19, xuu14, bdf, bdg, bdh)
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_[], bcd)) → new_ltEs9(xuu30000, xuu31000, bcd)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3100))) → new_primCmpNat1(Zero, xuu3100)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(app(ty_Either, hh), baa)) → new_esEs7(xuu40000, xuu3000, hh, baa)
new_compare13(xuu30000, xuu31000, app(ty_[], bba)) → new_compare0(xuu30000, xuu31000, bba)
new_lt15(xuu30000, xuu31000) → new_esEs8(new_compare18(xuu30000, xuu31000), LT)
new_esEs12(False, False) → True
new_esEs26(xuu40000, xuu3000, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs4(xuu40000, xuu3000, cff, cfg, cfh)
new_ltEs20(xuu3000, xuu3100, app(app(ty_@2, bef), beg)) → new_ltEs15(xuu3000, xuu3100, bef, beg)
new_ltEs19(xuu30001, xuu31001, app(ty_Ratio, bfd)) → new_ltEs14(xuu30001, xuu31001, bfd)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(ty_[], hd)) → new_esEs13(xuu40000, xuu3000, hd)
new_lt10(xuu30000, xuu31000, fa, fb, fc) → new_esEs8(new_compare14(xuu30000, xuu31000, fa, fb, fc), LT)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_esEs28(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_lt20(xuu30000, xuu31000, app(app(ty_Either, bhb), bhc)) → new_lt17(xuu30000, xuu31000, bhb, bhc)
new_esEs9(xuu30001, xuu31001, ty_Integer) → new_esEs11(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_@0, cha) → new_ltEs10(xuu30000, xuu31000)
new_ltEs20(xuu3000, xuu3100, app(app(app(ty_@3, ca), cb), cc)) → new_ltEs5(xuu3000, xuu3100, ca, cb, cc)
new_lt8(xuu30000, xuu31000, ty_Double) → new_lt14(xuu30000, xuu31000)
new_ltEs16(Nothing, Just(xuu31000), bbh) → True
new_primEqInt(Neg(Succ(xuu400000)), Neg(Succ(xuu30000))) → new_primEqNat0(xuu400000, xuu30000)
new_esEs23(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs13(:(xuu40000, xuu40001), :(xuu3000, xuu3001), bhd) → new_asAs(new_esEs23(xuu40000, xuu3000, bhd), new_esEs13(xuu40001, xuu3001, bhd))
new_esEs26(xuu40000, xuu3000, app(ty_[], cfe)) → new_esEs13(xuu40000, xuu3000, cfe)
new_primPlusNat1(Succ(xuu25200), Zero) → Succ(xuu25200)
new_primPlusNat1(Zero, Succ(xuu9400)) → Succ(xuu9400)
new_ltEs6(xuu30002, xuu31002, ty_Char) → new_ltEs18(xuu30002, xuu31002)
new_lt8(xuu30000, xuu31000, app(ty_Maybe, bf)) → new_lt5(xuu30000, xuu31000, bf)
new_ltEs8(True, True) → True
new_esEs16(xuu4000, xuu300) → new_primEqInt(xuu4000, xuu300)
new_primCmpNat1(Zero, xuu3000) → LT
new_esEs30(xuu19, xuu14, ty_Integer) → new_esEs11(xuu19, xuu14)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_Maybe, bch)) → new_ltEs16(xuu30000, xuu31000, bch)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Char, cha) → new_ltEs18(xuu30000, xuu31000)
new_ltEs12(EQ, EQ) → True
new_compare13(xuu30000, xuu31000, ty_Float) → new_compare25(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Integer) → new_ltEs7(xuu30000, xuu31000)
new_lt8(xuu30000, xuu31000, ty_Integer) → new_lt9(xuu30000, xuu31000)
new_esEs21(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs28(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_primEqInt(Neg(Zero), Neg(Succ(xuu30000))) → False
new_primEqInt(Neg(Succ(xuu400000)), Neg(Zero)) → False
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(ty_Either, dab), dac), cha) → new_ltEs4(xuu30000, xuu31000, dab, dac)
new_esEs8(EQ, EQ) → True
new_esEs6(Just(xuu40000), Just(xuu3000), ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs17(:%(xuu40000, xuu40001), :%(xuu3000, xuu3001), bdc) → new_asAs(new_esEs21(xuu40000, xuu3000, bdc), new_esEs20(xuu40001, xuu3001, bdc))
new_esEs23(xuu40000, xuu3000, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs4(xuu40000, xuu3000, cbh, cca, ccb)
new_compare24(xuu30000, xuu31000, True, bd, be) → EQ
new_esEs5(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), bhh, caa) → new_asAs(new_esEs28(xuu40000, xuu3000, bhh), new_esEs27(xuu40001, xuu3001, caa))
new_lt20(xuu30000, xuu31000, app(ty_Maybe, bha)) → new_lt5(xuu30000, xuu31000, bha)
new_ltEs7(xuu3000, xuu3100) → new_fsEs(new_compare9(xuu3000, xuu3100))
new_ltEs13(xuu3000, xuu3100) → new_fsEs(new_compare10(xuu3000, xuu3100))
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_ltEs19(xuu30001, xuu31001, app(ty_Maybe, bfg)) → new_ltEs16(xuu30001, xuu31001, bfg)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs26(xuu40000, xuu3000, app(app(ty_Either, cga), cgb)) → new_esEs7(xuu40000, xuu3000, cga, cgb)
new_esEs9(xuu30001, xuu31001, ty_Float) → new_esEs18(xuu30001, xuu31001)
new_ltEs14(xuu3000, xuu3100, cgf) → new_fsEs(new_compare8(xuu3000, xuu3100, cgf))
new_compare23(xuu30000, xuu31000, False, bg, bh) → new_compare11(xuu30000, xuu31000, new_ltEs4(xuu30000, xuu31000, bg, bh), bg, bh)
new_esEs6(Nothing, Nothing, cab) → True
new_ltEs6(xuu30002, xuu31002, app(ty_Maybe, dd)) → new_ltEs16(xuu30002, xuu31002, dd)
new_compare113(xuu30000, xuu31000, False, fa, fb, fc) → GT
new_ltEs20(xuu3000, xuu3100, app(ty_Maybe, bbh)) → new_ltEs16(xuu3000, xuu3100, bbh)
new_primEqInt(Pos(Succ(xuu400000)), Pos(Succ(xuu30000))) → new_primEqNat0(xuu400000, xuu30000)
new_lt20(xuu30000, xuu31000, app(ty_[], bge)) → new_lt12(xuu30000, xuu31000, bge)
new_lt5(xuu30000, xuu31000, bf) → new_esEs8(new_compare7(xuu30000, xuu31000, bf), LT)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_compare24(xuu30000, xuu31000, False, bd, be) → new_compare12(xuu30000, xuu31000, new_ltEs15(xuu30000, xuu31000, bd, be), bd, be)
new_compare12(xuu30000, xuu31000, True, bd, be) → LT
new_esEs30(xuu19, xuu14, ty_Int) → new_esEs16(xuu19, xuu14)
new_compare8(:%(xuu30000, xuu30001), :%(xuu31000, xuu31001), ty_Int) → new_compare10(new_sr0(xuu30000, xuu31001), new_sr0(xuu31000, xuu30001))
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_Ratio, cad)) → new_esEs17(xuu40000, xuu3000, cad)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(app(app(ty_@3, he), hf), hg)) → new_esEs4(xuu40000, xuu3000, he, hf, hg)
new_esEs6(Just(xuu40000), Nothing, cab) → False
new_esEs6(Nothing, Just(xuu3000), cab) → False
new_primEqNat0(Succ(xuu400000), Succ(xuu30000)) → new_primEqNat0(xuu400000, xuu30000)
new_esEs23(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, ty_Ordering) → new_esEs8(xuu40001, xuu3001)
new_lt13(xuu30000, xuu31000) → new_esEs8(new_compare16(xuu30000, xuu31000), LT)
new_lt8(xuu30000, xuu31000, ty_Bool) → new_lt11(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, ty_Double) → new_esEs15(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, ty_Bool) → new_esEs12(xuu30000, xuu31000)
new_lt14(xuu30000, xuu31000) → new_esEs8(new_compare17(xuu30000, xuu31000), LT)
new_lt7(xuu30001, xuu31001, ty_Float) → new_lt18(xuu30001, xuu31001)
new_primCompAux00(xuu180, LT) → LT
new_lt11(xuu30000, xuu31000) → new_esEs8(new_compare15(xuu30000, xuu31000), LT)
new_esEs24(xuu40002, xuu3002, ty_Ordering) → new_esEs8(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, app(ty_Ratio, da)) → new_ltEs14(xuu30002, xuu31002, da)
new_esEs23(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_ltEs19(xuu30001, xuu31001, ty_Bool) → new_ltEs8(xuu30001, xuu31001)
new_esEs28(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Int, fh) → new_esEs16(xuu40000, xuu3000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu30000))) → False
new_primEqInt(Pos(Succ(xuu400000)), Pos(Zero)) → False
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Float) → new_ltEs17(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, app(app(ty_Either, bg), bh)) → new_esEs7(xuu30000, xuu31000, bg, bh)
new_compare14(xuu30000, xuu31000, fa, fb, fc) → new_compare28(xuu30000, xuu31000, new_esEs4(xuu30000, xuu31000, fa, fb, fc), fa, fb, fc)
new_ltEs19(xuu30001, xuu31001, ty_Float) → new_ltEs17(xuu30001, xuu31001)
new_lt20(xuu30000, xuu31000, app(app(ty_@2, bgg), bgh)) → new_lt4(xuu30000, xuu31000, bgg, bgh)
new_esEs23(xuu40000, xuu3000, app(app(ty_@2, cce), ccf)) → new_esEs5(xuu40000, xuu3000, cce, ccf)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3100))) → LT
new_esEs29(xuu4000, xuu300, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs4(xuu4000, xuu300, bhe, bhf, bhg)
new_compare11(xuu30000, xuu31000, True, bg, bh) → LT
new_esEs9(xuu30001, xuu31001, app(ty_[], eb)) → new_esEs13(xuu30001, xuu31001, eb)
new_primPlusNat1(Succ(xuu25200), Succ(xuu9400)) → Succ(Succ(new_primPlusNat1(xuu25200, xuu9400)))
new_primEqInt(Neg(Succ(xuu400000)), Pos(xuu3000)) → False
new_primEqInt(Pos(Succ(xuu400000)), Neg(xuu3000)) → False
new_ltEs6(xuu30002, xuu31002, ty_Ordering) → new_ltEs12(xuu30002, xuu31002)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_Ratio, fg), fh) → new_esEs17(xuu40000, xuu3000, fg)
new_esEs29(xuu4000, xuu300, ty_Char) → new_esEs19(xuu4000, xuu300)
new_compare210(xuu300, xuu310, True, cgg) → EQ
new_ltEs12(GT, EQ) → False
new_esEs29(xuu4000, xuu300, app(app(ty_@2, bhh), caa)) → new_esEs5(xuu4000, xuu300, bhh, caa)
new_esEs24(xuu40002, xuu3002, app(ty_[], cda)) → new_esEs13(xuu40002, xuu3002, cda)
new_esEs29(xuu4000, xuu300, ty_@0) → new_esEs14(xuu4000, xuu300)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_[], che), cha) → new_ltEs9(xuu30000, xuu31000, che)
new_primCmpNat2(Zero, Succ(xuu31000)) → LT
new_lt19(xuu30000, xuu31000) → new_esEs8(new_compare26(xuu30000, xuu31000), LT)
new_esEs28(xuu40000, xuu3000, app(ty_Maybe, dea)) → new_esEs6(xuu40000, xuu3000, dea)
new_primEqInt(Neg(Zero), Pos(Succ(xuu30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu30000))) → False
new_esEs29(xuu4000, xuu300, ty_Integer) → new_esEs11(xuu4000, xuu300)
new_esEs30(xuu19, xuu14, app(ty_Ratio, bdd)) → new_esEs17(xuu19, xuu14, bdd)
new_primCompAux00(xuu180, EQ) → xuu180
new_esEs28(xuu40000, xuu3000, app(app(ty_Either, dde), ddf)) → new_esEs7(xuu40000, xuu3000, dde, ddf)
new_esEs10(xuu30000, xuu31000, ty_Int) → new_esEs16(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(app(ty_@2, dba), dbb)) → new_ltEs15(xuu30000, xuu31000, dba, dbb)
new_esEs25(xuu40001, xuu3001, ty_@0) → new_esEs14(xuu40001, xuu3001)
new_compare18(xuu30000, xuu31000) → new_compare27(xuu30000, xuu31000, new_esEs8(xuu30000, xuu31000))
new_compare13(xuu30000, xuu31000, app(app(ty_@2, bbc), bbd)) → new_compare6(xuu30000, xuu31000, bbc, bbd)
new_ltEs20(xuu3000, xuu3100, ty_Int) → new_ltEs13(xuu3000, xuu3100)
new_esEs10(xuu30000, xuu31000, ty_Char) → new_esEs19(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs30(xuu19, xuu14, ty_Bool) → new_esEs12(xuu19, xuu14)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_lt8(xuu30000, xuu31000, app(app(app(ty_@3, fa), fb), fc)) → new_lt10(xuu30000, xuu31000, fa, fb, fc)
new_compare28(xuu30000, xuu31000, False, fa, fb, fc) → new_compare113(xuu30000, xuu31000, new_ltEs5(xuu30000, xuu31000, fa, fb, fc), fa, fb, fc)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(app(ty_@3, gb), gc), gd), fh) → new_esEs4(xuu40000, xuu3000, gb, gc, gd)
new_esEs26(xuu40000, xuu3000, app(app(ty_@2, cgc), cgd)) → new_esEs5(xuu40000, xuu3000, cgc, cgd)
new_esEs22(xuu30000, xuu31000, ty_Float) → new_esEs18(xuu30000, xuu31000)
new_ltEs16(Just(xuu30000), Nothing, bbh) → False
new_esEs9(xuu30001, xuu31001, ty_Ordering) → new_esEs8(xuu30001, xuu31001)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs4(Right(xuu30000), Left(xuu31000), cgh, cha) → False
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs30(xuu19, xuu14, ty_@0) → new_esEs14(xuu19, xuu14)
new_esEs10(xuu30000, xuu31000, ty_@0) → new_esEs14(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_Maybe, ha), fh) → new_esEs6(xuu40000, xuu3000, ha)
new_esEs23(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_lt8(xuu30000, xuu31000, app(app(ty_@2, bd), be)) → new_lt4(xuu30000, xuu31000, bd, be)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs9(xuu30001, xuu31001, ty_Int) → new_esEs16(xuu30001, xuu31001)
new_esEs25(xuu40001, xuu3001, ty_Float) → new_esEs18(xuu40001, xuu3001)
new_esEs25(xuu40001, xuu3001, app(app(app(ty_@3, ced), cee), cef)) → new_esEs4(xuu40001, xuu3001, ced, cee, cef)
new_esEs27(xuu40001, xuu3001, ty_@0) → new_esEs14(xuu40001, xuu3001)
new_esEs28(xuu40000, xuu3000, app(app(ty_@2, ddg), ddh)) → new_esEs5(xuu40000, xuu3000, ddg, ddh)
new_esEs22(xuu30000, xuu31000, ty_Integer) → new_esEs11(xuu30000, xuu31000)
new_compare0(:(xuu30000, xuu30001), [], bae) → GT
new_lt8(xuu30000, xuu31000, ty_Ordering) → new_lt15(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Int) → new_lt6(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs4(xuu30000, xuu31000, bgb, bgc, bgd)
new_esEs22(xuu30000, xuu31000, app(ty_[], bge)) → new_esEs13(xuu30000, xuu31000, bge)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(ty_Maybe, dbc)) → new_ltEs16(xuu30000, xuu31000, dbc)
new_lt8(xuu30000, xuu31000, ty_Int) → new_lt6(xuu30000, xuu31000)
new_lt7(xuu30001, xuu31001, ty_@0) → new_lt13(xuu30001, xuu31001)
new_compare11(xuu30000, xuu31000, False, bg, bh) → GT
new_esEs25(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_primCmpInt(Pos(Succ(xuu3000)), Neg(xuu310)) → GT
new_lt7(xuu30001, xuu31001, ty_Int) → new_lt6(xuu30001, xuu31001)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Bool) → new_ltEs8(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, ty_Float) → new_esEs18(xuu40002, xuu3002)
new_esEs24(xuu40002, xuu3002, ty_Double) → new_esEs15(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, ty_Integer) → new_ltEs7(xuu30002, xuu31002)
new_primMulInt(Pos(xuu400000), Pos(xuu30000)) → Pos(new_primMulNat0(xuu400000, xuu30000))
new_esEs30(xuu19, xuu14, app(app(ty_@2, bec), bed)) → new_esEs5(xuu19, xuu14, bec, bed)
new_esEs24(xuu40002, xuu3002, ty_Integer) → new_esEs11(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, app(app(ty_Either, de), df)) → new_ltEs4(xuu30002, xuu31002, de, df)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_@0, fh) → new_esEs14(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, ty_Double) → new_esEs15(xuu40001, xuu3001)
new_primMulInt(Neg(xuu400000), Neg(xuu30000)) → Pos(new_primMulNat0(xuu400000, xuu30000))
new_primCmpNat2(Zero, Zero) → EQ
new_compare110(xuu30000, xuu31000, True) → LT
new_ltEs12(EQ, GT) → True
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(ty_Either, bda), bdb)) → new_ltEs4(xuu30000, xuu31000, bda, bdb)
new_compare13(xuu30000, xuu31000, ty_@0) → new_compare16(xuu30000, xuu31000)
new_ltEs20(xuu3000, xuu3100, ty_Float) → new_ltEs17(xuu3000, xuu3100)
new_esEs29(xuu4000, xuu300, app(ty_Ratio, bdc)) → new_esEs17(xuu4000, xuu300, bdc)
new_primEqNat0(Zero, Succ(xuu30000)) → False
new_primEqNat0(Succ(xuu400000), Zero) → False
new_ltEs8(False, False) → True
new_esEs25(xuu40001, xuu3001, app(ty_Ratio, ceb)) → new_esEs17(xuu40001, xuu3001, ceb)
new_esEs25(xuu40001, xuu3001, app(ty_Maybe, cfc)) → new_esEs6(xuu40001, xuu3001, cfc)
new_compare110(xuu30000, xuu31000, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Float) → new_esEs18(xuu40000, xuu3000)
new_compare113(xuu30000, xuu31000, True, fa, fb, fc) → LT
new_lt9(xuu30000, xuu31000) → new_esEs8(new_compare9(xuu30000, xuu31000), LT)
new_primPlusNat0(xuu104, xuu300000) → new_primPlusNat1(xuu104, Succ(xuu300000))
new_esEs10(xuu30000, xuu31000, app(ty_[], fd)) → new_esEs13(xuu30000, xuu31000, fd)
new_primCmpNat2(Succ(xuu30000), Succ(xuu31000)) → new_primCmpNat2(xuu30000, xuu31000)
new_primCmpInt(Pos(Succ(xuu3000)), Pos(xuu310)) → new_primCmpNat0(xuu3000, xuu310)
new_lt7(xuu30001, xuu31001, app(app(ty_@2, ed), ee)) → new_lt4(xuu30001, xuu31001, ed, ee)
new_compare13(xuu30000, xuu31000, ty_Char) → new_compare26(xuu30000, xuu31000)
new_esEs27(xuu40001, xuu3001, app(app(ty_@2, dce), dcf)) → new_esEs5(xuu40001, xuu3001, dce, dcf)
new_compare28(xuu30000, xuu31000, True, fa, fb, fc) → EQ
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Double) → new_esEs15(xuu40000, xuu3000)
new_primCmpNat0(xuu3000, Zero) → GT
new_compare13(xuu30000, xuu31000, app(ty_Ratio, bbb)) → new_compare8(xuu30000, xuu31000, bbb)
new_esEs10(xuu30000, xuu31000, ty_Integer) → new_esEs11(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Float) → new_lt18(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, app(app(ty_@2, bd), be)) → new_esEs5(xuu30000, xuu31000, bd, be)
new_esEs26(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare25(Float(xuu30000, xuu30001), Float(xuu31000, xuu31001)) → new_compare10(new_sr0(xuu30000, xuu31000), new_sr0(xuu30001, xuu31001))
new_esEs28(xuu40000, xuu3000, app(ty_Ratio, dch)) → new_esEs17(xuu40000, xuu3000, dch)
new_esEs23(xuu40000, xuu3000, app(ty_Ratio, cbf)) → new_esEs17(xuu40000, xuu3000, cbf)
new_esEs9(xuu30001, xuu31001, app(ty_Ratio, ec)) → new_esEs17(xuu30001, xuu31001, ec)
new_compare23(xuu30000, xuu31000, True, bg, bh) → EQ
new_esEs25(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3100))) → GT
new_lt7(xuu30001, xuu31001, ty_Ordering) → new_lt15(xuu30001, xuu31001)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(ty_[], dag)) → new_ltEs9(xuu30000, xuu31000, dag)
new_sr0(xuu40000, xuu3000) → new_primMulInt(xuu40000, xuu3000)
new_esEs26(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(app(ty_@3, caf), cag), cah)) → new_esEs4(xuu40000, xuu3000, caf, cag, cah)
new_lt8(xuu30000, xuu31000, app(app(ty_Either, bg), bh)) → new_lt17(xuu30000, xuu31000, bg, bh)
new_compare13(xuu30000, xuu31000, ty_Bool) → new_compare15(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Integer, cha) → new_ltEs7(xuu30000, xuu31000)
new_esEs19(Char(xuu40000), Char(xuu3000)) → new_primEqNat0(xuu40000, xuu3000)
new_esEs22(xuu30000, xuu31000, ty_Char) → new_esEs19(xuu30000, xuu31000)
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_Ratio, bce)) → new_ltEs14(xuu30000, xuu31000, bce)
new_esEs23(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs9(xuu30001, xuu31001, app(app(ty_@2, ed), ee)) → new_esEs5(xuu30001, xuu31001, ed, ee)
new_ltEs17(xuu3000, xuu3100) → new_fsEs(new_compare25(xuu3000, xuu3100))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs25(xuu40001, xuu3001, ty_Bool) → new_esEs12(xuu40001, xuu3001)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Char) → new_ltEs18(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_@0) → new_lt13(xuu30000, xuu31000)
new_esEs27(xuu40001, xuu3001, ty_Float) → new_esEs18(xuu40001, xuu3001)
new_compare9(Integer(xuu30000), Integer(xuu31000)) → new_primCmpInt(xuu30000, xuu31000)
new_asAs(False, xuu137) → False
new_esEs29(xuu4000, xuu300, ty_Bool) → new_esEs12(xuu4000, xuu300)
new_primMulInt(Pos(xuu400000), Neg(xuu30000)) → Neg(new_primMulNat0(xuu400000, xuu30000))
new_primMulInt(Neg(xuu400000), Pos(xuu30000)) → Neg(new_primMulNat0(xuu400000, xuu30000))
new_esEs13([], :(xuu3000, xuu3001), bhd) → False
new_esEs13(:(xuu40000, xuu40001), [], bhd) → False
new_primMulNat0(Succ(xuu4000000), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu300000)) → Zero
new_lt7(xuu30001, xuu31001, app(app(ty_Either, eg), eh)) → new_lt17(xuu30001, xuu31001, eg, eh)
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_Maybe, cbe)) → new_esEs6(xuu40000, xuu3000, cbe)
new_compare26(Char(xuu30000), Char(xuu31000)) → new_primCmpNat2(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_Ratio, chf), cha) → new_ltEs14(xuu30000, xuu31000, chf)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Double, fh) → new_esEs15(xuu40000, xuu3000)
new_ltEs20(xuu3000, xuu3100, ty_Integer) → new_ltEs7(xuu3000, xuu3100)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_[], ga), fh) → new_esEs13(xuu40000, xuu3000, ga)
new_esEs21(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_ltEs12(GT, GT) → True
new_ltEs20(xuu3000, xuu3100, ty_Double) → new_ltEs11(xuu3000, xuu3100)
new_esEs9(xuu30001, xuu31001, ty_Bool) → new_esEs12(xuu30001, xuu31001)
new_esEs10(xuu30000, xuu31000, app(ty_Maybe, bf)) → new_esEs6(xuu30000, xuu31000, bf)
new_ltEs19(xuu30001, xuu31001, ty_@0) → new_ltEs10(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Ordering, cha) → new_ltEs12(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Float, fh) → new_esEs18(xuu40000, xuu3000)
new_primCmpNat1(Succ(xuu3100), xuu3000) → new_primCmpNat2(xuu3100, xuu3000)
new_esEs23(xuu40000, xuu3000, app(ty_Maybe, ccg)) → new_esEs6(xuu40000, xuu3000, ccg)
new_primCmpNat2(Succ(xuu30000), Zero) → GT
new_lt7(xuu30001, xuu31001, app(ty_Ratio, ec)) → new_lt16(xuu30001, xuu31001, ec)
new_compare210(Just(xuu3000), Nothing, False, cgg) → GT
new_lt7(xuu30001, xuu31001, app(ty_Maybe, ef)) → new_lt5(xuu30001, xuu31001, ef)
new_lt8(xuu30000, xuu31000, ty_Float) → new_lt18(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, ty_Bool) → new_esEs12(xuu40002, xuu3002)
new_esEs25(xuu40001, xuu3001, app(ty_[], cec)) → new_esEs13(xuu40001, xuu3001, cec)
new_esEs23(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare27(xuu30000, xuu31000, True) → EQ
new_esEs10(xuu30000, xuu31000, ty_Float) → new_esEs18(xuu30000, xuu31000)
new_ltEs6(xuu30002, xuu31002, ty_Bool) → new_ltEs8(xuu30002, xuu31002)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Bool) → new_ltEs8(xuu30000, xuu31000)
new_compare17(Double(xuu30000, xuu30001), Double(xuu31000, xuu31001)) → new_compare10(new_sr0(xuu30000, xuu31000), new_sr0(xuu30001, xuu31001))
new_esEs12(False, True) → False
new_esEs12(True, False) → False
new_esEs28(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Int) → new_ltEs13(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Bool, fh) → new_esEs12(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_esEs29(xuu4000, xuu300, ty_Double) → new_esEs15(xuu4000, xuu300)
new_ltEs9(xuu3000, xuu3100, bae) → new_fsEs(new_compare0(xuu3000, xuu3100, bae))
new_esEs27(xuu40001, xuu3001, ty_Bool) → new_esEs12(xuu40001, xuu3001)
new_lt8(xuu30000, xuu31000, ty_Char) → new_lt19(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Float) → new_ltEs17(xuu30000, xuu31000)
new_ltEs19(xuu30001, xuu31001, app(app(app(ty_@3, beh), bfa), bfb)) → new_ltEs5(xuu30001, xuu31001, beh, bfa, bfb)
new_compare13(xuu30000, xuu31000, ty_Double) → new_compare17(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_ltEs18(xuu3000, xuu3100) → new_fsEs(new_compare26(xuu3000, xuu3100))
new_compare10(xuu30, xuu31) → new_primCmpInt(xuu30, xuu31)
new_esEs10(xuu30000, xuu31000, app(ty_Ratio, ff)) → new_esEs17(xuu30000, xuu31000, ff)
new_lt7(xuu30001, xuu31001, app(app(app(ty_@3, dg), dh), ea)) → new_lt10(xuu30001, xuu31001, dg, dh, ea)
new_ltEs12(EQ, LT) → False
new_esEs25(xuu40001, xuu3001, app(app(ty_@2, cfa), cfb)) → new_esEs5(xuu40001, xuu3001, cfa, cfb)
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_[], cae)) → new_esEs13(xuu40000, xuu3000, cae)
new_lt8(xuu30000, xuu31000, ty_@0) → new_lt13(xuu30000, xuu31000)
new_ltEs19(xuu30001, xuu31001, app(app(ty_@2, bfe), bff)) → new_ltEs15(xuu30001, xuu31001, bfe, bff)
new_compare13(xuu30000, xuu31000, app(app(ty_Either, bbf), bbg)) → new_compare19(xuu30000, xuu31000, bbf, bbg)
new_lt7(xuu30001, xuu31001, app(ty_[], eb)) → new_lt12(xuu30001, xuu31001, eb)
new_esEs22(xuu30000, xuu31000, ty_@0) → new_esEs14(xuu30000, xuu31000)
new_esEs23(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs29(xuu4000, xuu300, app(app(ty_Either, hb), fh)) → new_esEs7(xuu4000, xuu300, hb, fh)
new_compare112(xuu130, xuu131, False, cac) → GT
new_compare29(xuu30000, xuu31000, False) → new_compare111(xuu30000, xuu31000, new_ltEs8(xuu30000, xuu31000))
new_esEs22(xuu30000, xuu31000, app(ty_Ratio, bgf)) → new_esEs17(xuu30000, xuu31000, bgf)
new_ltEs19(xuu30001, xuu31001, ty_Integer) → new_ltEs7(xuu30001, xuu31001)
new_esEs30(xuu19, xuu14, ty_Ordering) → new_esEs8(xuu19, xuu14)
new_esEs10(xuu30000, xuu31000, ty_Ordering) → new_esEs8(xuu30000, xuu31000)
new_lt4(xuu30000, xuu31000, bd, be) → new_esEs8(new_compare6(xuu30000, xuu31000, bd, be), LT)
new_lt7(xuu30001, xuu31001, ty_Char) → new_lt19(xuu30001, xuu31001)
new_compare0([], :(xuu31000, xuu31001), bae) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs9(xuu30001, xuu31001, ty_Char) → new_esEs19(xuu30001, xuu31001)
new_primCompAux0(xuu30000, xuu31000, xuu174, bae) → new_primCompAux00(xuu174, new_compare13(xuu30000, xuu31000, bae))
new_esEs9(xuu30001, xuu31001, ty_Double) → new_esEs15(xuu30001, xuu31001)
new_asAs(True, xuu137) → xuu137
new_primMulNat0(Succ(xuu4000000), Succ(xuu300000)) → new_primPlusNat0(new_primMulNat0(xuu4000000, Succ(xuu300000)), xuu300000)
new_esEs27(xuu40001, xuu3001, app(ty_[], dbg)) → new_esEs13(xuu40001, xuu3001, dbg)
new_esEs27(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(ty_Either, cba), cbb)) → new_esEs7(xuu40000, xuu3000, cba, cbb)
new_esEs26(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_ltEs6(xuu30002, xuu31002, ty_Int) → new_ltEs13(xuu30002, xuu31002)
new_esEs9(xuu30001, xuu31001, app(app(ty_Either, eg), eh)) → new_esEs7(xuu30001, xuu31001, eg, eh)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Int) → new_ltEs13(xuu30000, xuu31000)
new_lt17(xuu30000, xuu31000, bg, bh) → new_esEs8(new_compare19(xuu30000, xuu31000, bg, bh), LT)
new_fsEs(xuu147) → new_not(new_esEs8(xuu147, GT))
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare27(xuu30000, xuu31000, False) → new_compare110(xuu30000, xuu31000, new_ltEs12(xuu30000, xuu31000))
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(ty_@2, bcf), bcg)) → new_ltEs15(xuu30000, xuu31000, bcf, bcg)
new_ltEs6(xuu30002, xuu31002, ty_Float) → new_ltEs17(xuu30002, xuu31002)
new_ltEs6(xuu30002, xuu31002, app(ty_[], cg)) → new_ltEs9(xuu30002, xuu31002, cg)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Bool, cha) → new_ltEs8(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, app(ty_Maybe, cea)) → new_esEs6(xuu40002, xuu3002, cea)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Char, fh) → new_esEs19(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, app(ty_Ratio, dbf)) → new_esEs17(xuu40001, xuu3001, dbf)
new_compare7(xuu30000, xuu31000, bf) → new_compare210(xuu30000, xuu31000, new_esEs6(xuu30000, xuu31000, bf), bf)
new_esEs24(xuu40002, xuu3002, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs4(xuu40002, xuu3002, cdb, cdc, cdd)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_primCompAux00(xuu180, GT) → GT
new_esEs25(xuu40001, xuu3001, app(app(ty_Either, ceg), ceh)) → new_esEs7(xuu40001, xuu3001, ceg, ceh)
new_esEs18(Float(xuu40000, xuu40001), Float(xuu3000, xuu3001)) → new_esEs16(new_sr0(xuu40000, xuu3000), new_sr0(xuu40001, xuu3001))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs12(GT, LT) → False
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(app(ty_@3, chb), chc), chd), cha) → new_ltEs5(xuu30000, xuu31000, chb, chc, chd)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(ty_Ratio, dah)) → new_ltEs14(xuu30000, xuu31000, dah)
new_esEs29(xuu4000, xuu300, ty_Ordering) → new_esEs8(xuu4000, xuu300)
new_lt7(xuu30001, xuu31001, ty_Integer) → new_lt9(xuu30001, xuu31001)
new_esEs28(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs5(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), ca, cb, cc) → new_pePe(new_lt8(xuu30000, xuu31000, ca), new_asAs(new_esEs10(xuu30000, xuu31000, ca), new_pePe(new_lt7(xuu30001, xuu31001, cb), new_asAs(new_esEs9(xuu30001, xuu31001, cb), new_ltEs6(xuu30002, xuu31002, cc)))))
new_primCmpInt(Neg(Succ(xuu3000)), Pos(xuu310)) → LT
new_esEs23(xuu40000, xuu3000, app(ty_[], cbg)) → new_esEs13(xuu40000, xuu3000, cbg)
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs5(xuu30000, xuu31000, bca, bcb, bcc)
new_esEs22(xuu30000, xuu31000, ty_Int) → new_esEs16(xuu30000, xuu31000)
new_not(True) → False
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(app(app(ty_@3, dad), dae), daf)) → new_ltEs5(xuu30000, xuu31000, dad, dae, daf)

