YES 12.878 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_C :: (Ord c, Ord a) => (b  ->  b  ->  b ->  FiniteMap (Either a c) b  ->  [(Either a c,b)]  ->  FiniteMap (Either a c) b) :: (Ord a, Ord c) => (b  ->  b  ->  b ->  FiniteMap (Either a c) b  ->  [(Either a c,b)]  ->  FiniteMap (Either a c) b)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

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



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

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



↳ HASKELL
  ↳ LR
HASKELL
      ↳ CR

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
fmToList0 key elt rest (key,elt: rest

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



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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (b  ->  a  ->  c  ->  c ->  c  ->  FiniteMap b a  ->  c
foldFM k z EmptyFM z
foldFM k z (Branch key elt _ fm_l fm_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 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 _ _ _ _) 
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 a b  ->  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_C :: (Ord b, Ord c) => (a  ->  a  ->  a ->  FiniteMap (Either c b) a  ->  [(Either c b,a)]  ->  FiniteMap (Either c b) a) :: (Ord b, Ord c) => (a  ->  a  ->  a ->  FiniteMap (Either c b) a  ->  [(Either c b,a)]  ->  FiniteMap (Either c b) a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
fmToList0 key elt rest (key,elt: rest

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



Replaced joker patterns by fresh variables and removed binding patterns.

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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (a  ->  c  ->  b  ->  b ->  b  ->  FiniteMap a c  ->  b
foldFM k z EmptyFM z
foldFM k z (Branch key elt vw fm_l fm_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 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 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 vx vy vz wu
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 wv ww wx wy
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 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



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)

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

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

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_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_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_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

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

is transformed to
gcd' x 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

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

  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 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 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  ->  b  ->  c  ->  c ->  c  ->  FiniteMap a b  ->  c
foldFM k z EmptyFM z
foldFM k z (Branch key elt vw 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 
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 vx vy vz wu
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 wv ww wx wy
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 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



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 vx vy vz wu) = 
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 wv ww wx wy) = 
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_size wxw wxx wxy = sizeFM wxw

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

mkBranchRight_ok wxw wxx wxy = mkBranchRight_ok0 wxw wxx wxy wxw wxy wxw

mkBranchLeft_size wxw wxx wxy = sizeFM wxx

mkBranchBalance_ok wxw wxx wxy = True

mkBranchUnbox wxw wxx wxy x = x

mkBranchLeft_ok0 wxw wxx wxy fm_l key EmptyFM = True
mkBranchLeft_ok0 wxw wxx wxy fm_l key (Branch left_key vx vy vz wu) = 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 wv ww wx wy) = key < mkBranchRight_ok0Smallest_right_key fm_r

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 wyw wxz (1 + mkBranchLeft_size wyv wyw wxz + mkBranchRight_size wyv wyw wxz)) 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
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

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

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)

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

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

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)

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)

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)

mkBalBranch6Size_r wyx wyy wyz wzu = sizeFM wyz

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)

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)

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 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)

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)

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

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

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
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

reduce2D wzy wzz = gcd wzy wzz

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'0 x y = gcd0Gcd' y (x `rem` y)

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

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

gcd0Gcd'1 True x wuy = x
gcd0Gcd'1 wuz wvu wvv = gcd0Gcd'0 wvu wvv



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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (c  ->  a  ->  b  ->  b ->  b  ->  FiniteMap c a  ->  b
foldFM k z EmptyFM z
foldFM k z (Branch key elt vw 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_R fm_L key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_R fm_L + mkBalBranch6Size_r key elt fm_R fm_L < 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 wzu

  
mkBalBranch6Size_r wyx wyy wyz wzu sizeFM wyz

  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 wxx wxy wxx

  
mkBranchLeft_ok0 wxw wxx wxy fm_l key EmptyFM True
mkBranchLeft_ok0 wxw wxx wxy fm_l key (Branch left_key vx vy vz wumkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key wzw fst (findMax wzw)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxx

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

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxw wxy wxw

  
mkBranchRight_ok0 wxw wxx wxy fm_r key EmptyFM True
mkBranchRight_ok0 wxw wxx wxy fm_r key (Branch right_key wv ww wx wykey < 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) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)))
mkBranchUnbox wxw wxx wxy 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



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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

  addListToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
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 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 :: (b  ->  c  ->  a  ->  a ->  a  ->  FiniteMap b c  ->  a
foldFM k z EmptyFM z
foldFM k z (Branch key elt vw 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_R fm_L key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_R fm_L + mkBalBranch6Size_r key elt fm_R fm_L < 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 wzu

  
mkBalBranch6Size_r wyx wyy wyz wzu sizeFM wyz

  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 wxx wxy wxx

  
mkBranchLeft_ok0 wxw wxx wxy fm_l key EmptyFM True
mkBranchLeft_ok0 wxw wxx wxy fm_l key (Branch left_key vx vy vz wumkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key wzw fst (findMax wzw)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxx

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

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxw wxy wxw

  
mkBranchRight_ok0 wxw wxx wxy fm_r key EmptyFM True
mkBranchRight_ok0 wxw wxx wxy fm_r key (Branch right_key wv ww wx wykey < 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) ( ->  (FiniteMap a b) ( ->  a (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(xuu500000), Succ(xuu40000)) → new_primEqNat(xuu500000, xuu40000)

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(xuu52000), Succ(xuu53000)) → new_primCmpNat(xuu52000, xuu53000)

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(xuu55200), Succ(xuu13100)) → new_primMinusNat(xuu55200, xuu13100)

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(xuu55200), Succ(xuu13100)) → new_primPlusNat(xuu55200, xuu13100)

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(xuu5000100), Succ(xuu400100)) → new_primMulNat(xuu5000100, Succ(xuu400100))

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_esEs0(:(xuu50000, xuu50001), :(xuu4000, xuu4001), app(app(ty_@2, fh), ga)) → new_esEs3(xuu50000, xuu4000, fh, ga)
new_esEs1(Left(xuu50000), Left(xuu4000), app(app(ty_@2, hb), hc), ge) → new_esEs3(xuu50000, xuu4000, hb, hc)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), h, app(ty_[], cg), cf) → new_esEs0(xuu50001, xuu4001, cg)
new_esEs2(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, baf), bag), bah)) → new_esEs(xuu50000, xuu4000, baf, bag, bah)
new_esEs3(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), bbg, app(ty_Maybe, bcf)) → new_esEs2(xuu50001, xuu4001, bcf)
new_esEs3(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), app(app(ty_Either, bdf), bdg), bdd) → new_esEs1(xuu50000, xuu4000, bdf, bdg)
new_esEs1(Left(xuu50000), Left(xuu4000), app(ty_[], gf), ge) → new_esEs0(xuu50000, xuu4000, gf)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), app(ty_Maybe, ed), ba, cf) → new_esEs2(xuu50000, xuu4000, ed)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), h, ba, app(ty_[], be)) → new_esEs0(xuu50002, xuu4002, be)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), h, ba, app(ty_Maybe, bh)) → new_esEs2(xuu50002, xuu4002, bh)
new_esEs3(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), app(app(app(ty_@3, bda), bdb), bdc), bdd) → new_esEs(xuu50000, xuu4000, bda, bdb, bdc)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), h, app(ty_Maybe, dc), cf) → new_esEs2(xuu50001, xuu4001, dc)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), h, app(app(ty_Either, da), db), cf) → new_esEs1(xuu50001, xuu4001, da, db)
new_esEs0(:(xuu50000, xuu50001), :(xuu4000, xuu4001), app(app(app(ty_@3, eh), fa), fb)) → new_esEs(xuu50000, xuu4000, eh, fa, fb)
new_esEs1(Right(xuu50000), Right(xuu4000), hd, app(ty_[], hh)) → new_esEs0(xuu50000, xuu4000, hh)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), app(app(app(ty_@3, df), dg), dh), ba, cf) → new_esEs(xuu50000, xuu4000, df, dg, dh)
new_esEs1(Left(xuu50000), Left(xuu4000), app(app(ty_Either, gg), gh), ge) → new_esEs1(xuu50000, xuu4000, gg, gh)
new_esEs2(Just(xuu50000), Just(xuu4000), app(ty_Maybe, bbd)) → new_esEs2(xuu50000, xuu4000, bbd)
new_esEs1(Right(xuu50000), Right(xuu4000), hd, app(app(ty_Either, baa), bab)) → new_esEs1(xuu50000, xuu4000, baa, bab)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), app(app(ty_Either, eb), ec), ba, cf) → new_esEs1(xuu50000, xuu4000, eb, ec)
new_esEs1(Right(xuu50000), Right(xuu4000), hd, app(app(app(ty_@3, he), hf), hg)) → new_esEs(xuu50000, xuu4000, he, hf, hg)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), h, ba, app(app(ty_@2, ca), cb)) → new_esEs3(xuu50002, xuu4002, ca, cb)
new_esEs3(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), bbg, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs(xuu50001, xuu4001, bbh, bca, bcb)
new_esEs3(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), bbg, app(app(ty_@2, bcg), bch)) → new_esEs3(xuu50001, xuu4001, bcg, bch)
new_esEs2(Just(xuu50000), Just(xuu4000), app(app(ty_Either, bbb), bbc)) → new_esEs1(xuu50000, xuu4000, bbb, bbc)
new_esEs3(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), app(ty_Maybe, bdh), bdd) → new_esEs2(xuu50000, xuu4000, bdh)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), app(app(ty_@2, ee), ef), ba, cf) → new_esEs3(xuu50000, xuu4000, ee, ef)
new_esEs3(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), bbg, app(app(ty_Either, bcd), bce)) → new_esEs1(xuu50001, xuu4001, bcd, bce)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), h, app(app(app(ty_@3, cc), cd), ce), cf) → new_esEs(xuu50001, xuu4001, cc, cd, ce)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), h, ba, app(app(ty_Either, bf), bg)) → new_esEs1(xuu50002, xuu4002, bf, bg)
new_esEs2(Just(xuu50000), Just(xuu4000), app(ty_[], bba)) → new_esEs0(xuu50000, xuu4000, bba)
new_esEs1(Left(xuu50000), Left(xuu4000), app(ty_Maybe, ha), ge) → new_esEs2(xuu50000, xuu4000, ha)
new_esEs3(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), app(app(ty_@2, bea), beb), bdd) → new_esEs3(xuu50000, xuu4000, bea, beb)
new_esEs1(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, gb), gc), gd), ge) → new_esEs(xuu50000, xuu4000, gb, gc, gd)
new_esEs3(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), bbg, app(ty_[], bcc)) → new_esEs0(xuu50001, xuu4001, bcc)
new_esEs0(:(xuu50000, xuu50001), :(xuu4000, xuu4001), app(ty_Maybe, fg)) → new_esEs2(xuu50000, xuu4000, fg)
new_esEs0(:(xuu50000, xuu50001), :(xuu4000, xuu4001), app(app(ty_Either, fd), ff)) → new_esEs1(xuu50000, xuu4000, fd, ff)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), app(ty_[], ea), ba, cf) → new_esEs0(xuu50000, xuu4000, ea)
new_esEs2(Just(xuu50000), Just(xuu4000), app(app(ty_@2, bbe), bbf)) → new_esEs3(xuu50000, xuu4000, bbe, bbf)
new_esEs0(:(xuu50000, xuu50001), :(xuu4000, xuu4001), app(ty_[], fc)) → new_esEs0(xuu50000, xuu4000, fc)
new_esEs1(Right(xuu50000), Right(xuu4000), hd, app(app(ty_@2, bad), bae)) → new_esEs3(xuu50000, xuu4000, bad, bae)
new_esEs3(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), app(ty_[], bde), bdd) → new_esEs0(xuu50000, xuu4000, bde)
new_esEs1(Right(xuu50000), Right(xuu4000), hd, app(ty_Maybe, bac)) → new_esEs2(xuu50000, xuu4000, bac)
new_esEs0(:(xuu50000, xuu50001), :(xuu4000, xuu4001), eg) → new_esEs0(xuu50001, xuu4001, eg)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), h, ba, app(app(app(ty_@3, bb), bc), bd)) → new_esEs(xuu50002, xuu4002, bb, bc, bd)
new_esEs(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), h, app(app(ty_@2, dd), de), cf) → new_esEs3(xuu50001, xuu4001, dd, de)