The set Q consists of the following terms:

new_primCompAux00(x0, EQ)
new_esEs9(x0, x1, ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs14(x0, x1, x2)
new_esEs9(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Double)
new_pePe(True, x0)
new_ltEs12(LT, LT)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, ty_Integer)
new_lt8(x0, x1, ty_@0)
new_compare13(x0, x1, ty_Char)
new_compare11(x0, x1, False, x2, x3)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs10(x0, x1, ty_Integer)
new_primCmpNat0(x0, Succ(x1))
new_compare13(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, ty_Float)
new_lt7(x0, x1, ty_Ordering)
new_compare28(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, ty_@0)
new_esEs12(False, False)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs6(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs16(x0, x1)
new_lt8(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, x2, x3, x4)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Ordering)
new_compare26(Char(x0), Char(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs30(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare210(Just(x0), Nothing, False, x1)
new_primPlusNat0(x0, x1)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs8(GT, GT)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_primCompAux00(x0, LT)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Float)
new_ltEs12(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_lt9(x0, x1)
new_ltEs8(True, True)
new_compare13(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs8(LT, LT)
new_primCompAux00(x0, GT)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs15(Double(x0, x1), Double(x2, x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Bool)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_lt7(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_Bool)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs23(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primMulNat0(Succ(x0), Zero)
new_ltEs16(Just(x0), Just(x1), ty_@0)
new_compare113(x0, x1, True, x2, x3, x4)
new_lt8(x0, x1, ty_Char)
new_compare13(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), Succ(x1))
new_ltEs18(x0, x1)
new_ltEs6(x0, x1, ty_Double)
new_ltEs10(x0, x1)
new_primEqNat0(Zero, Zero)
new_compare24(x0, x1, False, x2, x3)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Just(x0), Nothing, x1)
new_ltEs16(Just(x0), Just(x1), ty_Integer)
new_ltEs16(Nothing, Nothing, x0)
new_compare13(x0, x1, ty_Int)
new_ltEs7(x0, x1)
new_compare13(x0, x1, ty_@0)
new_lt15(x0, x1)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primMulNat0(Zero, Zero)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt8(x0, x1, ty_Float)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Ordering)
new_lt8(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt13(x0, x1)
new_lt16(x0, x1, x2)
new_esEs25(x0, x1, ty_Char)
new_compare6(x0, x1, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_primCmpNat1(Zero, x0)
new_compare13(x0, x1, app(ty_[], x2))
new_esEs14(@0, @0)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Double)
new_lt8(x0, x1, app(ty_[], x2))
new_ltEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare13(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs16(Nothing, Just(x0), x1)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare16(@0, @0)
new_compare111(x0, x1, True)
new_esEs25(x0, x1, ty_Bool)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs28(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt18(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare210(Nothing, Just(x0), False, x1)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Integer)
new_ltEs6(x0, x1, ty_Bool)
new_primCmpNat1(Succ(x0), x1)
new_lt5(x0, x1, x2)
new_primPlusNat1(Zero, Zero)
new_compare210(Just(x0), Just(x1), False, x2)
new_esEs24(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpNat2(Zero, Zero)
new_ltEs16(Just(x0), Just(x1), ty_Double)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs9(x0, x1, x2)
new_esEs9(x0, x1, ty_@0)
new_compare25(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat1(Succ(x0), Zero)
new_esEs23(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare10(x0, x1)
new_esEs30(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), ty_Bool)
new_ltEs11(x0, x1)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare7(x0, x1, x2)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs12(GT, EQ)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(EQ, GT)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs16(Just(x0), Just(x1), ty_Char)
new_sr(Integer(x0), Integer(x1))
new_esEs11(Integer(x0), Integer(x1))
new_compare12(x0, x1, False, x2, x3)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt7(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs12(True, True)
new_ltEs8(False, False)
new_esEs29(x0, x1, ty_Char)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Double)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Ordering)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs24(x0, x1, ty_Int)
new_compare27(x0, x1, False)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs20(x0, x1, ty_Ordering)
new_lt4(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primCmpNat0(x0, Zero)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, x2)
new_pePe(False, x0)
new_lt20(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs12(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, ty_Double)
new_compare29(x0, x1, True)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_compare9(Integer(x0), Integer(x1))
new_ltEs13(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt14(x0, x1)
new_esEs30(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare17(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs13([], :(x0, x1), x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs17(x0, x1)
new_compare14(x0, x1, x2, x3, x4)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare23(x0, x1, True, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_compare110(x0, x1, False)
new_esEs29(x0, x1, ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_fsEs(x0)
new_ltEs16(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_lt8(x0, x1, app(ty_Maybe, x2))
new_esEs19(Char(x0), Char(x1))
new_esEs30(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs20(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primCmpNat2(Succ(x0), Zero)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Ordering)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_lt7(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs6(Nothing, Just(x0), x1)
new_esEs29(x0, x1, ty_Ordering)
new_compare111(x0, x1, False)
new_esEs9(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_asAs(True, x0)
new_ltEs19(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_compare210(Nothing, Nothing, False, x0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs10(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs28(x0, x1, ty_Integer)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(False, True)
new_esEs12(True, False)
new_ltEs16(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2, x3)
new_compare13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_primCmpNat2(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare28(x0, x1, False, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Integer)
new_asAs(False, x0)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs16(Just(x0), Nothing, x1)
new_lt17(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_not(True)
new_ltEs6(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Integer)
new_compare23(x0, x1, False, x2, x3)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_not(False)
new_primPlusNat1(Zero, Succ(x0))
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt8(x0, x1, ty_Double)
new_compare18(x0, x1)
new_ltEs16(Just(x0), Just(x1), ty_Float)
new_esEs25(x0, x1, ty_@0)
new_esEs13(:(x0, x1), [], x2)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, ty_Double)
new_ltEs16(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(x0, x1)
new_compare210(x0, x1, True, x2)
new_esEs27(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, ty_Int)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt8(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Zero)
new_sr0(x0, x1)
new_esEs13([], [], x0)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs24(x0, x1, ty_Char)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Float)
new_compare11(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Bool)
new_ltEs12(EQ, LT)
new_ltEs12(LT, EQ)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_compare112(x0, x1, False, x2)
new_esEs10(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_compare12(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_compare112(x0, x1, True, x2)
new_lt7(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs12(GT, LT)
new_ltEs12(LT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare113(x0, x1, False, x2, x3, x4)
new_compare27(x0, x1, True)
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt8(x0, x1, ty_Int)
new_ltEs16(Just(x0), Just(x1), ty_Ordering)
new_compare0([], [], x0)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_ltEs16(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))

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

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



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

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

new_addToFM_C1(xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_addToFM_C(xuu34, Nothing, xuu401, h, ba)
new_addToFM_C2(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_addToFM_C(xuu33, Nothing, xuu401, h, ba)
new_addToFM_C(Branch(Nothing, xuu31, xuu32, xuu33, xuu34), Nothing, xuu401, h, ba) → new_addToFM_C1(xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C2(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, False, h, ba) → new_addToFM_C10(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Just(xuu300), False, h), GT), h, ba)
new_addToFM_C10(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_addToFM_C(xuu34, Nothing, xuu401, h, ba)
new_addToFM_C(Branch(Just(xuu300), xuu31, xuu32, xuu33, xuu34), Nothing, xuu401, h, ba) → new_addToFM_C2(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Just(xuu300), False, h), LT), h, ba)

The TRS R consists of the following rules:

new_esEs30(xuu19, xuu14, app(ty_Maybe, bee)) → new_esEs6(xuu19, xuu14, bee)
new_esEs25(xuu40001, xuu3001, ty_Char) → new_esEs19(xuu40001, xuu3001)
new_primCmpNat0(xuu3000, Succ(xuu3100)) → new_primCmpNat2(xuu3000, xuu3100)
new_ltEs19(xuu30001, xuu31001, ty_Ordering) → new_ltEs12(xuu30001, xuu31001)
new_ltEs6(xuu30002, xuu31002, app(app(ty_@2, db), dc)) → new_ltEs15(xuu30002, xuu31002, db, dc)
new_esEs28(xuu40000, xuu3000, app(ty_[], dda)) → new_esEs13(xuu40000, xuu3000, dda)
new_esEs23(xuu40000, xuu3000, app(app(ty_Either, ccc), ccd)) → new_esEs7(xuu40000, xuu3000, ccc, ccd)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(ty_@2, cbc), cbd)) → new_esEs5(xuu40000, xuu3000, cbc, cbd)
new_compare112(xuu130, xuu131, True, cac) → LT
new_esEs29(xuu4000, xuu300, ty_Int) → new_esEs16(xuu4000, xuu300)
new_ltEs20(xuu3000, xuu3100, ty_Char) → new_ltEs18(xuu3000, xuu3100)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(ty_Either, ge), gf), fh) → new_esEs7(xuu40000, xuu3000, ge, gf)
new_ltEs8(False, True) → True
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_esEs10(xuu30000, xuu31000, app(app(app(ty_@3, fa), fb), fc)) → new_esEs4(xuu30000, xuu31000, fa, fb, fc)
new_esEs27(xuu40001, xuu3001, ty_Char) → new_esEs19(xuu40001, xuu3001)
new_compare13(xuu30000, xuu31000, app(app(app(ty_@3, baf), bag), bah)) → new_compare14(xuu30000, xuu31000, baf, bag, bah)
new_ltEs10(xuu3000, xuu3100) → new_fsEs(new_compare16(xuu3000, xuu3100))
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Ordering) → new_ltEs12(xuu30000, xuu31000)
new_esEs13([], [], bhd) → True
new_ltEs12(LT, GT) → True
new_ltEs19(xuu30001, xuu31001, app(ty_[], bfc)) → new_ltEs9(xuu30001, xuu31001, bfc)
new_lt20(xuu30000, xuu31000, app(ty_Ratio, bgf)) → new_lt16(xuu30000, xuu31000, bgf)
new_lt7(xuu30001, xuu31001, ty_Bool) → new_lt11(xuu30001, xuu31001)
new_lt16(xuu30000, xuu31000, ff) → new_esEs8(new_compare8(xuu30000, xuu31000, ff), LT)
new_esEs4(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), bhe, bhf, bhg) → new_asAs(new_esEs26(xuu40000, xuu3000, bhe), new_asAs(new_esEs25(xuu40001, xuu3001, bhf), new_esEs24(xuu40002, xuu3002, bhg)))
new_esEs11(Integer(xuu40000), Integer(xuu3000)) → new_primEqInt(xuu40000, xuu3000)
new_esEs30(xuu19, xuu14, app(ty_[], bde)) → new_esEs13(xuu19, xuu14, bde)
new_esEs15(Double(xuu40000, xuu40001), Double(xuu3000, xuu3001)) → new_esEs16(new_sr0(xuu40000, xuu3000), new_sr0(xuu40001, xuu3001))
new_compare13(xuu30000, xuu31000, app(ty_Maybe, bbe)) → new_compare7(xuu30000, xuu31000, bbe)
new_esEs28(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs26(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_compare19(xuu30000, xuu31000, bg, bh) → new_compare23(xuu30000, xuu31000, new_esEs7(xuu30000, xuu31000, bg, bh), bg, bh)
new_ltEs19(xuu30001, xuu31001, ty_Double) → new_ltEs11(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(ty_@2, chg), chh), cha) → new_ltEs15(xuu30000, xuu31000, chg, chh)
new_primMulNat0(Zero, Zero) → Zero
new_esEs27(xuu40001, xuu3001, app(app(app(ty_@3, dbh), dca), dcb)) → new_esEs4(xuu40001, xuu3001, dbh, dca, dcb)
new_ltEs12(LT, LT) → True
new_compare29(xuu30000, xuu31000, True) → EQ
new_sr(Integer(xuu300000), Integer(xuu310010)) → Integer(new_primMulInt(xuu300000, xuu310010))
new_esEs12(True, True) → True
new_ltEs6(xuu30002, xuu31002, app(app(app(ty_@3, cd), ce), cf)) → new_ltEs5(xuu30002, xuu31002, cd, ce, cf)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_@0) → new_ltEs10(xuu30000, xuu31000)
new_ltEs15(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), bef, beg) → new_pePe(new_lt20(xuu30000, xuu31000, bef), new_asAs(new_esEs22(xuu30000, xuu31000, bef), new_ltEs19(xuu30001, xuu31001, beg)))
new_esEs23(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Integer) → new_ltEs7(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Double) → new_ltEs11(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(ty_Ratio, hc)) → new_esEs17(xuu40000, xuu3000, hc)
new_lt12(xuu30000, xuu31000, fd) → new_esEs8(new_compare0(xuu30000, xuu31000, fd), LT)
new_esEs24(xuu40002, xuu3002, ty_@0) → new_esEs14(xuu40002, xuu3002)
new_lt8(xuu30000, xuu31000, app(ty_[], fd)) → new_lt12(xuu30000, xuu31000, fd)
new_compare16(@0, @0) → EQ
new_esEs30(xuu19, xuu14, app(app(ty_Either, bea), beb)) → new_esEs7(xuu19, xuu14, bea, beb)
new_compare8(:%(xuu30000, xuu30001), :%(xuu31000, xuu31001), ty_Integer) → new_compare9(new_sr(xuu30000, xuu31001), new_sr(xuu31000, xuu30001))
new_lt20(xuu30000, xuu31000, ty_Double) → new_lt14(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Integer) → new_lt9(xuu30000, xuu31000)
new_ltEs12(LT, EQ) → True
new_ltEs20(xuu3000, xuu3100, app(ty_[], bae)) → new_ltEs9(xuu3000, xuu3100, bae)
new_lt8(xuu30000, xuu31000, app(ty_Ratio, ff)) → new_lt16(xuu30000, xuu31000, ff)
new_ltEs11(xuu3000, xuu3100) → new_fsEs(new_compare17(xuu3000, xuu3100))
new_esEs22(xuu30000, xuu31000, app(app(ty_@2, bgg), bgh)) → new_esEs5(xuu30000, xuu31000, bgg, bgh)
new_compare0(:(xuu30000, xuu30001), :(xuu31000, xuu31001), bae) → new_primCompAux0(xuu30000, xuu31000, new_compare0(xuu30001, xuu31001, bae), bae)
new_compare210(Nothing, Nothing, False, cgg) → LT
new_esEs24(xuu40002, xuu3002, app(app(ty_@2, cdg), cdh)) → new_esEs5(xuu40002, xuu3002, cdg, cdh)
new_esEs22(xuu30000, xuu31000, app(ty_Maybe, bha)) → new_esEs6(xuu30000, xuu31000, bha)
new_ltEs20(xuu3000, xuu3100, app(ty_Ratio, cgf)) → new_ltEs14(xuu3000, xuu3100, cgf)
new_esEs27(xuu40001, xuu3001, app(ty_Maybe, dcg)) → new_esEs6(xuu40001, xuu3001, dcg)
new_esEs26(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_esEs25(xuu40001, xuu3001, ty_Double) → new_esEs15(xuu40001, xuu3001)
new_compare15(xuu30000, xuu31000) → new_compare29(xuu30000, xuu31000, new_esEs12(xuu30000, xuu31000))
new_esEs29(xuu4000, xuu300, ty_Float) → new_esEs18(xuu4000, xuu300)
new_lt20(xuu30000, xuu31000, ty_Ordering) → new_lt15(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Char) → new_ltEs18(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, app(app(ty_Either, bhb), bhc)) → new_esEs7(xuu30000, xuu31000, bhb, bhc)
new_lt18(xuu30000, xuu31000) → new_esEs8(new_compare25(xuu30000, xuu31000), LT)
new_ltEs19(xuu30001, xuu31001, ty_Char) → new_ltEs18(xuu30001, xuu31001)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(ty_Maybe, bad)) → new_esEs6(xuu40000, xuu3000, bad)
new_ltEs19(xuu30001, xuu31001, app(app(ty_Either, bfh), bga)) → new_ltEs4(xuu30001, xuu31001, bfh, bga)
new_pePe(False, xuu163) → xuu163
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_esEs7(Left(xuu40000), Right(xuu3000), hb, fh) → False
new_esEs7(Right(xuu40000), Left(xuu3000), hb, fh) → False
new_lt20(xuu30000, xuu31000, ty_Bool) → new_lt11(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, ty_Bool) → new_esEs12(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Double, cha) → new_ltEs11(xuu30000, xuu31000)
new_compare6(xuu30000, xuu31000, bd, be) → new_compare24(xuu30000, xuu31000, new_esEs5(xuu30000, xuu31000, bd, be), bd, be)
new_esEs28(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, app(app(ty_Either, dcc), dcd)) → new_esEs7(xuu40001, xuu3001, dcc, dcd)
new_esEs20(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_ltEs20(xuu3000, xuu3100, ty_@0) → new_ltEs10(xuu3000, xuu3100)
new_compare13(xuu30000, xuu31000, ty_Int) → new_compare10(xuu30000, xuu31000)
new_esEs26(xuu40000, xuu3000, app(ty_Ratio, cfd)) → new_esEs17(xuu40000, xuu3000, cfd)
new_esEs22(xuu30000, xuu31000, ty_Double) → new_esEs15(xuu30000, xuu31000)
new_esEs26(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_ltEs20(xuu3000, xuu3100, app(app(ty_Either, cgh), cha)) → new_ltEs4(xuu3000, xuu3100, cgh, cha)
new_lt20(xuu30000, xuu31000, app(app(app(ty_@3, bgb), bgc), bgd)) → new_lt10(xuu30000, xuu31000, bgb, bgc, bgd)
new_esEs28(xuu40000, xuu3000, app(app(app(ty_@3, ddb), ddc), ddd)) → new_esEs4(xuu40000, xuu3000, ddb, ddc, ddd)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Double) → new_ltEs11(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(app(ty_Either, dbd), dbe)) → new_ltEs4(xuu30000, xuu31000, dbd, dbe)
new_esEs22(xuu30000, xuu31000, ty_Ordering) → new_esEs8(xuu30000, xuu31000)
new_compare111(xuu30000, xuu31000, False) → GT
new_compare111(xuu30000, xuu31000, True) → LT
new_esEs26(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_ltEs4(Left(xuu30000), Right(xuu31000), cgh, cha) → True
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(app(ty_@2, bab), bac)) → new_esEs5(xuu40000, xuu3000, bab, bac)
new_ltEs20(xuu3000, xuu3100, ty_Ordering) → new_ltEs12(xuu3000, xuu3100)
new_primCmpInt(Neg(Succ(xuu3000)), Neg(xuu310)) → new_primCmpNat1(xuu310, xuu3000)
new_lt6(xuu300, xuu310) → new_esEs8(new_compare10(xuu300, xuu310), LT)
new_ltEs20(xuu3000, xuu3100, ty_Bool) → new_ltEs8(xuu3000, xuu3100)
new_esEs8(LT, LT) → True
new_esEs30(xuu19, xuu14, ty_Float) → new_esEs18(xuu19, xuu14)
new_ltEs16(Nothing, Nothing, bbh) → True
new_lt20(xuu30000, xuu31000, ty_Char) → new_lt19(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Integer, fh) → new_esEs11(xuu40000, xuu3000)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_Maybe, daa), cha) → new_ltEs16(xuu30000, xuu31000, daa)
new_esEs25(xuu40001, xuu3001, ty_Ordering) → new_esEs8(xuu40001, xuu3001)
new_esEs20(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_esEs28(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_compare210(Nothing, Just(xuu3100), False, cgg) → LT
new_esEs24(xuu40002, xuu3002, app(app(ty_Either, cde), cdf)) → new_esEs7(xuu40002, xuu3002, cde, cdf)
new_ltEs6(xuu30002, xuu31002, ty_Double) → new_ltEs11(xuu30002, xuu31002)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_@0) → new_ltEs10(xuu30000, xuu31000)
new_pePe(True, xuu163) → True
new_compare0([], [], bae) → EQ
new_esEs24(xuu40002, xuu3002, ty_Int) → new_esEs16(xuu40002, xuu3002)
new_primEqNat0(Zero, Zero) → True
new_ltEs19(xuu30001, xuu31001, ty_Int) → new_ltEs13(xuu30001, xuu31001)
new_esEs29(xuu4000, xuu300, app(ty_Maybe, cab)) → new_esEs6(xuu4000, xuu300, cab)
new_compare210(Just(xuu3000), Just(xuu3100), False, cgg) → new_compare112(xuu3000, xuu3100, new_ltEs20(xuu3000, xuu3100, cgg), cgg)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(ty_@2, gg), gh), fh) → new_esEs5(xuu40000, xuu3000, gg, gh)
new_esEs26(xuu40000, xuu3000, app(ty_Maybe, cge)) → new_esEs6(xuu40000, xuu3000, cge)
new_esEs14(@0, @0) → True
new_esEs30(xuu19, xuu14, ty_Double) → new_esEs15(xuu19, xuu14)
new_esEs9(xuu30001, xuu31001, app(app(app(ty_@3, dg), dh), ea)) → new_esEs4(xuu30001, xuu31001, dg, dh, ea)
new_ltEs6(xuu30002, xuu31002, ty_@0) → new_ltEs10(xuu30002, xuu31002)
new_esEs29(xuu4000, xuu300, app(ty_[], bhd)) → new_esEs13(xuu4000, xuu300, bhd)
new_esEs9(xuu30001, xuu31001, app(ty_Maybe, ef)) → new_esEs6(xuu30001, xuu31001, ef)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Float, cha) → new_ltEs17(xuu30000, xuu31000)
new_esEs9(xuu30001, xuu31001, ty_@0) → new_esEs14(xuu30001, xuu31001)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Ordering, fh) → new_esEs8(xuu40000, xuu3000)
new_esEs24(xuu40002, xuu3002, app(ty_Ratio, cch)) → new_esEs17(xuu40002, xuu3002, cch)
new_compare13(xuu30000, xuu31000, ty_Integer) → new_compare9(xuu30000, xuu31000)
new_compare12(xuu30000, xuu31000, False, bd, be) → GT
new_esEs30(xuu19, xuu14, ty_Char) → new_esEs19(xuu19, xuu14)
new_compare13(xuu30000, xuu31000, ty_Ordering) → new_compare18(xuu30000, xuu31000)
new_lt7(xuu30001, xuu31001, ty_Double) → new_lt14(xuu30001, xuu31001)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Ordering) → new_ltEs12(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Int, cha) → new_ltEs13(xuu30000, xuu31000)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3100))) → new_primCmpNat0(xuu3100, Zero)
new_esEs26(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs24(xuu40002, xuu3002, ty_Char) → new_esEs19(xuu40002, xuu3002)
new_esEs8(GT, GT) → True
new_esEs30(xuu19, xuu14, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs4(xuu19, xuu14, bdf, bdg, bdh)
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_[], bcd)) → new_ltEs9(xuu30000, xuu31000, bcd)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3100))) → new_primCmpNat1(Zero, xuu3100)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(app(ty_Either, hh), baa)) → new_esEs7(xuu40000, xuu3000, hh, baa)
new_compare13(xuu30000, xuu31000, app(ty_[], bba)) → new_compare0(xuu30000, xuu31000, bba)
new_lt15(xuu30000, xuu31000) → new_esEs8(new_compare18(xuu30000, xuu31000), LT)
new_esEs12(False, False) → True
new_esEs26(xuu40000, xuu3000, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs4(xuu40000, xuu3000, cff, cfg, cfh)
new_ltEs20(xuu3000, xuu3100, app(app(ty_@2, bef), beg)) → new_ltEs15(xuu3000, xuu3100, bef, beg)
new_ltEs19(xuu30001, xuu31001, app(ty_Ratio, bfd)) → new_ltEs14(xuu30001, xuu31001, bfd)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(ty_[], hd)) → new_esEs13(xuu40000, xuu3000, hd)
new_lt10(xuu30000, xuu31000, fa, fb, fc) → new_esEs8(new_compare14(xuu30000, xuu31000, fa, fb, fc), LT)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_esEs28(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_lt20(xuu30000, xuu31000, app(app(ty_Either, bhb), bhc)) → new_lt17(xuu30000, xuu31000, bhb, bhc)
new_esEs9(xuu30001, xuu31001, ty_Integer) → new_esEs11(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_@0, cha) → new_ltEs10(xuu30000, xuu31000)
new_ltEs20(xuu3000, xuu3100, app(app(app(ty_@3, ca), cb), cc)) → new_ltEs5(xuu3000, xuu3100, ca, cb, cc)
new_lt8(xuu30000, xuu31000, ty_Double) → new_lt14(xuu30000, xuu31000)
new_ltEs16(Nothing, Just(xuu31000), bbh) → True
new_primEqInt(Neg(Succ(xuu400000)), Neg(Succ(xuu30000))) → new_primEqNat0(xuu400000, xuu30000)
new_esEs23(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs13(:(xuu40000, xuu40001), :(xuu3000, xuu3001), bhd) → new_asAs(new_esEs23(xuu40000, xuu3000, bhd), new_esEs13(xuu40001, xuu3001, bhd))
new_esEs26(xuu40000, xuu3000, app(ty_[], cfe)) → new_esEs13(xuu40000, xuu3000, cfe)
new_primPlusNat1(Succ(xuu25200), Zero) → Succ(xuu25200)
new_primPlusNat1(Zero, Succ(xuu9400)) → Succ(xuu9400)
new_ltEs6(xuu30002, xuu31002, ty_Char) → new_ltEs18(xuu30002, xuu31002)
new_lt8(xuu30000, xuu31000, app(ty_Maybe, bf)) → new_lt5(xuu30000, xuu31000, bf)
new_ltEs8(True, True) → True
new_esEs16(xuu4000, xuu300) → new_primEqInt(xuu4000, xuu300)
new_primCmpNat1(Zero, xuu3000) → LT
new_esEs30(xuu19, xuu14, ty_Integer) → new_esEs11(xuu19, xuu14)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_Maybe, bch)) → new_ltEs16(xuu30000, xuu31000, bch)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Char, cha) → new_ltEs18(xuu30000, xuu31000)
new_ltEs12(EQ, EQ) → True
new_compare13(xuu30000, xuu31000, ty_Float) → new_compare25(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Integer) → new_ltEs7(xuu30000, xuu31000)
new_lt8(xuu30000, xuu31000, ty_Integer) → new_lt9(xuu30000, xuu31000)
new_esEs21(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs28(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_primEqInt(Neg(Zero), Neg(Succ(xuu30000))) → False
new_primEqInt(Neg(Succ(xuu400000)), Neg(Zero)) → False
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(ty_Either, dab), dac), cha) → new_ltEs4(xuu30000, xuu31000, dab, dac)
new_esEs8(EQ, EQ) → True
new_esEs6(Just(xuu40000), Just(xuu3000), ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs17(:%(xuu40000, xuu40001), :%(xuu3000, xuu3001), bdc) → new_asAs(new_esEs21(xuu40000, xuu3000, bdc), new_esEs20(xuu40001, xuu3001, bdc))
new_esEs23(xuu40000, xuu3000, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs4(xuu40000, xuu3000, cbh, cca, ccb)
new_compare24(xuu30000, xuu31000, True, bd, be) → EQ
new_esEs5(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), bhh, caa) → new_asAs(new_esEs28(xuu40000, xuu3000, bhh), new_esEs27(xuu40001, xuu3001, caa))
new_lt20(xuu30000, xuu31000, app(ty_Maybe, bha)) → new_lt5(xuu30000, xuu31000, bha)
new_ltEs7(xuu3000, xuu3100) → new_fsEs(new_compare9(xuu3000, xuu3100))
new_ltEs13(xuu3000, xuu3100) → new_fsEs(new_compare10(xuu3000, xuu3100))
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_ltEs19(xuu30001, xuu31001, app(ty_Maybe, bfg)) → new_ltEs16(xuu30001, xuu31001, bfg)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs26(xuu40000, xuu3000, app(app(ty_Either, cga), cgb)) → new_esEs7(xuu40000, xuu3000, cga, cgb)
new_esEs9(xuu30001, xuu31001, ty_Float) → new_esEs18(xuu30001, xuu31001)
new_ltEs14(xuu3000, xuu3100, cgf) → new_fsEs(new_compare8(xuu3000, xuu3100, cgf))
new_compare23(xuu30000, xuu31000, False, bg, bh) → new_compare11(xuu30000, xuu31000, new_ltEs4(xuu30000, xuu31000, bg, bh), bg, bh)
new_esEs6(Nothing, Nothing, cab) → True
new_ltEs6(xuu30002, xuu31002, app(ty_Maybe, dd)) → new_ltEs16(xuu30002, xuu31002, dd)
new_compare113(xuu30000, xuu31000, False, fa, fb, fc) → GT
new_ltEs20(xuu3000, xuu3100, app(ty_Maybe, bbh)) → new_ltEs16(xuu3000, xuu3100, bbh)
new_primEqInt(Pos(Succ(xuu400000)), Pos(Succ(xuu30000))) → new_primEqNat0(xuu400000, xuu30000)
new_lt20(xuu30000, xuu31000, app(ty_[], bge)) → new_lt12(xuu30000, xuu31000, bge)
new_lt5(xuu30000, xuu31000, bf) → new_esEs8(new_compare7(xuu30000, xuu31000, bf), LT)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_compare24(xuu30000, xuu31000, False, bd, be) → new_compare12(xuu30000, xuu31000, new_ltEs15(xuu30000, xuu31000, bd, be), bd, be)
new_compare12(xuu30000, xuu31000, True, bd, be) → LT
new_esEs30(xuu19, xuu14, ty_Int) → new_esEs16(xuu19, xuu14)
new_compare8(:%(xuu30000, xuu30001), :%(xuu31000, xuu31001), ty_Int) → new_compare10(new_sr0(xuu30000, xuu31001), new_sr0(xuu31000, xuu30001))
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_Ratio, cad)) → new_esEs17(xuu40000, xuu3000, cad)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, app(app(app(ty_@3, he), hf), hg)) → new_esEs4(xuu40000, xuu3000, he, hf, hg)
new_esEs6(Just(xuu40000), Nothing, cab) → False
new_esEs6(Nothing, Just(xuu3000), cab) → False
new_primEqNat0(Succ(xuu400000), Succ(xuu30000)) → new_primEqNat0(xuu400000, xuu30000)
new_esEs23(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, ty_Ordering) → new_esEs8(xuu40001, xuu3001)
new_lt13(xuu30000, xuu31000) → new_esEs8(new_compare16(xuu30000, xuu31000), LT)
new_lt8(xuu30000, xuu31000, ty_Bool) → new_lt11(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, ty_Double) → new_esEs15(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, ty_Bool) → new_esEs12(xuu30000, xuu31000)
new_lt14(xuu30000, xuu31000) → new_esEs8(new_compare17(xuu30000, xuu31000), LT)
new_lt7(xuu30001, xuu31001, ty_Float) → new_lt18(xuu30001, xuu31001)
new_primCompAux00(xuu180, LT) → LT
new_lt11(xuu30000, xuu31000) → new_esEs8(new_compare15(xuu30000, xuu31000), LT)
new_esEs24(xuu40002, xuu3002, ty_Ordering) → new_esEs8(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, app(ty_Ratio, da)) → new_ltEs14(xuu30002, xuu31002, da)
new_esEs23(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_ltEs19(xuu30001, xuu31001, ty_Bool) → new_ltEs8(xuu30001, xuu31001)
new_esEs28(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Int, fh) → new_esEs16(xuu40000, xuu3000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu30000))) → False
new_primEqInt(Pos(Succ(xuu400000)), Pos(Zero)) → False
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Float) → new_ltEs17(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, app(app(ty_Either, bg), bh)) → new_esEs7(xuu30000, xuu31000, bg, bh)
new_compare14(xuu30000, xuu31000, fa, fb, fc) → new_compare28(xuu30000, xuu31000, new_esEs4(xuu30000, xuu31000, fa, fb, fc), fa, fb, fc)
new_ltEs19(xuu30001, xuu31001, ty_Float) → new_ltEs17(xuu30001, xuu31001)
new_lt20(xuu30000, xuu31000, app(app(ty_@2, bgg), bgh)) → new_lt4(xuu30000, xuu31000, bgg, bgh)
new_esEs23(xuu40000, xuu3000, app(app(ty_@2, cce), ccf)) → new_esEs5(xuu40000, xuu3000, cce, ccf)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3100))) → LT
new_esEs29(xuu4000, xuu300, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs4(xuu4000, xuu300, bhe, bhf, bhg)
new_compare11(xuu30000, xuu31000, True, bg, bh) → LT
new_esEs9(xuu30001, xuu31001, app(ty_[], eb)) → new_esEs13(xuu30001, xuu31001, eb)
new_primPlusNat1(Succ(xuu25200), Succ(xuu9400)) → Succ(Succ(new_primPlusNat1(xuu25200, xuu9400)))
new_primEqInt(Neg(Succ(xuu400000)), Pos(xuu3000)) → False
new_primEqInt(Pos(Succ(xuu400000)), Neg(xuu3000)) → False
new_ltEs6(xuu30002, xuu31002, ty_Ordering) → new_ltEs12(xuu30002, xuu31002)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_Ratio, fg), fh) → new_esEs17(xuu40000, xuu3000, fg)
new_esEs29(xuu4000, xuu300, ty_Char) → new_esEs19(xuu4000, xuu300)
new_compare210(xuu300, xuu310, True, cgg) → EQ
new_ltEs12(GT, EQ) → False
new_esEs29(xuu4000, xuu300, app(app(ty_@2, bhh), caa)) → new_esEs5(xuu4000, xuu300, bhh, caa)
new_esEs24(xuu40002, xuu3002, app(ty_[], cda)) → new_esEs13(xuu40002, xuu3002, cda)
new_esEs29(xuu4000, xuu300, ty_@0) → new_esEs14(xuu4000, xuu300)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_[], che), cha) → new_ltEs9(xuu30000, xuu31000, che)
new_primCmpNat2(Zero, Succ(xuu31000)) → LT
new_lt19(xuu30000, xuu31000) → new_esEs8(new_compare26(xuu30000, xuu31000), LT)
new_esEs28(xuu40000, xuu3000, app(ty_Maybe, dea)) → new_esEs6(xuu40000, xuu3000, dea)
new_primEqInt(Neg(Zero), Pos(Succ(xuu30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu30000))) → False
new_esEs29(xuu4000, xuu300, ty_Integer) → new_esEs11(xuu4000, xuu300)
new_esEs30(xuu19, xuu14, app(ty_Ratio, bdd)) → new_esEs17(xuu19, xuu14, bdd)
new_primCompAux00(xuu180, EQ) → xuu180
new_esEs28(xuu40000, xuu3000, app(app(ty_Either, dde), ddf)) → new_esEs7(xuu40000, xuu3000, dde, ddf)
new_esEs10(xuu30000, xuu31000, ty_Int) → new_esEs16(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(app(ty_@2, dba), dbb)) → new_ltEs15(xuu30000, xuu31000, dba, dbb)
new_esEs25(xuu40001, xuu3001, ty_@0) → new_esEs14(xuu40001, xuu3001)
new_compare18(xuu30000, xuu31000) → new_compare27(xuu30000, xuu31000, new_esEs8(xuu30000, xuu31000))
new_compare13(xuu30000, xuu31000, app(app(ty_@2, bbc), bbd)) → new_compare6(xuu30000, xuu31000, bbc, bbd)
new_ltEs20(xuu3000, xuu3100, ty_Int) → new_ltEs13(xuu3000, xuu3100)
new_esEs10(xuu30000, xuu31000, ty_Char) → new_esEs19(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs30(xuu19, xuu14, ty_Bool) → new_esEs12(xuu19, xuu14)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_lt8(xuu30000, xuu31000, app(app(app(ty_@3, fa), fb), fc)) → new_lt10(xuu30000, xuu31000, fa, fb, fc)
new_compare28(xuu30000, xuu31000, False, fa, fb, fc) → new_compare113(xuu30000, xuu31000, new_ltEs5(xuu30000, xuu31000, fa, fb, fc), fa, fb, fc)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(app(ty_@3, gb), gc), gd), fh) → new_esEs4(xuu40000, xuu3000, gb, gc, gd)
new_esEs26(xuu40000, xuu3000, app(app(ty_@2, cgc), cgd)) → new_esEs5(xuu40000, xuu3000, cgc, cgd)
new_esEs22(xuu30000, xuu31000, ty_Float) → new_esEs18(xuu30000, xuu31000)
new_ltEs16(Just(xuu30000), Nothing, bbh) → False
new_esEs9(xuu30001, xuu31001, ty_Ordering) → new_esEs8(xuu30001, xuu31001)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs4(Right(xuu30000), Left(xuu31000), cgh, cha) → False
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_esEs30(xuu19, xuu14, ty_@0) → new_esEs14(xuu19, xuu14)
new_esEs10(xuu30000, xuu31000, ty_@0) → new_esEs14(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_Maybe, ha), fh) → new_esEs6(xuu40000, xuu3000, ha)
new_esEs23(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_lt8(xuu30000, xuu31000, app(app(ty_@2, bd), be)) → new_lt4(xuu30000, xuu31000, bd, be)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs9(xuu30001, xuu31001, ty_Int) → new_esEs16(xuu30001, xuu31001)
new_esEs25(xuu40001, xuu3001, ty_Float) → new_esEs18(xuu40001, xuu3001)
new_esEs25(xuu40001, xuu3001, app(app(app(ty_@3, ced), cee), cef)) → new_esEs4(xuu40001, xuu3001, ced, cee, cef)
new_esEs27(xuu40001, xuu3001, ty_@0) → new_esEs14(xuu40001, xuu3001)
new_esEs28(xuu40000, xuu3000, app(app(ty_@2, ddg), ddh)) → new_esEs5(xuu40000, xuu3000, ddg, ddh)
new_esEs22(xuu30000, xuu31000, ty_Integer) → new_esEs11(xuu30000, xuu31000)
new_compare0(:(xuu30000, xuu30001), [], bae) → GT
new_lt8(xuu30000, xuu31000, ty_Ordering) → new_lt15(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Int) → new_lt6(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs4(xuu30000, xuu31000, bgb, bgc, bgd)
new_esEs22(xuu30000, xuu31000, app(ty_[], bge)) → new_esEs13(xuu30000, xuu31000, bge)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(ty_Maybe, dbc)) → new_ltEs16(xuu30000, xuu31000, dbc)
new_lt8(xuu30000, xuu31000, ty_Int) → new_lt6(xuu30000, xuu31000)
new_lt7(xuu30001, xuu31001, ty_@0) → new_lt13(xuu30001, xuu31001)
new_compare11(xuu30000, xuu31000, False, bg, bh) → GT
new_esEs25(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_primCmpInt(Pos(Succ(xuu3000)), Neg(xuu310)) → GT
new_lt7(xuu30001, xuu31001, ty_Int) → new_lt6(xuu30001, xuu31001)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Bool) → new_ltEs8(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, ty_Float) → new_esEs18(xuu40002, xuu3002)
new_esEs24(xuu40002, xuu3002, ty_Double) → new_esEs15(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, ty_Integer) → new_ltEs7(xuu30002, xuu31002)
new_primMulInt(Pos(xuu400000), Pos(xuu30000)) → Pos(new_primMulNat0(xuu400000, xuu30000))
new_esEs30(xuu19, xuu14, app(app(ty_@2, bec), bed)) → new_esEs5(xuu19, xuu14, bec, bed)
new_esEs24(xuu40002, xuu3002, ty_Integer) → new_esEs11(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, app(app(ty_Either, de), df)) → new_ltEs4(xuu30002, xuu31002, de, df)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_@0, fh) → new_esEs14(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, ty_Double) → new_esEs15(xuu40001, xuu3001)
new_primMulInt(Neg(xuu400000), Neg(xuu30000)) → Pos(new_primMulNat0(xuu400000, xuu30000))
new_primCmpNat2(Zero, Zero) → EQ
new_compare110(xuu30000, xuu31000, True) → LT
new_ltEs12(EQ, GT) → True
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(ty_Either, bda), bdb)) → new_ltEs4(xuu30000, xuu31000, bda, bdb)
new_compare13(xuu30000, xuu31000, ty_@0) → new_compare16(xuu30000, xuu31000)
new_ltEs20(xuu3000, xuu3100, ty_Float) → new_ltEs17(xuu3000, xuu3100)
new_esEs29(xuu4000, xuu300, app(ty_Ratio, bdc)) → new_esEs17(xuu4000, xuu300, bdc)
new_primEqNat0(Zero, Succ(xuu30000)) → False
new_primEqNat0(Succ(xuu400000), Zero) → False
new_ltEs8(False, False) → True
new_esEs25(xuu40001, xuu3001, app(ty_Ratio, ceb)) → new_esEs17(xuu40001, xuu3001, ceb)
new_esEs25(xuu40001, xuu3001, app(ty_Maybe, cfc)) → new_esEs6(xuu40001, xuu3001, cfc)
new_compare110(xuu30000, xuu31000, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Float) → new_esEs18(xuu40000, xuu3000)
new_compare113(xuu30000, xuu31000, True, fa, fb, fc) → LT
new_lt9(xuu30000, xuu31000) → new_esEs8(new_compare9(xuu30000, xuu31000), LT)
new_primPlusNat0(xuu104, xuu300000) → new_primPlusNat1(xuu104, Succ(xuu300000))
new_esEs10(xuu30000, xuu31000, app(ty_[], fd)) → new_esEs13(xuu30000, xuu31000, fd)
new_primCmpNat2(Succ(xuu30000), Succ(xuu31000)) → new_primCmpNat2(xuu30000, xuu31000)
new_primCmpInt(Pos(Succ(xuu3000)), Pos(xuu310)) → new_primCmpNat0(xuu3000, xuu310)
new_lt7(xuu30001, xuu31001, app(app(ty_@2, ed), ee)) → new_lt4(xuu30001, xuu31001, ed, ee)
new_compare13(xuu30000, xuu31000, ty_Char) → new_compare26(xuu30000, xuu31000)
new_esEs27(xuu40001, xuu3001, app(app(ty_@2, dce), dcf)) → new_esEs5(xuu40001, xuu3001, dce, dcf)
new_compare28(xuu30000, xuu31000, True, fa, fb, fc) → EQ
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Double) → new_esEs15(xuu40000, xuu3000)
new_primCmpNat0(xuu3000, Zero) → GT
new_compare13(xuu30000, xuu31000, app(ty_Ratio, bbb)) → new_compare8(xuu30000, xuu31000, bbb)
new_esEs10(xuu30000, xuu31000, ty_Integer) → new_esEs11(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Float) → new_lt18(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, app(app(ty_@2, bd), be)) → new_esEs5(xuu30000, xuu31000, bd, be)
new_esEs26(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare25(Float(xuu30000, xuu30001), Float(xuu31000, xuu31001)) → new_compare10(new_sr0(xuu30000, xuu31000), new_sr0(xuu30001, xuu31001))
new_esEs28(xuu40000, xuu3000, app(ty_Ratio, dch)) → new_esEs17(xuu40000, xuu3000, dch)
new_esEs23(xuu40000, xuu3000, app(ty_Ratio, cbf)) → new_esEs17(xuu40000, xuu3000, cbf)
new_esEs9(xuu30001, xuu31001, app(ty_Ratio, ec)) → new_esEs17(xuu30001, xuu31001, ec)
new_compare23(xuu30000, xuu31000, True, bg, bh) → EQ
new_esEs25(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3100))) → GT
new_lt7(xuu30001, xuu31001, ty_Ordering) → new_lt15(xuu30001, xuu31001)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(ty_[], dag)) → new_ltEs9(xuu30000, xuu31000, dag)
new_sr0(xuu40000, xuu3000) → new_primMulInt(xuu40000, xuu3000)
new_esEs26(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(app(ty_@3, caf), cag), cah)) → new_esEs4(xuu40000, xuu3000, caf, cag, cah)
new_lt8(xuu30000, xuu31000, app(app(ty_Either, bg), bh)) → new_lt17(xuu30000, xuu31000, bg, bh)
new_compare13(xuu30000, xuu31000, ty_Bool) → new_compare15(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Integer, cha) → new_ltEs7(xuu30000, xuu31000)
new_esEs19(Char(xuu40000), Char(xuu3000)) → new_primEqNat0(xuu40000, xuu3000)
new_esEs22(xuu30000, xuu31000, ty_Char) → new_esEs19(xuu30000, xuu31000)
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_Ratio, bce)) → new_ltEs14(xuu30000, xuu31000, bce)
new_esEs23(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs9(xuu30001, xuu31001, app(app(ty_@2, ed), ee)) → new_esEs5(xuu30001, xuu31001, ed, ee)
new_ltEs17(xuu3000, xuu3100) → new_fsEs(new_compare25(xuu3000, xuu3100))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs25(xuu40001, xuu3001, ty_Bool) → new_esEs12(xuu40001, xuu3001)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Char) → new_ltEs18(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_@0) → new_lt13(xuu30000, xuu31000)
new_esEs27(xuu40001, xuu3001, ty_Float) → new_esEs18(xuu40001, xuu3001)
new_compare9(Integer(xuu30000), Integer(xuu31000)) → new_primCmpInt(xuu30000, xuu31000)
new_asAs(False, xuu137) → False
new_esEs29(xuu4000, xuu300, ty_Bool) → new_esEs12(xuu4000, xuu300)
new_primMulInt(Pos(xuu400000), Neg(xuu30000)) → Neg(new_primMulNat0(xuu400000, xuu30000))
new_primMulInt(Neg(xuu400000), Pos(xuu30000)) → Neg(new_primMulNat0(xuu400000, xuu30000))
new_esEs13([], :(xuu3000, xuu3001), bhd) → False
new_esEs13(:(xuu40000, xuu40001), [], bhd) → False
new_primMulNat0(Succ(xuu4000000), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu300000)) → Zero
new_lt7(xuu30001, xuu31001, app(app(ty_Either, eg), eh)) → new_lt17(xuu30001, xuu31001, eg, eh)
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_Maybe, cbe)) → new_esEs6(xuu40000, xuu3000, cbe)
new_compare26(Char(xuu30000), Char(xuu31000)) → new_primCmpNat2(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_Ratio, chf), cha) → new_ltEs14(xuu30000, xuu31000, chf)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Double, fh) → new_esEs15(xuu40000, xuu3000)
new_ltEs20(xuu3000, xuu3100, ty_Integer) → new_ltEs7(xuu3000, xuu3100)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_[], ga), fh) → new_esEs13(xuu40000, xuu3000, ga)
new_esEs21(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_ltEs12(GT, GT) → True
new_ltEs20(xuu3000, xuu3100, ty_Double) → new_ltEs11(xuu3000, xuu3100)
new_esEs9(xuu30001, xuu31001, ty_Bool) → new_esEs12(xuu30001, xuu31001)
new_esEs10(xuu30000, xuu31000, app(ty_Maybe, bf)) → new_esEs6(xuu30000, xuu31000, bf)
new_ltEs19(xuu30001, xuu31001, ty_@0) → new_ltEs10(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Ordering, cha) → new_ltEs12(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Float, fh) → new_esEs18(xuu40000, xuu3000)
new_primCmpNat1(Succ(xuu3100), xuu3000) → new_primCmpNat2(xuu3100, xuu3000)
new_esEs23(xuu40000, xuu3000, app(ty_Maybe, ccg)) → new_esEs6(xuu40000, xuu3000, ccg)
new_primCmpNat2(Succ(xuu30000), Zero) → GT
new_lt7(xuu30001, xuu31001, app(ty_Ratio, ec)) → new_lt16(xuu30001, xuu31001, ec)
new_compare210(Just(xuu3000), Nothing, False, cgg) → GT
new_lt7(xuu30001, xuu31001, app(ty_Maybe, ef)) → new_lt5(xuu30001, xuu31001, ef)
new_lt8(xuu30000, xuu31000, ty_Float) → new_lt18(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, ty_Bool) → new_esEs12(xuu40002, xuu3002)
new_esEs25(xuu40001, xuu3001, app(ty_[], cec)) → new_esEs13(xuu40001, xuu3001, cec)
new_esEs23(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare27(xuu30000, xuu31000, True) → EQ
new_esEs10(xuu30000, xuu31000, ty_Float) → new_esEs18(xuu30000, xuu31000)
new_ltEs6(xuu30002, xuu31002, ty_Bool) → new_ltEs8(xuu30002, xuu31002)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Bool) → new_ltEs8(xuu30000, xuu31000)
new_compare17(Double(xuu30000, xuu30001), Double(xuu31000, xuu31001)) → new_compare10(new_sr0(xuu30000, xuu31000), new_sr0(xuu30001, xuu31001))
new_esEs12(False, True) → False
new_esEs12(True, False) → False
new_esEs28(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Int) → new_ltEs13(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Bool, fh) → new_esEs12(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_esEs29(xuu4000, xuu300, ty_Double) → new_esEs15(xuu4000, xuu300)
new_ltEs9(xuu3000, xuu3100, bae) → new_fsEs(new_compare0(xuu3000, xuu3100, bae))
new_esEs27(xuu40001, xuu3001, ty_Bool) → new_esEs12(xuu40001, xuu3001)
new_lt8(xuu30000, xuu31000, ty_Char) → new_lt19(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, ty_Float) → new_ltEs17(xuu30000, xuu31000)
new_ltEs19(xuu30001, xuu31001, app(app(app(ty_@3, beh), bfa), bfb)) → new_ltEs5(xuu30001, xuu31001, beh, bfa, bfb)
new_compare13(xuu30000, xuu31000, ty_Double) → new_compare17(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), hb, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_ltEs18(xuu3000, xuu3100) → new_fsEs(new_compare26(xuu3000, xuu3100))
new_compare10(xuu30, xuu31) → new_primCmpInt(xuu30, xuu31)
new_esEs10(xuu30000, xuu31000, app(ty_Ratio, ff)) → new_esEs17(xuu30000, xuu31000, ff)
new_lt7(xuu30001, xuu31001, app(app(app(ty_@3, dg), dh), ea)) → new_lt10(xuu30001, xuu31001, dg, dh, ea)
new_ltEs12(EQ, LT) → False
new_esEs25(xuu40001, xuu3001, app(app(ty_@2, cfa), cfb)) → new_esEs5(xuu40001, xuu3001, cfa, cfb)
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_[], cae)) → new_esEs13(xuu40000, xuu3000, cae)
new_lt8(xuu30000, xuu31000, ty_@0) → new_lt13(xuu30000, xuu31000)
new_ltEs19(xuu30001, xuu31001, app(app(ty_@2, bfe), bff)) → new_ltEs15(xuu30001, xuu31001, bfe, bff)
new_compare13(xuu30000, xuu31000, app(app(ty_Either, bbf), bbg)) → new_compare19(xuu30000, xuu31000, bbf, bbg)
new_lt7(xuu30001, xuu31001, app(ty_[], eb)) → new_lt12(xuu30001, xuu31001, eb)
new_esEs22(xuu30000, xuu31000, ty_@0) → new_esEs14(xuu30000, xuu31000)
new_esEs23(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs29(xuu4000, xuu300, app(app(ty_Either, hb), fh)) → new_esEs7(xuu4000, xuu300, hb, fh)
new_compare112(xuu130, xuu131, False, cac) → GT
new_compare29(xuu30000, xuu31000, False) → new_compare111(xuu30000, xuu31000, new_ltEs8(xuu30000, xuu31000))
new_esEs22(xuu30000, xuu31000, app(ty_Ratio, bgf)) → new_esEs17(xuu30000, xuu31000, bgf)
new_ltEs19(xuu30001, xuu31001, ty_Integer) → new_ltEs7(xuu30001, xuu31001)
new_esEs30(xuu19, xuu14, ty_Ordering) → new_esEs8(xuu19, xuu14)
new_esEs10(xuu30000, xuu31000, ty_Ordering) → new_esEs8(xuu30000, xuu31000)
new_lt4(xuu30000, xuu31000, bd, be) → new_esEs8(new_compare6(xuu30000, xuu31000, bd, be), LT)
new_lt7(xuu30001, xuu31001, ty_Char) → new_lt19(xuu30001, xuu31001)
new_compare0([], :(xuu31000, xuu31001), bae) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs9(xuu30001, xuu31001, ty_Char) → new_esEs19(xuu30001, xuu31001)
new_primCompAux0(xuu30000, xuu31000, xuu174, bae) → new_primCompAux00(xuu174, new_compare13(xuu30000, xuu31000, bae))
new_esEs9(xuu30001, xuu31001, ty_Double) → new_esEs15(xuu30001, xuu31001)
new_asAs(True, xuu137) → xuu137
new_primMulNat0(Succ(xuu4000000), Succ(xuu300000)) → new_primPlusNat0(new_primMulNat0(xuu4000000, Succ(xuu300000)), xuu300000)
new_esEs27(xuu40001, xuu3001, app(ty_[], dbg)) → new_esEs13(xuu40001, xuu3001, dbg)
new_esEs27(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(ty_Either, cba), cbb)) → new_esEs7(xuu40000, xuu3000, cba, cbb)
new_esEs26(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_ltEs6(xuu30002, xuu31002, ty_Int) → new_ltEs13(xuu30002, xuu31002)
new_esEs9(xuu30001, xuu31001, app(app(ty_Either, eg), eh)) → new_esEs7(xuu30001, xuu31001, eg, eh)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Int) → new_ltEs13(xuu30000, xuu31000)
new_lt17(xuu30000, xuu31000, bg, bh) → new_esEs8(new_compare19(xuu30000, xuu31000, bg, bh), LT)
new_fsEs(xuu147) → new_not(new_esEs8(xuu147, GT))
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare27(xuu30000, xuu31000, False) → new_compare110(xuu30000, xuu31000, new_ltEs12(xuu30000, xuu31000))
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(ty_@2, bcf), bcg)) → new_ltEs15(xuu30000, xuu31000, bcf, bcg)
new_ltEs6(xuu30002, xuu31002, ty_Float) → new_ltEs17(xuu30002, xuu31002)
new_ltEs6(xuu30002, xuu31002, app(ty_[], cg)) → new_ltEs9(xuu30002, xuu31002, cg)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Bool, cha) → new_ltEs8(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, app(ty_Maybe, cea)) → new_esEs6(xuu40002, xuu3002, cea)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Char, fh) → new_esEs19(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, app(ty_Ratio, dbf)) → new_esEs17(xuu40001, xuu3001, dbf)
new_compare7(xuu30000, xuu31000, bf) → new_compare210(xuu30000, xuu31000, new_esEs6(xuu30000, xuu31000, bf), bf)
new_esEs24(xuu40002, xuu3002, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs4(xuu40002, xuu3002, cdb, cdc, cdd)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_primCompAux00(xuu180, GT) → GT
new_esEs25(xuu40001, xuu3001, app(app(ty_Either, ceg), ceh)) → new_esEs7(xuu40001, xuu3001, ceg, ceh)
new_esEs18(Float(xuu40000, xuu40001), Float(xuu3000, xuu3001)) → new_esEs16(new_sr0(xuu40000, xuu3000), new_sr0(xuu40001, xuu3001))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs12(GT, LT) → False
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(app(ty_@3, chb), chc), chd), cha) → new_ltEs5(xuu30000, xuu31000, chb, chc, chd)
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(ty_Ratio, dah)) → new_ltEs14(xuu30000, xuu31000, dah)
new_esEs29(xuu4000, xuu300, ty_Ordering) → new_esEs8(xuu4000, xuu300)
new_lt7(xuu30001, xuu31001, ty_Integer) → new_lt9(xuu30001, xuu31001)
new_esEs28(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs5(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), ca, cb, cc) → new_pePe(new_lt8(xuu30000, xuu31000, ca), new_asAs(new_esEs10(xuu30000, xuu31000, ca), new_pePe(new_lt7(xuu30001, xuu31001, cb), new_asAs(new_esEs9(xuu30001, xuu31001, cb), new_ltEs6(xuu30002, xuu31002, cc)))))
new_primCmpInt(Neg(Succ(xuu3000)), Pos(xuu310)) → LT
new_esEs23(xuu40000, xuu3000, app(ty_[], cbg)) → new_esEs13(xuu40000, xuu3000, cbg)
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs5(xuu30000, xuu31000, bca, bcb, bcc)
new_esEs22(xuu30000, xuu31000, ty_Int) → new_esEs16(xuu30000, xuu31000)
new_not(True) → False
new_ltEs4(Right(xuu30000), Right(xuu31000), cgh, app(app(app(ty_@3, dad), dae), daf)) → new_ltEs5(xuu30000, xuu31000, dad, dae, daf)

The set Q consists of the following terms:

new_primCompAux00(x0, EQ)
new_esEs9(x0, x1, ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs14(x0, x1, x2)
new_esEs9(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Double)
new_pePe(True, x0)
new_ltEs12(LT, LT)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, ty_Integer)
new_lt8(x0, x1, ty_@0)
new_compare13(x0, x1, ty_Char)
new_compare11(x0, x1, False, x2, x3)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs10(x0, x1, ty_Integer)
new_primCmpNat0(x0, Succ(x1))
new_compare13(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, ty_Float)
new_lt7(x0, x1, ty_Ordering)
new_compare28(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, ty_@0)
new_esEs12(False, False)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs6(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs16(x0, x1)
new_lt8(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, x2, x3, x4)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Ordering)
new_compare26(Char(x0), Char(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs30(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare210(Just(x0), Nothing, False, x1)
new_primPlusNat0(x0, x1)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs8(GT, GT)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_primCompAux00(x0, LT)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Float)
new_ltEs12(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_lt9(x0, x1)
new_ltEs8(True, True)
new_compare13(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs8(LT, LT)
new_primCompAux00(x0, GT)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs15(Double(x0, x1), Double(x2, x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Bool)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_lt7(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_Bool)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs23(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primMulNat0(Succ(x0), Zero)
new_ltEs16(Just(x0), Just(x1), ty_@0)
new_compare113(x0, x1, True, x2, x3, x4)
new_lt8(x0, x1, ty_Char)
new_compare13(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), Succ(x1))
new_ltEs18(x0, x1)
new_ltEs6(x0, x1, ty_Double)
new_ltEs10(x0, x1)
new_primEqNat0(Zero, Zero)
new_compare24(x0, x1, False, x2, x3)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Just(x0), Nothing, x1)
new_ltEs16(Just(x0), Just(x1), ty_Integer)
new_ltEs16(Nothing, Nothing, x0)
new_compare13(x0, x1, ty_Int)
new_ltEs7(x0, x1)
new_compare13(x0, x1, ty_@0)
new_lt15(x0, x1)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primMulNat0(Zero, Zero)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt8(x0, x1, ty_Float)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Ordering)
new_lt8(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt13(x0, x1)
new_lt16(x0, x1, x2)
new_esEs25(x0, x1, ty_Char)
new_compare6(x0, x1, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_primCmpNat1(Zero, x0)
new_compare13(x0, x1, app(ty_[], x2))
new_esEs14(@0, @0)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Double)
new_lt8(x0, x1, app(ty_[], x2))
new_ltEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare13(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs16(Nothing, Just(x0), x1)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare16(@0, @0)
new_compare111(x0, x1, True)
new_esEs25(x0, x1, ty_Bool)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs28(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt18(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare210(Nothing, Just(x0), False, x1)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Integer)
new_ltEs6(x0, x1, ty_Bool)
new_primCmpNat1(Succ(x0), x1)
new_lt5(x0, x1, x2)
new_primPlusNat1(Zero, Zero)
new_compare210(Just(x0), Just(x1), False, x2)
new_esEs24(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpNat2(Zero, Zero)
new_ltEs16(Just(x0), Just(x1), ty_Double)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs9(x0, x1, x2)
new_esEs9(x0, x1, ty_@0)
new_compare25(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat1(Succ(x0), Zero)
new_esEs23(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare10(x0, x1)
new_esEs30(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), ty_Bool)
new_ltEs11(x0, x1)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare7(x0, x1, x2)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs12(GT, EQ)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(EQ, GT)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs16(Just(x0), Just(x1), ty_Char)
new_sr(Integer(x0), Integer(x1))
new_esEs11(Integer(x0), Integer(x1))
new_compare12(x0, x1, False, x2, x3)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt7(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs12(True, True)
new_ltEs8(False, False)
new_esEs29(x0, x1, ty_Char)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Double)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Ordering)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs24(x0, x1, ty_Int)
new_compare27(x0, x1, False)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs20(x0, x1, ty_Ordering)
new_lt4(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primCmpNat0(x0, Zero)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, x2)
new_pePe(False, x0)
new_lt20(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs12(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, ty_Double)
new_compare29(x0, x1, True)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_compare9(Integer(x0), Integer(x1))
new_ltEs13(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt14(x0, x1)
new_esEs30(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare17(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs13([], :(x0, x1), x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs17(x0, x1)
new_compare14(x0, x1, x2, x3, x4)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare23(x0, x1, True, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_compare110(x0, x1, False)
new_esEs29(x0, x1, ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_fsEs(x0)
new_ltEs16(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_lt8(x0, x1, app(ty_Maybe, x2))
new_esEs19(Char(x0), Char(x1))
new_esEs30(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs20(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primCmpNat2(Succ(x0), Zero)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Ordering)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_lt7(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs6(Nothing, Just(x0), x1)
new_esEs29(x0, x1, ty_Ordering)
new_compare111(x0, x1, False)
new_esEs9(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_asAs(True, x0)
new_ltEs19(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_compare210(Nothing, Nothing, False, x0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs10(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs28(x0, x1, ty_Integer)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(False, True)
new_esEs12(True, False)
new_ltEs16(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2, x3)
new_compare13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_primCmpNat2(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare28(x0, x1, False, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Integer)
new_asAs(False, x0)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs16(Just(x0), Nothing, x1)
new_lt17(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_not(True)
new_ltEs6(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Integer)
new_compare23(x0, x1, False, x2, x3)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_not(False)
new_primPlusNat1(Zero, Succ(x0))
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt8(x0, x1, ty_Double)
new_compare18(x0, x1)
new_ltEs16(Just(x0), Just(x1), ty_Float)
new_esEs25(x0, x1, ty_@0)
new_esEs13(:(x0, x1), [], x2)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, ty_Double)
new_ltEs16(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(x0, x1)
new_compare210(x0, x1, True, x2)
new_esEs27(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, ty_Int)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt8(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Zero)
new_sr0(x0, x1)
new_esEs13([], [], x0)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs24(x0, x1, ty_Char)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Float)
new_compare11(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Bool)
new_ltEs12(EQ, LT)
new_ltEs12(LT, EQ)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_compare112(x0, x1, False, x2)
new_esEs10(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_compare12(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_compare112(x0, x1, True, x2)
new_lt7(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs12(GT, LT)
new_ltEs12(LT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare113(x0, x1, False, x2, x3, x4)
new_compare27(x0, x1, True)
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt8(x0, x1, ty_Int)
new_ltEs16(Just(x0), Just(x1), ty_Ordering)
new_compare0([], [], x0)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_ltEs16(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ AND
                                        ↳ QDP
                                        ↳ QDP
                                          ↳ UsableRulesProof
QDP
                                              ↳ QReductionProof
                                  ↳ QDP

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

new_addToFM_C1(xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_addToFM_C(xuu34, Nothing, xuu401, h, ba)
new_addToFM_C2(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_addToFM_C(xuu33, Nothing, xuu401, h, ba)
new_addToFM_C(Branch(Nothing, xuu31, xuu32, xuu33, xuu34), Nothing, xuu401, h, ba) → new_addToFM_C1(xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C2(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, False, h, ba) → new_addToFM_C10(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Just(xuu300), False, h), GT), h, ba)
new_addToFM_C10(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_addToFM_C(xuu34, Nothing, xuu401, h, ba)
new_addToFM_C(Branch(Just(xuu300), xuu31, xuu32, xuu33, xuu34), Nothing, xuu401, h, ba) → new_addToFM_C2(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Just(xuu300), False, h), LT), h, ba)