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_compare2(Left(@2(xuu52000, xuu52001)), Left(@2(xuu53000, xuu53001)), False, app(app(ty_@2, bag), app(ty_Maybe, bbg)), hd) → new_ltEs2(xuu52001, xuu53001, bbg)
new_compare(:(xuu52000, xuu52001), :(xuu53000, xuu53001), bdb) → new_primCompAux(xuu52000, xuu53000, new_compare1(xuu52001, xuu53001, bdb), bdb)
new_ltEs1(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), bag, app(app(ty_@2, bbe), bbf)) → new_ltEs1(xuu52001, xuu53001, bbe, bbf)
new_ltEs(Right(xuu52000), Right(xuu53000), cb, app(ty_Maybe, dc)) → new_ltEs2(xuu52000, xuu53000, dc)
new_compare2(Left(Left(xuu52000)), Left(Left(xuu53000)), False, app(app(ty_Either, app(app(app(ty_@3, bc), bd), be)), bb), hd) → new_ltEs0(xuu52000, xuu53000, bc, bd, be)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), app(ty_Maybe, ef), dg, dh) → new_compare22(xuu52000, xuu53000, new_esEs7(xuu52000, xuu53000, ef), ef)
new_ltEs(Right(xuu52000), Right(xuu53000), cb, app(app(ty_Either, cc), cd)) → new_ltEs(xuu52000, xuu53000, cc, cd)
new_compare2(Left(:(xuu52000, xuu52001)), Left(:(xuu53000, xuu53001)), False, app(ty_[], bdb), hd) → new_primCompAux(xuu52000, xuu53000, new_compare1(xuu52001, xuu53001, bdb), bdb)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), app(app(app(ty_@3, ea), eb), ec), dg, dh) → new_compare20(xuu52000, xuu53000, new_esEs5(xuu52000, xuu53000, ea, eb, ec), ea, eb, ec)
new_compare2(Left(Right(xuu52000)), Left(Right(xuu53000)), False, app(app(ty_Either, cb), app(app(ty_Either, cc), cd)), hd) → new_ltEs(xuu52000, xuu53000, cc, cd)
new_ltEs1(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), bag, app(ty_Maybe, bbg)) → new_ltEs2(xuu52001, xuu53001, bbg)
new_ltEs2(Just(xuu