The TRS R consists of the following rules:

new_compare210(Nothing, Just(xuu3100), False, cgg) → LT
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_compare210(xuu300, xuu310, True, cgg) → EQ
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False

The set Q consists of the following terms:

new_primCompAux00(x0, EQ)
new_esEs9(x0, x1, ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs14(x0, x1, x2)
new_esEs9(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Double)
new_pePe(True, x0)
new_ltEs12(LT, LT)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, ty_Integer)
new_lt8(x0, x1, ty_@0)
new_compare13(x0, x1, ty_Char)
new_compare11(x0, x1, False, x2, x3)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs10(x0, x1, ty_Integer)
new_primCmpNat0(x0, Succ(x1))
new_compare13(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, ty_Float)
new_lt7(x0, x1, ty_Ordering)
new_compare28(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, ty_@0)
new_esEs12(False, False)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs6(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs16(x0, x1)
new_lt8(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, x2, x3, x4)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Ordering)
new_compare26(Char(x0), Char(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs30(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare210(Just(x0), Nothing, False, x1)
new_primPlusNat0(x0, x1)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs8(GT, GT)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_primCompAux00(x0, LT)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Float)
new_ltEs12(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_lt9(x0, x1)
new_ltEs8(True, True)
new_compare13(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs8(LT, LT)
new_primCompAux00(x0, GT)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs15(Double(x0, x1), Double(x2, x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Bool)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_lt7(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_Bool)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs23(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primMulNat0(Succ(x0), Zero)
new_ltEs16(Just(x0), Just(x1), ty_@0)
new_compare113(x0, x1, True, x2, x3, x4)
new_lt8(x0, x1, ty_Char)
new_compare13(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), Succ(x1))
new_ltEs18(x0, x1)
new_ltEs6(x0, x1, ty_Double)
new_ltEs10(x0, x1)
new_primEqNat0(Zero, Zero)
new_compare24(x0, x1, False, x2, x3)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Just(x0), Nothing, x1)
new_ltEs16(Just(x0), Just(x1), ty_Integer)
new_ltEs16(Nothing, Nothing, x0)
new_compare13(x0, x1, ty_Int)
new_ltEs7(x0, x1)
new_compare13(x0, x1, ty_@0)
new_lt15(x0, x1)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primMulNat0(Zero, Zero)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt8(x0, x1, ty_Float)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Ordering)
new_lt8(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt13(x0, x1)
new_lt16(x0, x1, x2)
new_esEs25(x0, x1, ty_Char)
new_compare6(x0, x1, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_primCmpNat1(Zero, x0)
new_compare13(x0, x1, app(ty_[], x2))
new_esEs14(@0, @0)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Double)
new_lt8(x0, x1, app(ty_[], x2))
new_ltEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare13(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs16(Nothing, Just(x0), x1)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare16(@0, @0)
new_compare111(x0, x1, True)
new_esEs25(x0, x1, ty_Bool)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs28(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt18(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare210(Nothing, Just(x0), False, x1)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Integer)
new_ltEs6(x0, x1, ty_Bool)
new_primCmpNat1(Succ(x0), x1)
new_lt5(x0, x1, x2)
new_primPlusNat1(Zero, Zero)
new_compare210(Just(x0), Just(x1), False, x2)
new_esEs24(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpNat2(Zero, Zero)
new_ltEs16(Just(x0), Just(x1), ty_Double)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs9(x0, x1, x2)
new_esEs9(x0, x1, ty_@0)
new_compare25(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat1(Succ(x0), Zero)
new_esEs23(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare10(x0, x1)
new_esEs30(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), ty_Bool)
new_ltEs11(x0, x1)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare7(x0, x1, x2)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs12(GT, EQ)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(EQ, GT)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs16(Just(x0), Just(x1), ty_Char)
new_sr(Integer(x0), Integer(x1))
new_esEs11(Integer(x0), Integer(x1))
new_compare12(x0, x1, False, x2, x3)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt7(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs12(True, True)
new_ltEs8(False, False)
new_esEs29(x0, x1, ty_Char)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Double)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Ordering)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs24(x0, x1, ty_Int)
new_compare27(x0, x1, False)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs20(x0, x1, ty_Ordering)
new_lt4(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primCmpNat0(x0, Zero)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, x2)
new_pePe(False, x0)
new_lt20(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs12(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, ty_Double)
new_compare29(x0, x1, True)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_compare9(Integer(x0), Integer(x1))
new_ltEs13(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt14(x0, x1)
new_esEs30(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare17(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs13([], :(x0, x1), x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs17(x0, x1)
new_compare14(x0, x1, x2, x3, x4)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare23(x0, x1, True, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_compare110(x0, x1, False)
new_esEs29(x0, x1, ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_fsEs(x0)
new_ltEs16(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_lt8(x0, x1, app(ty_Maybe, x2))
new_esEs19(Char(x0), Char(x1))
new_esEs30(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs20(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primCmpNat2(Succ(x0), Zero)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Ordering)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_lt7(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs6(Nothing, Just(x0), x1)
new_esEs29(x0, x1, ty_Ordering)
new_compare111(x0, x1, False)
new_esEs9(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_asAs(True, x0)
new_ltEs19(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_compare210(Nothing, Nothing, False, x0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs10(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs28(x0, x1, ty_Integer)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(False, True)
new_esEs12(True, False)
new_ltEs16(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2, x3)
new_compare13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_primCmpNat2(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare28(x0, x1, False, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Integer)
new_asAs(False, x0)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs16(Just(x0), Nothing, x1)
new_lt17(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_not(True)
new_ltEs6(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Integer)
new_compare23(x0, x1, False, x2, x3)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_not(False)
new_primPlusNat1(Zero, Succ(x0))
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt8(x0, x1, ty_Double)
new_compare18(x0, x1)
new_ltEs16(Just(x0), Just(x1), ty_Float)
new_esEs25(x0, x1, ty_@0)
new_esEs13(:(x0, x1), [], x2)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, ty_Double)
new_ltEs16(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(x0, x1)
new_compare210(x0, x1, True, x2)
new_esEs27(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, ty_Int)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt8(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Zero)
new_sr0(x0, x1)
new_esEs13([], [], x0)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs24(x0, x1, ty_Char)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Float)
new_compare11(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Bool)
new_ltEs12(EQ, LT)
new_ltEs12(LT, EQ)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_compare112(x0, x1, False, x2)
new_esEs10(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_compare12(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_compare112(x0, x1, True, x2)
new_lt7(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs12(GT, LT)
new_ltEs12(LT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare113(x0, x1, False, x2, x3, x4)
new_compare27(x0, x1, True)
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt8(x0, x1, ty_Int)
new_ltEs16(Just(x0), Just(x1), ty_Ordering)
new_compare0([], [], x0)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_ltEs16(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primCompAux00(x0, EQ)
new_esEs9(x0, x1, ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs14(x0, x1, x2)
new_esEs9(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Double)
new_pePe(True, x0)
new_ltEs12(LT, LT)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs24(x0, x1, ty_Integer)
new_lt8(x0, x1, ty_@0)
new_compare13(x0, x1, ty_Char)
new_compare11(x0, x1, False, x2, x3)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs10(x0, x1, ty_Integer)
new_primCmpNat0(x0, Succ(x1))
new_compare13(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, ty_Float)
new_lt7(x0, x1, ty_Ordering)
new_compare28(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, ty_@0)
new_esEs12(False, False)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs6(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs16(x0, x1)
new_lt8(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, x2, x3, x4)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Ordering)
new_compare26(Char(x0), Char(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs30(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primPlusNat0(x0, x1)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_primCompAux00(x0, LT)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Float)
new_ltEs12(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_lt9(x0, x1)
new_ltEs8(True, True)
new_compare13(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_primCompAux00(x0, GT)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs15(Double(x0, x1), Double(x2, x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Bool)
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_lt7(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primMulNat0(Succ(x0), Zero)
new_ltEs16(Just(x0), Just(x1), ty_@0)
new_compare113(x0, x1, True, x2, x3, x4)
new_lt8(x0, x1, ty_Char)
new_compare13(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), Succ(x1))
new_ltEs18(x0, x1)
new_ltEs6(x0, x1, ty_Double)
new_ltEs10(x0, x1)
new_primEqNat0(Zero, Zero)
new_compare24(x0, x1, False, x2, x3)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Just(x0), Nothing, x1)
new_ltEs16(Just(x0), Just(x1), ty_Integer)
new_ltEs16(Nothing, Nothing, x0)
new_compare13(x0, x1, ty_Int)
new_ltEs7(x0, x1)
new_compare13(x0, x1, ty_@0)
new_lt15(x0, x1)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primMulNat0(Zero, Zero)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_lt8(x0, x1, ty_Float)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Ordering)
new_lt8(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt13(x0, x1)
new_lt16(x0, x1, x2)
new_esEs25(x0, x1, ty_Char)
new_compare6(x0, x1, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_primCmpNat1(Zero, x0)
new_compare13(x0, x1, app(ty_[], x2))
new_esEs14(@0, @0)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Double)
new_lt8(x0, x1, app(ty_[], x2))
new_ltEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare13(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs16(Nothing, Just(x0), x1)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare16(@0, @0)
new_compare111(x0, x1, True)
new_esEs25(x0, x1, ty_Bool)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs28(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt18(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Integer)
new_ltEs6(x0, x1, ty_Bool)
new_primCmpNat1(Succ(x0), x1)
new_lt5(x0, x1, x2)
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpNat2(Zero, Zero)
new_ltEs16(Just(x0), Just(x1), ty_Double)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs9(x0, x1, x2)
new_esEs9(x0, x1, ty_@0)
new_compare25(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat1(Succ(x0), Zero)
new_esEs23(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare10(x0, x1)
new_esEs30(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), ty_Bool)
new_ltEs11(x0, x1)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare7(x0, x1, x2)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs12(GT, EQ)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(EQ, GT)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs16(Just(x0), Just(x1), ty_Char)
new_sr(Integer(x0), Integer(x1))
new_esEs11(Integer(x0), Integer(x1))
new_compare12(x0, x1, False, x2, x3)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt7(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs12(True, True)
new_ltEs8(False, False)
new_esEs29(x0, x1, ty_Char)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Double)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Ordering)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs24(x0, x1, ty_Int)
new_compare27(x0, x1, False)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs20(x0, x1, ty_Ordering)
new_lt4(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primCmpNat0(x0, Zero)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, x2)
new_pePe(False, x0)
new_lt20(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs12(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, ty_Double)
new_compare29(x0, x1, True)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_compare9(Integer(x0), Integer(x1))
new_ltEs13(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt14(x0, x1)
new_esEs30(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare17(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs13([], :(x0, x1), x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs17(x0, x1)
new_compare14(x0, x1, x2, x3, x4)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare23(x0, x1, True, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_compare110(x0, x1, False)
new_esEs29(x0, x1, ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, False)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_fsEs(x0)
new_ltEs16(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_lt8(x0, x1, app(ty_Maybe, x2))
new_esEs19(Char(x0), Char(x1))
new_esEs30(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs20(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primCmpNat2(Succ(x0), Zero)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Ordering)
new_lt7(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs6(Nothing, Just(x0), x1)
new_esEs29(x0, x1, ty_Ordering)
new_compare111(x0, x1, False)
new_esEs9(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_asAs(True, x0)
new_ltEs19(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs10(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs28(x0, x1, ty_Integer)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(False, True)
new_esEs12(True, False)
new_ltEs16(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2, x3)
new_compare13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_primCmpNat2(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare28(x0, x1, False, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Integer)
new_asAs(False, x0)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs16(Just(x0), Nothing, x1)
new_lt17(x0, x1, x2, x3)
new_esEs25(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_not(True)
new_ltEs6(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Integer)
new_compare23(x0, x1, False, x2, x3)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_not(False)
new_primPlusNat1(Zero, Succ(x0))
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt8(x0, x1, ty_Double)
new_compare18(x0, x1)
new_ltEs16(Just(x0), Just(x1), ty_Float)
new_esEs25(x0, x1, ty_@0)
new_esEs13(:(x0, x1), [], x2)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, ty_Double)
new_ltEs16(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(x0, x1)
new_esEs27(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, ty_Int)
new_lt8(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Zero)
new_sr0(x0, x1)
new_esEs13([], [], x0)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs24(x0, x1, ty_Char)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Float)
new_compare11(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Bool)
new_ltEs12(EQ, LT)
new_ltEs12(LT, EQ)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_compare112(x0, x1, False, x2)
new_esEs10(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_compare12(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_compare112(x0, x1, True, x2)
new_lt7(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs12(GT, LT)
new_ltEs12(LT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare113(x0, x1, False, x2, x3, x4)
new_compare27(x0, x1, True)
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt8(x0, x1, ty_Int)
new_ltEs16(Just(x0), Just(x1), ty_Ordering)
new_compare0([], [], x0)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_ltEs16(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))



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

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

new_addToFM_C1(xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_addToFM_C(xuu34, Nothing, xuu401, h, ba)
new_addToFM_C2(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_addToFM_C(xuu33, Nothing, xuu401, h, ba)
new_addToFM_C(Branch(Nothing, xuu31, xuu32, xuu33, xuu34), Nothing, xuu401, h, ba) → new_addToFM_C1(xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C2(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, False, h, ba) → new_addToFM_C10(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Just(xuu300), False, h), GT), h, ba)
new_addToFM_C10(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_addToFM_C(xuu34, Nothing, xuu401, h, ba)
new_addToFM_C(Branch(Just(xuu300), xuu31, xuu32, xuu33, xuu34), Nothing, xuu401, h, ba) → new_addToFM_C2(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Just(xuu300), False, h), LT), h, ba)

The TRS R consists of the following rules:

new_compare210(Nothing, Just(xuu3100), False, cgg) → LT
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_compare210(xuu300, xuu310, True, cgg) → EQ
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False

The set Q consists of the following terms:

new_compare210(Just(x0), Nothing, False, x1)
new_esEs8(GT, GT)
new_esEs8(LT, LT)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_compare210(Nothing, Just(x0), False, x1)
new_compare210(Just(x0), Just(x1), False, x2)
new_esEs8(EQ, EQ)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_compare210(Nothing, Nothing, False, x0)
new_compare210(x0, x1, True, x2)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)

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

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



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

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

new_foldl(xuu3, :(xuu40, xuu41), h, ba) → new_foldl(new_addListToFM_CAdd(xuu3, xuu40, h, ba), xuu41, h, ba)

The TRS R consists of the following rules:

new_esEs30(xuu19, xuu14, app(ty_Maybe, deb)) → new_esEs6(xuu19, xuu14, deb)
new_esEs25(xuu40001, xuu3001, ty_Char) → new_esEs19(xuu40001, xuu3001)
new_ltEs6(xuu30002, xuu31002, app(app(ty_@2, chd), che)) → new_ltEs15(xuu30002, xuu31002, chd, che)
new_esEs28(xuu40000, xuu3000, app(ty_[], cfa)) → new_esEs13(xuu40000, xuu3000, cfa)
new_ltEs19(xuu30001, xuu31001, ty_Ordering) → new_ltEs12(xuu30001, xuu31001)
new_primCmpNat0(xuu3000, Succ(xuu3100)) → new_primCmpNat2(xuu3000, xuu3100)
new_esEs23(xuu40000, xuu3000, app(app(ty_Either, bdf), bdg)) → new_esEs7(xuu40000, xuu3000, bdf, bdg)
new_compare112(xuu130, xuu131, True, bbd) → LT
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(ty_@2, bce), bcf)) → new_esEs5(xuu40000, xuu3000, bce, bcf)
new_esEs29(xuu4000, xuu300, ty_Int) → new_esEs16(xuu4000, xuu300)
new_ltEs20(xuu3000, xuu3100, ty_Char) → new_ltEs18(xuu3000, xuu3100)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(ty_Either, cc), cd), bf) → new_esEs7(xuu40000, xuu3000, cc, cd)
new_ltEs8(False, True) → True
new_esEs7(Right(xuu40000), Right(xuu3000), da, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_esEs10(xuu30000, xuu31000, app(app(app(ty_@3, gc), gd), ge)) → new_esEs4(xuu30000, xuu31000, gc, gd, ge)
new_esEs27(xuu40001, xuu3001, ty_Char) → new_esEs19(xuu40001, xuu3001)
new_compare13(xuu30000, xuu31000, app(app(app(ty_@3, dbe), dbf), dbg)) → new_compare14(xuu30000, xuu31000, dbe, dbf, dbg)
new_ltEs10(xuu3000, xuu3100) → new_fsEs(new_compare16(xuu3000, xuu3100))
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Ordering) → new_ltEs12(xuu30000, xuu31000)
new_ltEs12(LT, GT) → True
new_esEs13([], [], bch) → True
new_ltEs19(xuu30001, xuu31001, app(ty_[], hc)) → new_ltEs9(xuu30001, xuu31001, hc)
new_lt20(xuu30000, xuu31000, app(ty_Ratio, baf)) → new_lt16(xuu30000, xuu31000, baf)
new_lt7(xuu30001, xuu31001, ty_Bool) → new_lt11(xuu30001, xuu31001)
new_lt16(xuu30000, xuu31000, dbd) → new_esEs8(new_compare8(xuu30000, xuu31000, dbd), LT)
new_esEs4(@3(xuu40000, xuu40001, xuu40002), @3(xuu3000, xuu3001, xuu3002), bec, bed, bee) → new_asAs(new_esEs26(xuu40000, xuu3000, bec), new_asAs(new_esEs25(xuu40001, xuu3001, bed), new_esEs24(xuu40002, xuu3002, bee)))
new_esEs11(Integer(xuu40000), Integer(xuu3000)) → new_primEqInt(xuu40000, xuu3000)
new_esEs30(xuu19, xuu14, app(ty_[], ddb)) → new_esEs13(xuu19, xuu14, ddb)
new_esEs15(Double(xuu40000, xuu40001), Double(xuu3000, xuu3001)) → new_esEs16(new_sr0(xuu40000, xuu3000), new_sr0(xuu40001, xuu3001))
new_addToFM_C22(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_mkBalBranch(xuu300, xuu31, new_addToFM_C0(xuu33, Nothing, xuu401, h, ba), xuu34, h, ba)
new_esEs28(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_compare13(xuu30000, xuu31000, app(ty_Maybe, dcd)) → new_compare7(xuu30000, xuu31000, dcd)
new_esEs26(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_compare19(xuu30000, xuu31000, cgb, cgc) → new_compare23(xuu30000, xuu31000, new_esEs7(xuu30000, xuu31000, cgb, cgc), cgb, cgc)
new_ltEs19(xuu30001, xuu31001, ty_Double) → new_ltEs11(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(ty_@2, cbd), cbe), caf) → new_ltEs15(xuu30000, xuu31000, cbd, cbe)
new_sizeFM0(Branch(xuu2100, xuu2101, xuu2102, xuu2103, xuu2104), ga, gb) → xuu2102
new_mkBalBranch6Size_l(xuu31, xuu33, xuu34, h, ba) → new_sizeFM(xuu33, h, ba)
new_primMulNat0(Zero, Zero) → Zero
new_esEs27(xuu40001, xuu3001, app(app(app(ty_@3, cdh), cea), ceb)) → new_esEs4(xuu40001, xuu3001, cdh, cea, ceb)
new_ltEs12(LT, LT) → True
new_compare29(xuu30000, xuu31000, True) → EQ
new_sr(Integer(xuu300000), Integer(xuu310010)) → Integer(new_primMulInt(xuu300000, xuu310010))
new_esEs12(True, True) → True
new_addToFM_C13(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_mkBalBranch(xuu300, xuu31, xuu33, new_addToFM_C0(xuu34, Nothing, xuu401, h, ba), h, ba)
new_ltEs6(xuu30002, xuu31002, app(app(app(ty_@3, cgg), cgh), cha)) → new_ltEs5(xuu30002, xuu31002, cgg, cgh, cha)
new_mkBalBranch6MkBalBranch11(xuu31, xuu330, xuu331, xuu332, xuu333, xuu334, xuu34, True, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), xuu330, xuu331, xuu333, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Nothing, xuu31, xuu334, xuu34, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_@0) → new_ltEs10(xuu30000, xuu31000)
new_ltEs15(@2(xuu30000, xuu30001), @2(xuu31000, xuu31001), gf, gg) → new_pePe(new_lt20(xuu30000, xuu31000, gf), new_asAs(new_esEs22(xuu30000, xuu31000, gf), new_ltEs19(xuu30001, xuu31001, gg)))
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, ty_Double) → new_ltEs11(xuu30000, xuu31000)
new_esEs23(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Integer) → new_ltEs7(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), da, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_addToFM_C16(xuu14, xuu15, xuu16, xuu17, xuu18, xuu19, xuu20, True, dcg, dch) → new_mkBalBranch(xuu14, xuu15, xuu17, new_addToFM_C0(xuu18, Just(xuu19), xuu20, dcg, dch), dcg, dch)
new_esEs7(Right(xuu40000), Right(xuu3000), da, app(ty_Ratio, db)) → new_esEs17(xuu40000, xuu3000, db)
new_lt12(xuu30000, xuu31000, dbc) → new_esEs8(new_compare0(xuu30000, xuu31000, dbc), LT)
new_esEs24(xuu40002, xuu3002, ty_@0) → new_esEs14(xuu40002, xuu3002)
new_lt8(xuu30000, xuu31000, app(ty_[], dbc)) → new_lt12(xuu30000, xuu31000, dbc)
new_compare16(@0, @0) → EQ
new_esEs30(xuu19, xuu14, app(app(ty_Either, ddf), ddg)) → new_esEs7(xuu19, xuu14, ddf, ddg)
new_compare8(:%(xuu30000, xuu30001), :%(xuu31000, xuu31001), ty_Integer) → new_compare9(new_sr(xuu30000, xuu31001), new_sr(xuu31000, xuu30001))
new_lt20(xuu30000, xuu31000, ty_Double) → new_lt14(xuu30000, xuu31000)
new_mkBalBranch6MkBalBranch11(xuu31, xuu330, xuu331, xuu332, xuu333, EmptyFM, xuu34, False, h, ba) → error([])
new_lt20(xuu30000, xuu31000, ty_Integer) → new_lt9(xuu30000, xuu31000)
new_ltEs12(LT, EQ) → True
new_ltEs20(xuu3000, xuu3100, app(ty_[], cad)) → new_ltEs9(xuu3000, xuu3100, cad)
new_lt8(xuu30000, xuu31000, app(ty_Ratio, dbd)) → new_lt16(xuu30000, xuu31000, dbd)
new_ltEs11(xuu3000, xuu3100) → new_fsEs(new_compare17(xuu3000, xuu3100))
new_esEs22(xuu30000, xuu31000, app(app(ty_@2, bag), bah)) → new_esEs5(xuu30000, xuu31000, bag, bah)
new_compare0(:(xuu30000, xuu30001), :(xuu31000, xuu31001), cad) → new_primCompAux0(xuu30000, xuu31000, new_compare0(xuu30001, xuu31001, cad), cad)
new_compare210(Nothing, Nothing, False, dec) → LT
new_esEs24(xuu40002, xuu3002, app(app(ty_@2, bfe), bff)) → new_esEs5(xuu40002, xuu3002, bfe, bff)
new_esEs22(xuu30000, xuu31000, app(ty_Maybe, bba)) → new_esEs6(xuu30000, xuu31000, bba)
new_ltEs20(xuu3000, xuu3100, app(ty_Ratio, cae)) → new_ltEs14(xuu3000, xuu3100, cae)
new_esEs27(xuu40001, xuu3001, app(ty_Maybe, ceg)) → new_esEs6(xuu40001, xuu3001, ceg)
new_esEs26(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_esEs25(xuu40001, xuu3001, ty_Double) → new_esEs15(xuu40001, xuu3001)
new_compare15(xuu30000, xuu31000) → new_compare29(xuu30000, xuu31000, new_esEs12(xuu30000, xuu31000))
new_mkBranch(xuu206, xuu207, xuu208, xuu209, xuu210, ga, gb) → Branch(xuu207, xuu208, new_primPlusInt(new_primPlusInt(Pos(Succ(Zero)), new_sizeFM0(xuu209, ga, gb)), new_sizeFM0(xuu210, ga, gb)), xuu209, xuu210)
new_mkBalBranch6Size_r0(xuu300, xuu31, xuu25, xuu34, h, ba) → new_sizeFM(xuu34, h, ba)
new_esEs29(xuu4000, xuu300, ty_Float) → new_esEs18(xuu4000, xuu300)
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, ty_Char) → new_ltEs18(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Ordering) → new_lt15(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, app(app(ty_Either, bbb), bbc)) → new_esEs7(xuu30000, xuu31000, bbb, bbc)
new_ltEs19(xuu30001, xuu31001, ty_Char) → new_ltEs18(xuu30001, xuu31001)
new_lt18(xuu30000, xuu31000) → new_esEs8(new_compare25(xuu30000, xuu31000), LT)
new_esEs7(Right(xuu40000), Right(xuu3000), da, app(ty_Maybe, ec)) → new_esEs6(xuu40000, xuu3000, ec)
new_ltEs19(xuu30001, xuu31001, app(app(ty_Either, hh), baa)) → new_ltEs4(xuu30001, xuu31001, hh, baa)
new_pePe(False, xuu163) → xuu163
new_esEs7(Right(xuu40000), Right(xuu3000), da, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_esEs7(Left(xuu40000), Right(xuu3000), da, bf) → False
new_esEs7(Right(xuu40000), Left(xuu3000), da, bf) → False
new_lt20(xuu30000, xuu31000, ty_Bool) → new_lt11(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, ty_Bool) → new_esEs12(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Double, caf) → new_ltEs11(xuu30000, xuu31000)
new_compare6(xuu30000, xuu31000, bb, bc) → new_compare24(xuu30000, xuu31000, new_esEs5(xuu30000, xuu31000, bb, bc), bb, bc)
new_esEs28(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, app(app(ty_Either, cec), ced)) → new_esEs7(xuu40001, xuu3001, cec, ced)
new_esEs20(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_ltEs20(xuu3000, xuu3100, ty_@0) → new_ltEs10(xuu3000, xuu3100)
new_mkBalBranch6MkBalBranch3(xuu300, xuu31, xuu25, xuu34, False, h, ba) → new_mkBranch(Succ(Zero), Just(xuu300), xuu31, xuu25, xuu34, app(ty_Maybe, h), ba)
new_addToFM_C16(xuu14, xuu15, xuu16, xuu17, xuu18, xuu19, xuu20, False, dcg, dch) → Branch(Just(xuu19), new_addListToFM0(xuu15, xuu20, dch), xuu16, xuu17, xuu18)
new_compare13(xuu30000, xuu31000, ty_Int) → new_compare10(xuu30000, xuu31000)
new_esEs26(xuu40000, xuu3000, app(ty_Ratio, bhb)) → new_esEs17(xuu40000, xuu3000, bhb)
new_esEs22(xuu30000, xuu31000, ty_Double) → new_esEs15(xuu30000, xuu31000)
new_esEs26(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_ltEs20(xuu3000, xuu3100, app(app(ty_Either, cca), caf)) → new_ltEs4(xuu3000, xuu3100, cca, caf)
new_esEs28(xuu40000, xuu3000, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs4(xuu40000, xuu3000, cfb, cfc, cfd)
new_lt20(xuu30000, xuu31000, app(app(app(ty_@3, bab), bac), bad)) → new_lt10(xuu30000, xuu31000, bab, bac, bad)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Double) → new_ltEs11(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, app(app(ty_Either, cdb), cdc)) → new_ltEs4(xuu30000, xuu31000, cdb, cdc)
new_esEs22(xuu30000, xuu31000, ty_Ordering) → new_esEs8(xuu30000, xuu31000)
new_compare111(xuu30000, xuu31000, False) → GT
new_compare111(xuu30000, xuu31000, True) → LT
new_esEs26(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_ltEs4(Left(xuu30000), Right(xuu31000), cca, caf) → True
new_primCmpInt1(EmptyFM, xuu31, xuu34, h, ba) → new_primCmpInt(new_primPlusInt(Pos(Zero), new_mkBalBranch6Size_r(xuu31, EmptyFM, xuu34, h, ba)), Pos(Succ(Succ(Zero))))
new_esEs7(Right(xuu40000), Right(xuu3000), da, app(app(ty_@2, ea), eb)) → new_esEs5(xuu40000, xuu3000, ea, eb)
new_ltEs20(xuu3000, xuu3100, ty_Ordering) → new_ltEs12(xuu3000, xuu3100)
new_lt6(xuu300, xuu310) → new_esEs8(new_compare10(xuu300, xuu310), LT)
new_primCmpInt(Neg(Succ(xuu3000)), Neg(xuu310)) → new_primCmpNat1(xuu310, xuu3000)
new_addToFM_C14(xuu31, xuu32, xuu33, xuu34, xuu401, False, h, ba) → Branch(Nothing, new_addListToFM0(xuu31, xuu401, ba), xuu32, xuu33, xuu34)
new_mkBalBranch6MkBalBranch110(xuu300, xuu31, xuu250, xuu251, xuu252, xuu253, xuu254, xuu34, True, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), xuu250, xuu251, xuu253, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Just(xuu300), xuu31, xuu254, xuu34, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_mkBalBranch6MkBalBranch010(xuu31, xuu33, xuu340, xuu341, xuu342, Branch(xuu3430, xuu3431, xuu3432, xuu3433, xuu3434), xuu344, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), xuu3430, xuu3431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), Nothing, xuu31, xuu33, xuu3433, app(ty_Maybe, h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), xuu340, xuu341, xuu3434, xuu344, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_mkBalBranch6MkBalBranch11(xuu31, xuu330, xuu331, xuu332, xuu333, Branch(xuu3340, xuu3341, xuu3342, xuu3343, xuu3344), xuu34, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), xuu3340, xuu3341, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), xuu330, xuu331, xuu333, xuu3343, app(ty_Maybe, h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), Nothing, xuu31, xuu3344, xuu34, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_ltEs20(xuu3000, xuu3100, ty_Bool) → new_ltEs8(xuu3000, xuu3100)
new_esEs8(LT, LT) → True
new_esEs30(xuu19, xuu14, ty_Float) → new_esEs18(xuu19, xuu14)
new_primCmpInt0(Branch(xuu250, xuu251, xuu252, xuu253, xuu254), xuu300, xuu31, xuu34, h, ba) → new_primCmpInt(new_primPlusInt(xuu252, new_mkBalBranch6Size_r0(xuu300, xuu31, Branch(xuu250, xuu251, xuu252, xuu253, xuu254), xuu34, h, ba)), Pos(Succ(Succ(Zero))))
new_ltEs16(Nothing, Nothing, ed) → True
new_lt20(xuu30000, xuu31000, ty_Char) → new_lt19(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_Maybe, cbf), caf) → new_ltEs16(xuu30000, xuu31000, cbf)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Integer, bf) → new_esEs11(xuu40000, xuu3000)
new_esEs25(xuu40001, xuu3001, ty_Ordering) → new_esEs8(xuu40001, xuu3001)
new_esEs28(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_esEs20(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_compare210(Nothing, Just(xuu3100), False, dec) → LT
new_ltEs6(xuu30002, xuu31002, ty_Double) → new_ltEs11(xuu30002, xuu31002)
new_esEs24(xuu40002, xuu3002, app(app(ty_Either, bfc), bfd)) → new_esEs7(xuu40002, xuu3002, bfc, bfd)
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, ty_@0) → new_ltEs10(xuu30000, xuu31000)
new_pePe(True, xuu163) → True
new_compare0([], [], cad) → EQ
new_esEs24(xuu40002, xuu3002, ty_Int) → new_esEs16(xuu40002, xuu3002)
new_ltEs19(xuu30001, xuu31001, ty_Int) → new_ltEs13(xuu30001, xuu31001)
new_primEqNat0(Zero, Zero) → True
new_mkBalBranch6MkBalBranch30(xuu31, EmptyFM, xuu34, True, h, ba) → error([])
new_esEs29(xuu4000, xuu300, app(ty_Maybe, bbe)) → new_esEs6(xuu4000, xuu300, bbe)
new_compare210(Just(xuu3000), Just(xuu3100), False, dec) → new_compare112(xuu3000, xuu3100, new_ltEs20(xuu3000, xuu3100, dec), dec)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(ty_@2, ce), cf), bf) → new_esEs5(xuu40000, xuu3000, ce, cf)
new_esEs26(xuu40000, xuu3000, app(ty_Maybe, cac)) → new_esEs6(xuu40000, xuu3000, cac)
new_esEs14(@0, @0) → True
new_mkBalBranch6MkBalBranch5(xuu31, xuu33, xuu34, False, h, ba) → new_mkBalBranch6MkBalBranch4(xuu31, xuu33, xuu34, new_gt(new_mkBalBranch6Size_r(xuu31, xuu33, xuu34, h, ba), new_sr0(new_sIZE_RATIO, new_mkBalBranch6Size_l(xuu31, xuu33, xuu34, h, ba))), h, ba)
new_esEs30(xuu19, xuu14, ty_Double) → new_esEs15(xuu19, xuu14)
new_gt(xuu88, xuu87) → new_esEs8(new_compare10(xuu88, xuu87), GT)
new_esEs9(xuu30001, xuu31001, app(app(app(ty_@3, daa), dab), dac)) → new_esEs4(xuu30001, xuu31001, daa, dab, dac)
new_ltEs6(xuu30002, xuu31002, ty_@0) → new_ltEs10(xuu30002, xuu31002)
new_esEs9(xuu30001, xuu31001, app(ty_Maybe, dah)) → new_esEs6(xuu30001, xuu31001, dah)
new_esEs29(xuu4000, xuu300, app(ty_[], bch)) → new_esEs13(xuu4000, xuu300, bch)
new_mkBalBranch6MkBalBranch5(xuu31, xuu33, xuu34, True, h, ba) → new_mkBranch(Zero, Nothing, xuu31, xuu33, xuu34, app(ty_Maybe, h), ba)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Float, caf) → new_ltEs17(xuu30000, xuu31000)
new_esEs9(xuu30001, xuu31001, ty_@0) → new_esEs14(xuu30001, xuu31001)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Ordering, bf) → new_esEs8(xuu40000, xuu3000)
new_esEs24(xuu40002, xuu3002, app(ty_Ratio, bef)) → new_esEs17(xuu40002, xuu3002, bef)
new_compare13(xuu30000, xuu31000, ty_Integer) → new_compare9(xuu30000, xuu31000)
new_mkBalBranch6MkBalBranch4(xuu31, xuu33, xuu34, False, h, ba) → new_mkBalBranch6MkBalBranch30(xuu31, xuu33, xuu34, new_gt(new_mkBalBranch6Size_l(xuu31, xuu33, xuu34, h, ba), new_sr0(new_sIZE_RATIO, new_mkBalBranch6Size_r(xuu31, xuu33, xuu34, h, ba))), h, ba)
new_addToFM_C0(Branch(Just(xuu300), xuu31, xuu32, xuu33, xuu34), Nothing, xuu401, h, ba) → new_addToFM_C22(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Just(xuu300), False, h), LT), h, ba)
new_compare12(xuu30000, xuu31000, False, bb, bc) → GT
new_esEs30(xuu19, xuu14, ty_Char) → new_esEs19(xuu19, xuu14)
new_compare13(xuu30000, xuu31000, ty_Ordering) → new_compare18(xuu30000, xuu31000)
new_lt7(xuu30001, xuu31001, ty_Double) → new_lt14(xuu30001, xuu31001)
new_primPlusInt(Neg(xuu2520), Neg(xuu940)) → Neg(new_primPlusNat1(xuu2520, xuu940))
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, ty_Ordering) → new_ltEs12(xuu30000, xuu31000)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Int, caf) → new_ltEs13(xuu30000, xuu31000)
new_esEs26(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3100))) → new_primCmpNat0(xuu3100, Zero)
new_esEs24(xuu40002, xuu3002, ty_Char) → new_esEs19(xuu40002, xuu3002)
new_esEs8(GT, GT) → True
new_esEs30(xuu19, xuu14, app(app(app(ty_@3, ddc), ddd), dde)) → new_esEs4(xuu19, xuu14, ddc, ddd, dde)
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_[], eh)) → new_ltEs9(xuu30000, xuu31000, eh)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3100))) → new_primCmpNat1(Zero, xuu3100)
new_esEs7(Right(xuu40000), Right(xuu3000), da, app(app(ty_Either, dg), dh)) → new_esEs7(xuu40000, xuu3000, dg, dh)
new_compare13(xuu30000, xuu31000, app(ty_[], dbh)) → new_compare0(xuu30000, xuu31000, dbh)
new_lt15(xuu30000, xuu31000) → new_esEs8(new_compare18(xuu30000, xuu31000), LT)
new_esEs12(False, False) → True
new_esEs26(xuu40000, xuu3000, app(app(app(ty_@3, bhd), bhe), bhf)) → new_esEs4(xuu40000, xuu3000, bhd, bhe, bhf)
new_ltEs20(xuu3000, xuu3100, app(app(ty_@2, gf), gg)) → new_ltEs15(xuu3000, xuu3100, gf, gg)
new_esEs7(Right(xuu40000), Right(xuu3000), da, app(ty_[], dc)) → new_esEs13(xuu40000, xuu3000, dc)
new_ltEs19(xuu30001, xuu31001, app(ty_Ratio, hd)) → new_ltEs14(xuu30001, xuu31001, hd)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_lt10(xuu30000, xuu31000, gc, gd, ge) → new_esEs8(new_compare14(xuu30000, xuu31000, gc, gd, ge), LT)
new_esEs28(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs9(xuu30001, xuu31001, ty_Integer) → new_esEs11(xuu30001, xuu31001)
new_lt20(xuu30000, xuu31000, app(app(ty_Either, bbb), bbc)) → new_lt17(xuu30000, xuu31000, bbb, bbc)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_@0, caf) → new_ltEs10(xuu30000, xuu31000)
new_ltEs20(xuu3000, xuu3100, app(app(app(ty_@3, cgd), cge), cgf)) → new_ltEs5(xuu3000, xuu3100, cgd, cge, cgf)
new_lt8(xuu30000, xuu31000, ty_Double) → new_lt14(xuu30000, xuu31000)
new_ltEs16(Nothing, Just(xuu31000), ed) → True
new_primEqInt(Neg(Succ(xuu400000)), Neg(Succ(xuu30000))) → new_primEqNat0(xuu400000, xuu30000)
new_mkBalBranch6MkBalBranch50(xuu300, xuu31, xuu25, xuu34, False, h, ba) → new_mkBalBranch6MkBalBranch40(xuu300, xuu31, xuu25, xuu34, new_gt(new_mkBalBranch6Size_r0(xuu300, xuu31, xuu25, xuu34, h, ba), new_sr0(new_sIZE_RATIO, new_mkBalBranch6Size_l0(xuu300, xuu31, xuu25, xuu34, h, ba))), h, ba)
new_esEs26(xuu40000, xuu3000, app(ty_[], bhc)) → new_esEs13(xuu40000, xuu3000, bhc)
new_esEs23(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs13(:(xuu40000, xuu40001), :(xuu3000, xuu3001), bch) → new_asAs(new_esEs23(xuu40000, xuu3000, bch), new_esEs13(xuu40001, xuu3001, bch))
new_primPlusNat1(Succ(xuu25200), Zero) → Succ(xuu25200)
new_primPlusNat1(Zero, Succ(xuu9400)) → Succ(xuu9400)
new_ltEs6(xuu30002, xuu31002, ty_Char) → new_ltEs18(xuu30002, xuu31002)
new_lt8(xuu30000, xuu31000, app(ty_Maybe, bd)) → new_lt5(xuu30000, xuu31000, bd)
new_ltEs8(True, True) → True
new_esEs16(xuu4000, xuu300) → new_primEqInt(xuu4000, xuu300)
new_primCmpNat1(Zero, xuu3000) → LT
new_mkBalBranch6MkBalBranch30(xuu31, Branch(xuu330, xuu331, xuu332, xuu333, xuu334), xuu34, True, h, ba) → new_mkBalBranch6MkBalBranch11(xuu31, xuu330, xuu331, xuu332, xuu333, xuu334, xuu34, new_lt6(new_sizeFM(xuu334, h, ba), new_sr0(Pos(Succ(Succ(Zero))), new_sizeFM(xuu333, h, ba))), h, ba)
new_esEs30(xuu19, xuu14, ty_Integer) → new_esEs11(xuu19, xuu14)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_Maybe, fd)) → new_ltEs16(xuu30000, xuu31000, fd)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Char, caf) → new_ltEs18(xuu30000, xuu31000)
new_ltEs12(EQ, EQ) → True
new_compare13(xuu30000, xuu31000, ty_Float) → new_compare25(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, ty_Integer) → new_ltEs7(xuu30000, xuu31000)
new_esEs21(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_lt8(xuu30000, xuu31000, ty_Integer) → new_lt9(xuu30000, xuu31000)
new_mkBalBranch6MkBalBranch40(xuu300, xuu31, xuu25, Branch(xuu340, xuu341, xuu342, xuu343, xuu344), True, h, ba) → new_mkBalBranch6MkBalBranch01(xuu300, xuu31, xuu25, xuu340, xuu341, xuu342, xuu343, xuu344, new_lt6(new_sizeFM(xuu343, h, ba), new_sr0(Pos(Succ(Succ(Zero))), new_sizeFM(xuu344, h, ba))), h, ba)
new_esEs28(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(ty_Either, cbg), cbh), caf) → new_ltEs4(xuu30000, xuu31000, cbg, cbh)
new_primEqInt(Neg(Succ(xuu400000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu30000))) → False
new_esEs8(EQ, EQ) → True
new_addListToFM0(xuu31, xuu401, ba) → xuu401
new_mkBalBranch6MkBalBranch01(xuu300, xuu31, xuu25, xuu340, xuu341, xuu342, xuu343, xuu344, True, h, ba) → new_mkBranch(Succ(Succ(Zero)), xuu340, xuu341, new_mkBranch(Succ(Succ(Succ(Zero))), Just(xuu300), xuu31, xuu25, xuu343, app(ty_Maybe, h), ba), xuu344, app(ty_Maybe, h), ba)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_@0) → new_esEs14(xuu40000, xuu3000)
new_addToFM_C0(Branch(Nothing, xuu31, xuu32, xuu33, xuu34), Nothing, xuu401, h, ba) → new_addToFM_C14(xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Nothing, True, h), GT), h, ba)
new_mkBalBranch(xuu300, xuu31, xuu25, xuu34, h, ba) → new_mkBalBranch6MkBalBranch50(xuu300, xuu31, xuu25, xuu34, new_esEs8(new_primCmpInt0(xuu25, xuu300, xuu31, xuu34, h, ba), LT), h, ba)
new_esEs17(:%(xuu40000, xuu40001), :%(xuu3000, xuu3001), fh) → new_asAs(new_esEs21(xuu40000, xuu3000, fh), new_esEs20(xuu40001, xuu3001, fh))
new_esEs23(xuu40000, xuu3000, app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs4(xuu40000, xuu3000, bdc, bdd, bde)
new_compare24(xuu30000, xuu31000, True, bb, bc) → EQ
new_esEs5(@2(xuu40000, xuu40001), @2(xuu3000, xuu3001), cdd, cde) → new_asAs(new_esEs28(xuu40000, xuu3000, cdd), new_esEs27(xuu40001, xuu3001, cde))
new_lt20(xuu30000, xuu31000, app(ty_Maybe, bba)) → new_lt5(xuu30000, xuu31000, bba)
new_ltEs7(xuu3000, xuu3100) → new_fsEs(new_compare9(xuu3000, xuu3100))
new_ltEs13(xuu3000, xuu3100) → new_fsEs(new_compare10(xuu3000, xuu3100))
new_esEs7(Right(xuu40000), Right(xuu3000), da, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_ltEs19(xuu30001, xuu31001, app(ty_Maybe, hg)) → new_ltEs16(xuu30001, xuu31001, hg)
new_esEs26(xuu40000, xuu3000, app(app(ty_Either, bhg), bhh)) → new_esEs7(xuu40000, xuu3000, bhg, bhh)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_mkBalBranch6MkBalBranch30(xuu31, xuu33, xuu34, False, h, ba) → new_mkBranch(Succ(Zero), Nothing, xuu31, xuu33, xuu34, app(ty_Maybe, h), ba)
new_esEs9(xuu30001, xuu31001, ty_Float) → new_esEs18(xuu30001, xuu31001)
new_ltEs14(xuu3000, xuu3100, cae) → new_fsEs(new_compare8(xuu3000, xuu3100, cae))
new_primMinusNat0(Succ(xuu25200), Zero) → Pos(Succ(xuu25200))
new_compare23(xuu30000, xuu31000, False, cgb, cgc) → new_compare11(xuu30000, xuu31000, new_ltEs4(xuu30000, xuu31000, cgb, cgc), cgb, cgc)
new_sizeFM(EmptyFM, h, ba) → Pos(Zero)
new_ltEs6(xuu30002, xuu31002, app(ty_Maybe, chf)) → new_ltEs16(xuu30002, xuu31002, chf)
new_compare113(xuu30000, xuu31000, False, gc, gd, ge) → GT
new_esEs6(Nothing, Nothing, bbe) → True
new_ltEs20(xuu3000, xuu3100, app(ty_Maybe, ed)) → new_ltEs16(xuu3000, xuu3100, ed)
new_primEqInt(Pos(Succ(xuu400000)), Pos(Succ(xuu30000))) → new_primEqNat0(xuu400000, xuu30000)
new_lt20(xuu30000, xuu31000, app(ty_[], bae)) → new_lt12(xuu30000, xuu31000, bae)
new_lt5(xuu30000, xuu31000, bd) → new_esEs8(new_compare7(xuu30000, xuu31000, bd), LT)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_compare24(xuu30000, xuu31000, False, bb, bc) → new_compare12(xuu30000, xuu31000, new_ltEs15(xuu30000, xuu31000, bb, bc), bb, bc)
new_compare12(xuu30000, xuu31000, True, bb, bc) → LT
new_esEs30(xuu19, xuu14, ty_Int) → new_esEs16(xuu19, xuu14)
new_compare8(:%(xuu30000, xuu30001), :%(xuu31000, xuu31001), ty_Int) → new_compare10(new_sr0(xuu30000, xuu31001), new_sr0(xuu31000, xuu30001))
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_Ratio, bbf)) → new_esEs17(xuu40000, xuu3000, bbf)
new_esEs7(Right(xuu40000), Right(xuu3000), da, app(app(app(ty_@3, dd), de), df)) → new_esEs4(xuu40000, xuu3000, dd, de, df)
new_esEs6(Nothing, Just(xuu3000), bbe) → False
new_esEs6(Just(xuu40000), Nothing, bbe) → False
new_primEqNat0(Succ(xuu400000), Succ(xuu30000)) → new_primEqNat0(xuu400000, xuu30000)
new_esEs27(xuu40001, xuu3001, ty_Ordering) → new_esEs8(xuu40001, xuu3001)
new_esEs23(xuu40000, xuu3000, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_lt13(xuu30000, xuu31000) → new_esEs8(new_compare16(xuu30000, xuu31000), LT)
new_lt8(xuu30000, xuu31000, ty_Bool) → new_lt11(xuu30000, xuu31000)
new_esEs10(xuu30000, xuu31000, ty_Double) → new_esEs15(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, ty_Bool) → new_esEs12(xuu30000, xuu31000)
new_lt14(xuu30000, xuu31000) → new_esEs8(new_compare17(xuu30000, xuu31000), LT)
new_lt7(xuu30001, xuu31001, ty_Float) → new_lt18(xuu30001, xuu31001)
new_primCompAux00(xuu180, LT) → LT
new_lt11(xuu30000, xuu31000) → new_esEs8(new_compare15(xuu30000, xuu31000), LT)
new_esEs24(xuu40002, xuu3002, ty_Ordering) → new_esEs8(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, app(ty_Ratio, chc)) → new_ltEs14(xuu30002, xuu31002, chc)
new_esEs23(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_addListToFM_CAdd(xuu3, @2(xuu400, xuu401), h, ba) → new_addToFM_C0(xuu3, xuu400, xuu401, h, ba)
new_ltEs19(xuu30001, xuu31001, ty_Bool) → new_ltEs8(xuu30001, xuu31001)
new_esEs28(xuu40000, xuu3000, ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Int, bf) → new_esEs16(xuu40000, xuu3000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Float) → new_ltEs17(xuu30000, xuu31000)
new_primEqInt(Pos(Succ(xuu400000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu30000))) → False
new_esEs10(xuu30000, xuu31000, app(app(ty_Either, cgb), cgc)) → new_esEs7(xuu30000, xuu31000, cgb, cgc)
new_compare14(xuu30000, xuu31000, gc, gd, ge) → new_compare28(xuu30000, xuu31000, new_esEs4(xuu30000, xuu31000, gc, gd, ge), gc, gd, ge)
new_addToFM_C23(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, True, h, ba) → new_mkBalBranch0(xuu31, new_addToFM_C0(xuu33, Just(xuu4000), xuu401, h, ba), xuu34, h, ba)
new_ltEs19(xuu30001, xuu31001, ty_Float) → new_ltEs17(xuu30001, xuu31001)
new_lt20(xuu30000, xuu31000, app(app(ty_@2, bag), bah)) → new_lt4(xuu30000, xuu31000, bag, bah)
new_esEs23(xuu40000, xuu3000, app(app(ty_@2, bdh), bea)) → new_esEs5(xuu40000, xuu3000, bdh, bea)
new_esEs29(xuu4000, xuu300, app(app(app(ty_@3, bec), bed), bee)) → new_esEs4(xuu4000, xuu300, bec, bed, bee)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3100))) → LT
new_compare11(xuu30000, xuu31000, True, cgb, cgc) → LT
new_esEs9(xuu30001, xuu31001, app(ty_[], dad)) → new_esEs13(xuu30001, xuu31001, dad)
new_primPlusNat1(Succ(xuu25200), Succ(xuu9400)) → Succ(Succ(new_primPlusNat1(xuu25200, xuu9400)))
new_ltEs6(xuu30002, xuu31002, ty_Ordering) → new_ltEs12(xuu30002, xuu31002)
new_primEqInt(Pos(Succ(xuu400000)), Neg(xuu3000)) → False
new_primEqInt(Neg(Succ(xuu400000)), Pos(xuu3000)) → False
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_Ratio, be), bf) → new_esEs17(xuu40000, xuu3000, be)
new_addToFM_C15(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, False, h, ba) → Branch(Just(xuu4000), new_addListToFM0(xuu31, xuu401, ba), xuu32, xuu33, xuu34)
new_esEs29(xuu4000, xuu300, ty_Char) → new_esEs19(xuu4000, xuu300)
new_compare210(xuu300, xuu310, True, dec) → EQ
new_ltEs12(GT, EQ) → False
new_mkBalBranch6MkBalBranch3(xuu300, xuu31, EmptyFM, xuu34, True, h, ba) → error([])
new_primPlusInt(Pos(xuu2520), Neg(xuu940)) → new_primMinusNat0(xuu2520, xuu940)
new_primPlusInt(Neg(xuu2520), Pos(xuu940)) → new_primMinusNat0(xuu940, xuu2520)
new_esEs29(xuu4000, xuu300, app(app(ty_@2, cdd), cde)) → new_esEs5(xuu4000, xuu300, cdd, cde)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_[], cbb), caf) → new_ltEs9(xuu30000, xuu31000, cbb)
new_esEs24(xuu40002, xuu3002, app(ty_[], beg)) → new_esEs13(xuu40002, xuu3002, beg)
new_esEs29(xuu4000, xuu300, ty_@0) → new_esEs14(xuu4000, xuu300)
new_mkBalBranch6MkBalBranch4(xuu31, xuu33, Branch(xuu340, xuu341, xuu342, xuu343, xuu344), True, h, ba) → new_mkBalBranch6MkBalBranch010(xuu31, xuu33, xuu340, xuu341, xuu342, xuu343, xuu344, new_lt6(new_sizeFM(xuu343, h, ba), new_sr0(Pos(Succ(Succ(Zero))), new_sizeFM(xuu344, h, ba))), h, ba)
new_lt19(xuu30000, xuu31000) → new_esEs8(new_compare26(xuu30000, xuu31000), LT)
new_primCmpNat2(Zero, Succ(xuu31000)) → LT
new_esEs28(xuu40000, xuu3000, app(ty_Maybe, cga)) → new_esEs6(xuu40000, xuu3000, cga)
new_esEs29(xuu4000, xuu300, ty_Integer) → new_esEs11(xuu4000, xuu300)
new_primEqInt(Pos(Zero), Neg(Succ(xuu30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu30000))) → False
new_esEs30(xuu19, xuu14, app(ty_Ratio, dda)) → new_esEs17(xuu19, xuu14, dda)
new_primCompAux00(xuu180, EQ) → xuu180
new_esEs28(xuu40000, xuu3000, app(app(ty_Either, cfe), cff)) → new_esEs7(xuu40000, xuu3000, cfe, cff)
new_esEs10(xuu30000, xuu31000, ty_Int) → new_esEs16(xuu30000, xuu31000)
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, app(app(ty_@2, ccg), cch)) → new_ltEs15(xuu30000, xuu31000, ccg, cch)
new_esEs25(xuu40001, xuu3001, ty_@0) → new_esEs14(xuu40001, xuu3001)
new_compare18(xuu30000, xuu31000) → new_compare27(xuu30000, xuu31000, new_esEs8(xuu30000, xuu31000))
new_mkBalBranch6MkBalBranch110(xuu300, xuu31, xuu250, xuu251, xuu252, xuu253, Branch(xuu2540, xuu2541, xuu2542, xuu2543, xuu2544), xuu34, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), xuu2540, xuu2541, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), xuu250, xuu251, xuu253, xuu2543, app(ty_Maybe, h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), Just(xuu300), xuu31, xuu2544, xuu34, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_compare13(xuu30000, xuu31000, app(app(ty_@2, dcb), dcc)) → new_compare6(xuu30000, xuu31000, dcb, dcc)
new_ltEs20(xuu3000, xuu3100, ty_Int) → new_ltEs13(xuu3000, xuu3100)
new_esEs10(xuu30000, xuu31000, ty_Char) → new_esEs19(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), da, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs30(xuu19, xuu14, ty_Bool) → new_esEs12(xuu19, xuu14)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_addToFM_C0(Branch(Just(xuu300), xuu31, xuu32, xuu33, xuu34), Just(xuu4000), xuu401, h, ba) → new_addToFM_C24(xuu300, xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, new_esEs8(new_compare210(Just(xuu4000), Just(xuu300), new_esEs29(xuu4000, xuu300, h), h), LT), h, ba)
new_emptyFM(h, ba) → EmptyFM
new_lt8(xuu30000, xuu31000, app(app(app(ty_@3, gc), gd), ge)) → new_lt10(xuu30000, xuu31000, gc, gd, ge)
new_compare28(xuu30000, xuu31000, False, gc, gd, ge) → new_compare113(xuu30000, xuu31000, new_ltEs5(xuu30000, xuu31000, gc, gd, ge), gc, gd, ge)
new_esEs26(xuu40000, xuu3000, app(app(ty_@2, caa), cab)) → new_esEs5(xuu40000, xuu3000, caa, cab)
new_esEs7(Left(xuu40000), Left(xuu3000), app(app(app(ty_@3, bh), ca), cb), bf) → new_esEs4(xuu40000, xuu3000, bh, ca, cb)
new_ltEs16(Just(xuu30000), Nothing, ed) → False
new_esEs22(xuu30000, xuu31000, ty_Float) → new_esEs18(xuu30000, xuu31000)
new_esEs9(xuu30001, xuu31001, ty_Ordering) → new_esEs8(xuu30001, xuu31001)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs4(Right(xuu30000), Left(xuu31000), cca, caf) → False
new_esEs7(Right(xuu40000), Right(xuu3000), da, ty_Integer) → new_esEs11(xuu40000, xuu3000)
new_mkBalBranch6Size_r(xuu31, xuu33, xuu34, h, ba) → new_sizeFM(xuu34, h, ba)
new_esEs30(xuu19, xuu14, ty_@0) → new_esEs14(xuu19, xuu14)
new_esEs10(xuu30000, xuu31000, ty_@0) → new_esEs14(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_Maybe, cg), bf) → new_esEs6(xuu40000, xuu3000, cg)
new_esEs23(xuu40000, xuu3000, ty_Float) → new_esEs18(xuu40000, xuu3000)
new_lt8(xuu30000, xuu31000, app(app(ty_@2, bb), bc)) → new_lt4(xuu30000, xuu31000, bb, bc)
new_esEs7(Right(xuu40000), Right(xuu3000), da, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_addToFM_C0(Branch(Nothing, xuu31, xuu32, xuu33, xuu34), Just(xuu4000), xuu401, h, ba) → new_addToFM_C23(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, new_esEs8(new_compare210(Just(xuu4000), Nothing, False, h), LT), h, ba)
new_esEs9(xuu30001, xuu31001, ty_Int) → new_esEs16(xuu30001, xuu31001)
new_addToFM_C22(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, False, h, ba) → new_addToFM_C13(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, new_esEs8(new_compare210(Nothing, Just(xuu300), False, h), GT), h, ba)
new_esEs25(xuu40001, xuu3001, ty_Float) → new_esEs18(xuu40001, xuu3001)
new_esEs25(xuu40001, xuu3001, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs4(xuu40001, xuu3001, bgb, bgc, bgd)
new_esEs27(xuu40001, xuu3001, ty_@0) → new_esEs14(xuu40001, xuu3001)
new_mkBalBranch6MkBalBranch40(xuu300, xuu31, xuu25, EmptyFM, True, h, ba) → error([])
new_esEs28(xuu40000, xuu3000, app(app(ty_@2, cfg), cfh)) → new_esEs5(xuu40000, xuu3000, cfg, cfh)
new_esEs22(xuu30000, xuu31000, ty_Integer) → new_esEs11(xuu30000, xuu31000)
new_compare0(:(xuu30000, xuu30001), [], cad) → GT
new_mkBalBranch6MkBalBranch010(xuu31, xuu33, xuu340, xuu341, xuu342, xuu343, xuu344, True, h, ba) → new_mkBranch(Succ(Succ(Zero)), xuu340, xuu341, new_mkBranch(Succ(Succ(Succ(Zero))), Nothing, xuu31, xuu33, xuu343, app(ty_Maybe, h), ba), xuu344, app(ty_Maybe, h), ba)
new_lt8(xuu30000, xuu31000, ty_Ordering) → new_lt15(xuu30000, xuu31000)
new_addToFM_C23(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, False, h, ba) → new_addToFM_C15(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, new_esEs8(new_compare210(Just(xuu4000), Nothing, False, h), GT), h, ba)
new_lt20(xuu30000, xuu31000, ty_Int) → new_lt6(xuu30000, xuu31000)
new_esEs22(xuu30000, xuu31000, app(app(app(ty_@3, bab), bac), bad)) → new_esEs4(xuu30000, xuu31000, bab, bac, bad)
new_esEs22(xuu30000, xuu31000, app(ty_[], bae)) → new_esEs13(xuu30000, xuu31000, bae)
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, app(ty_Maybe, cda)) → new_ltEs16(xuu30000, xuu31000, cda)
new_lt7(xuu30001, xuu31001, ty_@0) → new_lt13(xuu30001, xuu31001)
new_lt8(xuu30000, xuu31000, ty_Int) → new_lt6(xuu30000, xuu31000)
new_compare11(xuu30000, xuu31000, False, cgb, cgc) → GT
new_esEs25(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_lt7(xuu30001, xuu31001, ty_Int) → new_lt6(xuu30001, xuu31001)
new_primCmpInt(Pos(Succ(xuu3000)), Neg(xuu310)) → GT
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, ty_Bool) → new_ltEs8(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, ty_Float) → new_esEs18(xuu40002, xuu3002)
new_esEs24(xuu40002, xuu3002, ty_Double) → new_esEs15(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, ty_Integer) → new_ltEs7(xuu30002, xuu31002)
new_primMulInt(Pos(xuu400000), Pos(xuu30000)) → Pos(new_primMulNat0(xuu400000, xuu30000))
new_esEs30(xuu19, xuu14, app(app(ty_@2, ddh), dea)) → new_esEs5(xuu19, xuu14, ddh, dea)
new_mkBalBranch6MkBalBranch40(xuu300, xuu31, xuu25, xuu34, False, h, ba) → new_mkBalBranch6MkBalBranch3(xuu300, xuu31, xuu25, xuu34, new_gt(new_mkBalBranch6Size_l0(xuu300, xuu31, xuu25, xuu34, h, ba), new_sr0(new_sIZE_RATIO, new_mkBalBranch6Size_r0(xuu300, xuu31, xuu25, xuu34, h, ba))), h, ba)
new_esEs24(xuu40002, xuu3002, ty_Integer) → new_esEs11(xuu40002, xuu3002)
new_ltEs6(xuu30002, xuu31002, app(app(ty_Either, chg), chh)) → new_ltEs4(xuu30002, xuu31002, chg, chh)
new_esEs27(xuu40001, xuu3001, ty_Double) → new_esEs15(xuu40001, xuu3001)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_@0, bf) → new_esEs14(xuu40000, xuu3000)
new_primMulInt(Neg(xuu400000), Neg(xuu30000)) → Pos(new_primMulNat0(xuu400000, xuu30000))
new_primCmpNat2(Zero, Zero) → EQ
new_compare110(xuu30000, xuu31000, True) → LT
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(ty_Either, ff), fg)) → new_ltEs4(xuu30000, xuu31000, ff, fg)
new_ltEs12(EQ, GT) → True
new_compare13(xuu30000, xuu31000, ty_@0) → new_compare16(xuu30000, xuu31000)
new_ltEs20(xuu3000, xuu3100, ty_Float) → new_ltEs17(xuu3000, xuu3100)
new_ltEs8(False, False) → True
new_esEs29(xuu4000, xuu300, app(ty_Ratio, fh)) → new_esEs17(xuu4000, xuu300, fh)
new_primEqNat0(Succ(xuu400000), Zero) → False
new_primEqNat0(Zero, Succ(xuu30000)) → False
new_esEs25(xuu40001, xuu3001, app(ty_Ratio, bfh)) → new_esEs17(xuu40001, xuu3001, bfh)
new_esEs25(xuu40001, xuu3001, app(ty_Maybe, bha)) → new_esEs6(xuu40001, xuu3001, bha)
new_compare110(xuu30000, xuu31000, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt9(xuu30000, xuu31000) → new_esEs8(new_compare9(xuu30000, xuu31000), LT)
new_compare113(xuu30000, xuu31000, True, gc, gd, ge) → LT
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Float) → new_esEs18(xuu40000, xuu3000)
new_primPlusNat0(xuu104, xuu300000) → new_primPlusNat1(xuu104, Succ(xuu300000))
new_esEs10(xuu30000, xuu31000, app(ty_[], dbc)) → new_esEs13(xuu30000, xuu31000, dbc)
new_primCmpInt(Pos(Succ(xuu3000)), Pos(xuu310)) → new_primCmpNat0(xuu3000, xuu310)
new_primCmpNat2(Succ(xuu30000), Succ(xuu31000)) → new_primCmpNat2(xuu30000, xuu31000)
new_lt7(xuu30001, xuu31001, app(app(ty_@2, daf), dag)) → new_lt4(xuu30001, xuu31001, daf, dag)
new_compare13(xuu30000, xuu31000, ty_Char) → new_compare26(xuu30000, xuu31000)
new_esEs27(xuu40001, xuu3001, app(app(ty_@2, cee), cef)) → new_esEs5(xuu40001, xuu3001, cee, cef)
new_compare28(xuu30000, xuu31000, True, gc, gd, ge) → EQ
new_primCmpNat0(xuu3000, Zero) → GT
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Double) → new_esEs15(xuu40000, xuu3000)
new_compare13(xuu30000, xuu31000, app(ty_Ratio, dca)) → new_compare8(xuu30000, xuu31000, dca)
new_esEs10(xuu30000, xuu31000, ty_Integer) → new_esEs11(xuu30000, xuu31000)
new_lt20(xuu30000, xuu31000, ty_Float) → new_lt18(xuu30000, xuu31000)
new_sizeFM(Branch(xuu340, xuu341, xuu342, xuu343, xuu344), h, ba) → xuu342
new_sizeFM0(EmptyFM, ga, gb) → Pos(Zero)
new_primCmpInt0(EmptyFM, xuu300, xuu31, xuu34, h, ba) → new_primCmpInt(new_primPlusInt(Pos(Zero), new_mkBalBranch6Size_r0(xuu300, xuu31, EmptyFM, xuu34, h, ba)), Pos(Succ(Succ(Zero))))
new_esEs10(xuu30000, xuu31000, app(app(ty_@2, bb), bc)) → new_esEs5(xuu30000, xuu31000, bb, bc)
new_esEs26(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare25(Float(xuu30000, xuu30001), Float(xuu31000, xuu31001)) → new_compare10(new_sr0(xuu30000, xuu31000), new_sr0(xuu30001, xuu31001))
new_esEs28(xuu40000, xuu3000, app(ty_Ratio, ceh)) → new_esEs17(xuu40000, xuu3000, ceh)
new_addToFM_C24(xuu14, xuu15, xuu16, xuu17, xuu18, xuu19, xuu20, False, dcg, dch) → new_addToFM_C16(xuu14, xuu15, xuu16, xuu17, xuu18, xuu19, xuu20, new_esEs8(new_compare210(Just(xuu19), Just(xuu14), new_esEs30(xuu19, xuu14, dcg), dcg), GT), dcg, dch)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_esEs23(xuu40000, xuu3000, app(ty_Ratio, bda)) → new_esEs17(xuu40000, xuu3000, bda)
new_esEs9(xuu30001, xuu31001, app(ty_Ratio, dae)) → new_esEs17(xuu30001, xuu31001, dae)
new_compare23(xuu30000, xuu31000, True, cgb, cgc) → EQ
new_esEs25(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3100))) → GT
new_lt7(xuu30001, xuu31001, ty_Ordering) → new_lt15(xuu30001, xuu31001)
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, app(ty_[], cce)) → new_ltEs9(xuu30000, xuu31000, cce)
new_sr0(xuu40000, xuu3000) → new_primMulInt(xuu40000, xuu3000)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_esEs26(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs4(xuu40000, xuu3000, bbh, bca, bcb)
new_lt8(xuu30000, xuu31000, app(app(ty_Either, cgb), cgc)) → new_lt17(xuu30000, xuu31000, cgb, cgc)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Integer, caf) → new_ltEs7(xuu30000, xuu31000)
new_compare13(xuu30000, xuu31000, ty_Bool) → new_compare15(xuu30000, xuu31000)
new_esEs19(Char(xuu40000), Char(xuu3000)) → new_primEqNat0(xuu40000, xuu3000)
new_ltEs16(Just(xuu30000), Just(xuu31000), app(ty_Ratio, fa)) → new_ltEs14(xuu30000, xuu31000, fa)
new_esEs22(xuu30000, xuu31000, ty_Char) → new_esEs19(xuu30000, xuu31000)
new_esEs23(xuu40000, xuu3000, ty_@0) → new_esEs14(xuu40000, xuu3000)
new_primPlusInt(Pos(xuu2520), Pos(xuu940)) → Pos(new_primPlusNat1(xuu2520, xuu940))
new_esEs9(xuu30001, xuu31001, app(app(ty_@2, daf), dag)) → new_esEs5(xuu30001, xuu31001, daf, dag)
new_ltEs17(xuu3000, xuu3100) → new_fsEs(new_compare25(xuu3000, xuu3100))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs25(xuu40001, xuu3001, ty_Bool) → new_esEs12(xuu40001, xuu3001)
new_mkBalBranch6Size_l0(xuu300, xuu31, xuu25, xuu34, h, ba) → new_sizeFM(xuu25, h, ba)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Char) → new_ltEs18(xuu30000, xuu31000)
new_primCmpInt1(Branch(xuu330, xuu331, xuu332, xuu333, xuu334), xuu31, xuu34, h, ba) → new_primCmpInt(new_primPlusInt(xuu332, new_mkBalBranch6Size_r(xuu31, Branch(xuu330, xuu331, xuu332, xuu333, xuu334), xuu34, h, ba)), Pos(Succ(Succ(Zero))))
new_lt20(xuu30000, xuu31000, ty_@0) → new_lt13(xuu30000, xuu31000)
new_esEs27(xuu40001, xuu3001, ty_Float) → new_esEs18(xuu40001, xuu3001)
new_addToFM_C15(xuu31, xuu32, xuu33, xuu34, xuu4000, xuu401, True, h, ba) → new_mkBalBranch0(xuu31, xuu33, new_addToFM_C0(xuu34, Just(xuu4000), xuu401, h, ba), h, ba)
new_compare9(Integer(xuu30000), Integer(xuu31000)) → new_primCmpInt(xuu30000, xuu31000)
new_mkBalBranch6MkBalBranch50(xuu300, xuu31, xuu25, xuu34, True, h, ba) → new_mkBranch(Zero, Just(xuu300), xuu31, xuu25, xuu34, app(ty_Maybe, h), ba)
new_asAs(False, xuu137) → False
new_esEs29(xuu4000, xuu300, ty_Bool) → new_esEs12(xuu4000, xuu300)
new_primMulInt(Pos(xuu400000), Neg(xuu30000)) → Neg(new_primMulNat0(xuu400000, xuu30000))
new_primMulInt(Neg(xuu400000), Pos(xuu30000)) → Neg(new_primMulNat0(xuu400000, xuu30000))
new_mkBalBranch6MkBalBranch01(xuu300, xuu31, xuu25, xuu340, xuu341, xuu342, Branch(xuu3430, xuu3431, xuu3432, xuu3433, xuu3434), xuu344, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), xuu3430, xuu3431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), Just(xuu300), xuu31, xuu25, xuu3433, app(ty_Maybe, h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), xuu340, xuu341, xuu3434, xuu344, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_esEs13(:(xuu40000, xuu40001), [], bch) → False
new_esEs13([], :(xuu3000, xuu3001), bch) → False
new_primMulNat0(Succ(xuu4000000), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu300000)) → Zero
new_lt7(xuu30001, xuu31001, app(app(ty_Either, dba), dbb)) → new_lt17(xuu30001, xuu31001, dba, dbb)
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_Maybe, bcg)) → new_esEs6(xuu40000, xuu3000, bcg)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(ty_Ratio, cbc), caf) → new_ltEs14(xuu30000, xuu31000, cbc)
new_compare26(Char(xuu30000), Char(xuu31000)) → new_primCmpNat2(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Double, bf) → new_esEs15(xuu40000, xuu3000)
new_ltEs20(xuu3000, xuu3100, ty_Integer) → new_ltEs7(xuu3000, xuu3100)
new_esEs7(Left(xuu40000), Left(xuu3000), app(ty_[], bg), bf) → new_esEs13(xuu40000, xuu3000, bg)
new_esEs21(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_ltEs12(GT, GT) → True
new_ltEs20(xuu3000, xuu3100, ty_Double) → new_ltEs11(xuu3000, xuu3100)
new_esEs9(xuu30001, xuu31001, ty_Bool) → new_esEs12(xuu30001, xuu31001)
new_esEs10(xuu30000, xuu31000, app(ty_Maybe, bd)) → new_esEs6(xuu30000, xuu31000, bd)
new_ltEs19(xuu30001, xuu31001, ty_@0) → new_ltEs10(xuu30001, xuu31001)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Ordering, caf) → new_ltEs12(xuu30000, xuu31000)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Float, bf) → new_esEs18(xuu40000, xuu3000)
new_primCmpNat1(Succ(xuu3100), xuu3000) → new_primCmpNat2(xuu3100, xuu3000)
new_esEs23(xuu40000, xuu3000, app(ty_Maybe, beb)) → new_esEs6(xuu40000, xuu3000, beb)
new_primCmpNat2(Succ(xuu30000), Zero) → GT
new_lt7(xuu30001, xuu31001, app(ty_Ratio, dae)) → new_lt16(xuu30001, xuu31001, dae)
new_compare210(Just(xuu3000), Nothing, False, dec) → GT
new_lt7(xuu30001, xuu31001, app(ty_Maybe, dah)) → new_lt5(xuu30001, xuu31001, dah)
new_lt8(xuu30000, xuu31000, ty_Float) → new_lt18(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, ty_Bool) → new_esEs12(xuu40002, xuu3002)
new_mkBalBranch6MkBalBranch01(xuu300, xuu31, xuu25, xuu340, xuu341, xuu342, EmptyFM, xuu344, False, h, ba) → error([])
new_esEs25(xuu40001, xuu3001, app(ty_[], bga)) → new_esEs13(xuu40001, xuu3001, bga)
new_esEs23(xuu40000, xuu3000, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare27(xuu30000, xuu31000, True) → EQ
new_esEs10(xuu30000, xuu31000, ty_Float) → new_esEs18(xuu30000, xuu31000)
new_ltEs6(xuu30002, xuu31002, ty_Bool) → new_ltEs8(xuu30002, xuu31002)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Bool) → new_ltEs8(xuu30000, xuu31000)
new_compare17(Double(xuu30000, xuu30001), Double(xuu31000, xuu31001)) → new_compare10(new_sr0(xuu30000, xuu31000), new_sr0(xuu30001, xuu31001))
new_esEs28(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs12(False, True) → False
new_esEs12(True, False) → False
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, ty_Int) → new_ltEs13(xuu30000, xuu31000)
new_mkBalBranch6MkBalBranch010(xuu31, xuu33, xuu340, xuu341, xuu342, EmptyFM, xuu344, False, h, ba) → error([])
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Bool, bf) → new_esEs12(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, ty_Int) → new_esEs16(xuu40001, xuu3001)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Char) → new_esEs19(xuu40000, xuu3000)
new_primMinusNat0(Zero, Succ(xuu9400)) → Neg(Succ(xuu9400))
new_esEs27(xuu40001, xuu3001, ty_Bool) → new_esEs12(xuu40001, xuu3001)
new_ltEs9(xuu3000, xuu3100, cad) → new_fsEs(new_compare0(xuu3000, xuu3100, cad))
new_esEs29(xuu4000, xuu300, ty_Double) → new_esEs15(xuu4000, xuu300)
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, ty_Float) → new_ltEs17(xuu30000, xuu31000)
new_lt8(xuu30000, xuu31000, ty_Char) → new_lt19(xuu30000, xuu31000)
new_ltEs19(xuu30001, xuu31001, app(app(app(ty_@3, gh), ha), hb)) → new_ltEs5(xuu30001, xuu31001, gh, ha, hb)
new_compare13(xuu30000, xuu31000, ty_Double) → new_compare17(xuu30000, xuu31000)
new_esEs7(Right(xuu40000), Right(xuu3000), da, ty_Int) → new_esEs16(xuu40000, xuu3000)
new_ltEs18(xuu3000, xuu3100) → new_fsEs(new_compare26(xuu3000, xuu3100))
new_compare10(xuu30, xuu31) → new_primCmpInt(xuu30, xuu31)
new_esEs10(xuu30000, xuu31000, app(ty_Ratio, dbd)) → new_esEs17(xuu30000, xuu31000, dbd)
new_lt7(xuu30001, xuu31001, app(app(app(ty_@3, daa), dab), dac)) → new_lt10(xuu30001, xuu31001, daa, dab, dac)
new_ltEs12(EQ, LT) → False
new_esEs25(xuu40001, xuu3001, app(app(ty_@2, bgg), bgh)) → new_esEs5(xuu40001, xuu3001, bgg, bgh)
new_esEs6(Just(xuu40000), Just(xuu3000), app(ty_[], bbg)) → new_esEs13(xuu40000, xuu3000, bbg)
new_lt8(xuu30000, xuu31000, ty_@0) → new_lt13(xuu30000, xuu31000)
new_ltEs19(xuu30001, xuu31001, app(app(ty_@2, he), hf)) → new_ltEs15(xuu30001, xuu31001, he, hf)
new_compare13(xuu30000, xuu31000, app(app(ty_Either, dce), dcf)) → new_compare19(xuu30000, xuu31000, dce, dcf)
new_lt7(xuu30001, xuu31001, app(ty_[], dad)) → new_lt12(xuu30001, xuu31001, dad)
new_esEs22(xuu30000, xuu31000, ty_@0) → new_esEs14(xuu30000, xuu31000)
new_esEs23(xuu40000, xuu3000, ty_Char) → new_esEs19(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Ordering) → new_esEs8(xuu40000, xuu3000)
new_esEs29(xuu4000, xuu300, app(app(ty_Either, da), bf)) → new_esEs7(xuu4000, xuu300, da, bf)
new_compare112(xuu130, xuu131, False, bbd) → GT
new_compare29(xuu30000, xuu31000, False) → new_compare111(xuu30000, xuu31000, new_ltEs8(xuu30000, xuu31000))
new_esEs22(xuu30000, xuu31000, app(ty_Ratio, baf)) → new_esEs17(xuu30000, xuu31000, baf)
new_ltEs19(xuu30001, xuu31001, ty_Integer) → new_ltEs7(xuu30001, xuu31001)
new_esEs30(xuu19, xuu14, ty_Ordering) → new_esEs8(xuu19, xuu14)
new_addToFM_C24(xuu14, xuu15, xuu16, xuu17, xuu18, xuu19, xuu20, True, dcg, dch) → new_mkBalBranch(xuu14, xuu15, new_addToFM_C0(xuu17, Just(xuu19), xuu20, dcg, dch), xuu18, dcg, dch)
new_addToFM_C13(xuu300, xuu31, xuu32, xuu33, xuu34, xuu401, False, h, ba) → Branch(Nothing, new_addListToFM0(xuu31, xuu401, ba), xuu32, xuu33, xuu34)
new_esEs10(xuu30000, xuu31000, ty_Ordering) → new_esEs8(xuu30000, xuu31000)
new_lt4(xuu30000, xuu31000, bb, bc) → new_esEs8(new_compare6(xuu30000, xuu31000, bb, bc), LT)
new_lt7(xuu30001, xuu31001, ty_Char) → new_lt19(xuu30001, xuu31001)
new_compare0([], :(xuu31000, xuu31001), cad) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs9(xuu30001, xuu31001, ty_Char) → new_esEs19(xuu30001, xuu31001)
new_primCompAux0(xuu30000, xuu31000, xuu174, cad) → new_primCompAux00(xuu174, new_compare13(xuu30000, xuu31000, cad))
new_addToFM_C0(EmptyFM, xuu400, xuu401, h, ba) → Branch(xuu400, xuu401, Pos(Succ(Zero)), new_emptyFM(h, ba), new_emptyFM(h, ba))
new_esEs9(xuu30001, xuu31001, ty_Double) → new_esEs15(xuu30001, xuu31001)
new_asAs(True, xuu137) → xuu137
new_addToFM_C14(xuu31, xuu32, xuu33, xuu34, xuu401, True, h, ba) → new_mkBalBranch0(xuu31, xuu33, new_addToFM_C0(xuu34, Nothing, xuu401, h, ba), h, ba)
new_primMulNat0(Succ(xuu4000000), Succ(xuu300000)) → new_primPlusNat0(new_primMulNat0(xuu4000000, Succ(xuu300000)), xuu300000)
new_esEs27(xuu40001, xuu3001, app(ty_[], cdg)) → new_esEs13(xuu40001, xuu3001, cdg)
new_esEs27(xuu40001, xuu3001, ty_Integer) → new_esEs11(xuu40001, xuu3001)
new_mkBalBranch6MkBalBranch110(xuu300, xuu31, xuu250, xuu251, xuu252, xuu253, EmptyFM, xuu34, False, h, ba) → error([])
new_esEs26(xuu40000, xuu3000, ty_Double) → new_esEs15(xuu40000, xuu3000)
new_esEs6(Just(xuu40000), Just(xuu3000), app(app(ty_Either, bcc), bcd)) → new_esEs7(xuu40000, xuu3000, bcc, bcd)
new_ltEs6(xuu30002, xuu31002, ty_Int) → new_ltEs13(xuu30002, xuu31002)
new_mkBalBranch6MkBalBranch3(xuu300, xuu31, Branch(xuu250, xuu251, xuu252, xuu253, xuu254), xuu34, True, h, ba) → new_mkBalBranch6MkBalBranch110(xuu300, xuu31, xuu250, xuu251, xuu252, xuu253, xuu254, xuu34, new_lt6(new_sizeFM(xuu254, h, ba), new_sr0(Pos(Succ(Succ(Zero))), new_sizeFM(xuu253, h, ba))), h, ba)
new_esEs9(xuu30001, xuu31001, app(app(ty_Either, dba), dbb)) → new_esEs7(xuu30001, xuu31001, dba, dbb)
new_ltEs16(Just(xuu30000), Just(xuu31000), ty_Int) → new_ltEs13(xuu30000, xuu31000)
new_lt17(xuu30000, xuu31000, cgb, cgc) → new_esEs8(new_compare19(xuu30000, xuu31000, cgb, cgc), LT)
new_fsEs(xuu147) → new_not(new_esEs8(xuu147, GT))
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Int) → new_esEs16(xuu40000, xuu3000)
new_compare27(xuu30000, xuu31000, False) → new_compare110(xuu30000, xuu31000, new_ltEs12(xuu30000, xuu31000))
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(ty_@2, fb), fc)) → new_ltEs15(xuu30000, xuu31000, fb, fc)
new_ltEs6(xuu30002, xuu31002, ty_Float) → new_ltEs17(xuu30002, xuu31002)
new_ltEs6(xuu30002, xuu31002, app(ty_[], chb)) → new_ltEs9(xuu30002, xuu31002, chb)
new_ltEs4(Left(xuu30000), Left(xuu31000), ty_Bool, caf) → new_ltEs8(xuu30000, xuu31000)
new_esEs24(xuu40002, xuu3002, app(ty_Maybe, bfg)) → new_esEs6(xuu40002, xuu3002, bfg)
new_esEs7(Left(xuu40000), Left(xuu3000), ty_Char, bf) → new_esEs19(xuu40000, xuu3000)
new_esEs27(xuu40001, xuu3001, app(ty_Ratio, cdf)) → new_esEs17(xuu40001, xuu3001, cdf)
new_compare7(xuu30000, xuu31000, bd) → new_compare210(xuu30000, xuu31000, new_esEs6(xuu30000, xuu31000, bd), bd)
new_esEs24(xuu40002, xuu3002, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs4(xuu40002, xuu3002, beh, bfa, bfb)
new_mkBalBranch6MkBalBranch4(xuu31, xuu33, EmptyFM, True, h, ba) → error([])
new_esEs6(Just(xuu40000), Just(xuu3000), ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_primCompAux00(xuu180, GT) → GT
new_esEs25(xuu40001, xuu3001, app(app(ty_Either, bge), bgf)) → new_esEs7(xuu40001, xuu3001, bge, bgf)
new_esEs18(Float(xuu40000, xuu40001), Float(xuu3000, xuu3001)) → new_esEs16(new_sr0(xuu40000, xuu3000), new_sr0(xuu40001, xuu3001))
new_ltEs12(GT, LT) → False
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, app(ty_Ratio, ccf)) → new_ltEs14(xuu30000, xuu31000, ccf)
new_ltEs4(Left(xuu30000), Left(xuu31000), app(app(app(ty_@3, cag), cah), cba), caf) → new_ltEs5(xuu30000, xuu31000, cag, cah, cba)
new_esEs29(xuu4000, xuu300, ty_Ordering) → new_esEs8(xuu4000, xuu300)
new_mkBalBranch0(xuu31, xuu33, xuu34, h, ba) → new_mkBalBranch6MkBalBranch5(xuu31, xuu33, xuu34, new_esEs8(new_primCmpInt1(xuu33, xuu31, xuu34, h, ba), LT), h, ba)
new_lt7(xuu30001, xuu31001, ty_Integer) → new_lt9(xuu30001, xuu31001)
new_esEs28(xuu40000, xuu3000, ty_Bool) → new_esEs12(xuu40000, xuu3000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs5(@3(xuu30000, xuu30001, xuu30002), @3(xuu31000, xuu31001, xuu31002), cgd, cge, cgf) → new_pePe(new_lt8(xuu30000, xuu31000, cgd), new_asAs(new_esEs10(xuu30000, xuu31000, cgd), new_pePe(new_lt7(xuu30001, xuu31001, cge), new_asAs(new_esEs9(xuu30001, xuu31001, cge), new_ltEs6(xuu30002, xuu31002, cgf)))))
new_primCmpInt(Neg(Succ(xuu3000)), Pos(xuu310)) → LT
new_ltEs16(Just(xuu30000), Just(xuu31000), app(app(app(ty_@3, ee), ef), eg)) → new_ltEs5(xuu30000, xuu31000, ee, ef, eg)
new_esEs23(xuu40000, xuu3000, app(ty_[], bdb)) → new_esEs13(xuu40000, xuu3000, bdb)
new_esEs22(xuu30000, xuu31000, ty_Int) → new_esEs16(xuu30000, xuu31000)
new_not(True) → False
new_primMinusNat0(Succ(xuu25200), Succ(xuu9400)) → new_primMinusNat0(xuu25200, xuu9400)
new_ltEs4(Right(xuu30000), Right(xuu31000), cca, app(app(app(ty_@3, ccb), ccc), ccd)) → new_ltEs5(xuu30000, xuu31000, ccb, ccc, ccd)

The set Q consists of the following terms:

new_primCompAux00(x0, EQ)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, ty_@0)
new_compare210(Nothing, Just(x0), False, x1)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, True, x3, x4)
new_addToFM_C13(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, True, x4, x5)
new_esEs9(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_primMinusNat0(Zero, Zero)
new_pePe(True, x0)
new_ltEs12(LT, LT)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs13(:(x0, x1), [], x2)
new_esEs24(x0, x1, ty_Integer)
new_lt8(x0, x1, ty_@0)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare13(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare113(x0, x1, False, x2, x3, x4)
new_lt8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, x2)
new_mkBalBranch6MkBalBranch4(x0, x1, x2, False, x3, x4)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Integer)
new_primCmpInt1(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_primCmpNat0(x0, Succ(x1))
new_lt17(x0, x1, x2, x3)
new_compare13(x0, x1, ty_Float)
new_esEs10(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, ty_Float)
new_lt7(x0, x1, ty_Ordering)
new_compare210(Just(x0), Nothing, False, x1)
new_ltEs19(x0, x1, ty_@0)
new_esEs12(False, False)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Char)
new_ltEs6(x0, x1, ty_Ordering)
new_addToFM_C0(Branch(Nothing, x0, x1, x2, x3), Just(x4), x5, x6, x7)
new_esEs9(x0, x1, ty_Bool)
new_esEs16(x0, x1)
new_lt8(x0, x1, ty_Integer)
new_compare210(x0, x1, True, x2)
new_esEs30(x0, x1, ty_@0)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs20(x0, x1, ty_Float)
new_lt8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, False, x4, x5)
new_esEs9(x0, x1, ty_Ordering)
new_compare26(Char(x0), Char(x1))
new_esEs30(x0, x1, ty_Int)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Nothing, x1)
new_primPlusNat0(x0, x1)
new_esEs9(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs8(GT, GT)
new_esEs27(x0, x1, ty_Bool)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_primCompAux00(x0, LT)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt7(x0, x1, ty_Float)
new_lt8(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Float)
new_ltEs12(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_sizeFM(EmptyFM, x0, x1)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1)
new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_ltEs8(True, True)
new_compare13(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs8(LT, LT)
new_primCompAux00(x0, GT)
new_esEs21(x0, x1, ty_Int)
new_esEs18(Float(x0, x1), Float(x2, x3))
new_compare112(x0, x1, True, x2)
new_lt7(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs15(Double(x0, x1), Double(x2, x3))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Char)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs21(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Integer)
new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs10(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs23(x0, x1, ty_Double)
new_esEs10(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_esEs22(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs16(Just(x0), Just(x1), ty_@0)
new_lt8(x0, x1, ty_Char)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4)
new_primCmpNat2(Succ(x0), Succ(x1))
new_compare0([], [], x0)
new_ltEs18(x0, x1)
new_ltEs6(x0, x1, ty_Double)
new_ltEs10(x0, x1)
new_primEqNat0(Zero, Zero)
new_compare13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt8(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, app(ty_Ratio, x2))
new_primMinusNat0(Succ(x0), Succ(x1))
new_ltEs16(Just(x0), Just(x1), ty_Integer)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, EmptyFM, x5, False, x6, x7)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_addToFM_C14(x0, x1, x2, x3, x4, False, x5, x6)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare13(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_compare112(x0, x1, False, x2)
new_ltEs7(x0, x1)
new_compare13(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt15(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_compare113(x0, x1, True, x2, x3, x4)
new_primMulNat0(Zero, Zero)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs30(x0, x1, ty_Char)
new_lt8(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Int)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs23(x0, x1, ty_Ordering)
new_lt8(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare13(x0, x1, app(app(ty_@2, x2), x3))
new_addToFM_C15(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_lt6(x0, x1)
new_sIZE_RATIO
new_addToFM_C0(Branch(Nothing, x0, x1, x2, x3), Nothing, x4, x5, x6)
new_mkBalBranch6MkBalBranch3(x0, x1, Branch(x2, x3, x4, x5, x6), x7, True, x8, x9)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1)
new_esEs25(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs6(x0, x1, ty_@0)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True)
new_primCmpNat1(Zero, x0)
new_gt(x0, x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs14(@0, @0)
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs19(x0, x1, ty_Bool)
new_addListToFM_CAdd(x0, @2(x1, x2), x3, x4)
new_lt7(x0, x1, ty_Double)
new_sizeFM0(EmptyFM, x0, x1)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1, True, x2, x3)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, False, x12, x13)
new_compare6(x0, x1, x2, x3)
new_compare13(x0, x1, ty_Bool)
new_mkBalBranch0(x0, x1, x2, x3, x4)
new_primCmpInt1(EmptyFM, x0, x1, x2, x3)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_emptyFM(x0, x1)
new_ltEs16(Nothing, Just(x0), x1)
new_compare16(@0, @0)
new_compare111(x0, x1, True)
new_esEs25(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare12(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Integer)
new_lt8(x0, x1, app(ty_Ratio, x2))
new_primMinusNat0(Succ(x0), Zero)
new_lt7(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_addToFM_C13(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_lt7(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Double)
new_mkBalBranch6Size_r0(x0, x1, x2, x3, x4, x5)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt18(x0, x1)
new_compare14(x0, x1, x2, x3, x4)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_compare7(x0, x1, x2)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_lt20(x0, x1, ty_Integer)
new_addListToFM0(x0, x1, x2)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_ltEs6(x0, x1, ty_Bool)
new_addToFM_C0(EmptyFM, x0, x1, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primPlusNat1(Zero, Zero)
new_lt16(x0, x1, x2)
new_esEs24(x0, x1, ty_Float)
new_primCmpNat2(Zero, Zero)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs16(Just(x0), Just(x1), ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs9(x0, x1, ty_@0)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_compare25(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs29(x0, x1, ty_Int)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_ltEs19(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Float)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primPlusNat1(Succ(x0), Zero)
new_esEs23(x0, x1, ty_@0)
new_addToFM_C14(x0, x1, x2, x3, x4, True, x5, x6)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_compare10(x0, x1)
new_esEs30(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), ty_Bool)
new_ltEs11(x0, x1)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, EmptyFM, True, x3, x4)
new_ltEs16(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs20(x0, x1, ty_Integer)
new_ltEs12(EQ, GT)
new_ltEs12(GT, EQ)
new_ltEs16(Just(x0), Just(x1), ty_Char)
new_sr(Integer(x0), Integer(x1))
new_compare24(x0, x1, True, x2, x3)
new_esEs11(Integer(x0), Integer(x1))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_ltEs9(x0, x1, x2)
new_lt7(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs6(Nothing, Nothing, x0)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, False, x3, x4)
new_compare210(Just(x0), Just(x1), False, x2)
new_esEs12(True, True)
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(False, False)
new_ltEs6(x0, x1, app(ty_[], x2))
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, False, x4, x5)
new_esEs29(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, False, x11, x12)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs24(x0, x1, ty_Int)
new_compare27(x0, x1, False)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt7(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_addToFM_C0(Branch(Just(x0), x1, x2, x3, x4), Nothing, x5, x6, x7)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs16(Just(x0), Nothing, x1)
new_primCmpNat0(x0, Zero)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4)
new_pePe(False, x0)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Double)
new_ltEs12(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, ty_Double)
new_compare29(x0, x1, True)
new_esEs23(x0, x1, ty_Integer)
new_compare9(Integer(x0), Integer(x1))
new_ltEs13(x0, x1)
new_lt14(x0, x1)
new_esEs30(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare17(Double(x0, x1), Double(x2, x3))
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_lt10(x0, x1, x2, x3, x4)
new_ltEs17(x0, x1)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, False, x3, x4)
new_mkBalBranch6MkBalBranch4(x0, x1, EmptyFM, True, x2, x3)
new_compare110(x0, x1, False)
new_compare13(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare28(x0, x1, False, x2, x3, x4)
new_mkBalBranch6Size_l0(x0, x1, x2, x3, x4, x5)
new_esEs28(x0, x1, ty_Char)
new_primCompAux0(x0, x1, x2, x3)
new_lt12(x0, x1, x2)
new_compare0([], :(x0, x1), x2)
new_compare29(x0, x1, False)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_fsEs(x0)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_compare0(:(x0, x1), [], x2)
new_compare28(x0, x1, True, x2, x3, x4)
new_ltEs20(x0, x1, ty_Bool)
new_lt8(x0, x1, app(ty_[], x2))
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(Char(x0), Char(x1))
new_esEs30(x0, x1, ty_Double)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_ltEs20(x0, x1, ty_Char)
new_primCmpNat2(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Double)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare23(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_ltEs16(Nothing, Nothing, x0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, False, x11, x12)
new_lt7(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, False)
new_esEs9(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_lt7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_asAs(True, x0)
new_ltEs19(x0, x1, ty_Float)
new_compare11(x0, x1, False, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Float)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs15(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs10(x0, x1, ty_@0)
new_addToFM_C22(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_esEs28(x0, x1, ty_Int)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, Branch(x3, x4, x5, x6, x7), True, x8, x9)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare11(x0, x1, True, x2, x3)
new_esEs25(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs28(x0, x1, ty_Integer)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, EmptyFM, x6, False, x7, x8)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(False, True)
new_esEs12(True, False)
new_esEs29(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_mkBalBranch6MkBalBranch4(x0, x1, Branch(x2, x3, x4, x5, x6), True, x7, x8)
new_esEs27(x0, x1, ty_Double)
new_primCmpNat2(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Ordering)
new_compare23(x0, x1, False, x2, x3)
new_primCmpInt0(EmptyFM, x0, x1, x2, x3, x4)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs13([], :(x0, x1), x2)
new_esEs20(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_asAs(False, x0)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusInt(Neg(x0), Pos(x1))
new_primPlusInt(Pos(x0), Neg(x1))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, ty_Float)
new_not(True)
new_ltEs6(x0, x1, ty_Int)
new_compare13(x0, x1, ty_Integer)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs14(x0, x1, x2)
new_ltEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_addToFM_C16(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_ltEs19(x0, x1, ty_Ordering)
new_addToFM_C16(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_addToFM_C15(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_not(False)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat1(Zero, Succ(x0))
new_lt7(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_lt8(x0, x1, ty_Double)
new_compare18(x0, x1)
new_ltEs16(Just(x0), Just(x1), ty_Float)
new_esEs25(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, ty_Double)
new_lt4(x0, x1, x2, x3)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare13(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, False, x12, x13)
new_compare15(x0, x1)
new_esEs13([], [], x0)
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_lt8(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Zero)
new_sr0(x0, x1)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs24(x0, x1, ty_Char)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_lt7(x0, x1, ty_Bool)
new_mkBalBranch6MkBalBranch30(x0, EmptyFM, x1, True, x2, x3)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, x3, False, x4, x5)
new_esEs27(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Float)
new_mkBalBranch6MkBalBranch3(x0, x1, EmptyFM, x2, True, x3, x4)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs28(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusInt(Pos(x0), Pos(x1))
new_ltEs12(EQ, LT)
new_ltEs12(LT, EQ)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Double)
new_mkBalBranch6MkBalBranch30(x0, Branch(x1, x2, x3, x4, x5), x6, True, x7, x8)
new_addToFM_C0(Branch(Just(x0), x1, x2, x3, x4), Just(x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_Integer)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt7(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Float)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primMinusNat0(Zero, Succ(x0))
new_primPlusInt(Neg(x0), Neg(x1))
new_esEs6(Nothing, Just(x0), x1)
new_lt7(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs12(GT, LT)
new_ltEs12(LT, GT)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9)
new_esEs27(x0, x1, ty_Char)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_addToFM_C22(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, True)
new_esEs26(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Char)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_Double)
new_lt8(x0, x1, ty_Int)
new_ltEs16(Just(x0), Just(x1), ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare24(x0, x1, False, x2, x3)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, EmptyFM, x5, False, x6, x7)
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs16(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, ty_@0)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, EmptyFM, x6, False, x7, x8)
new_ltEs6(x0, x1, ty_Char)
new_primCmpInt0(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8, x9)
new_compare210(Nothing, Nothing, False, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Int)

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: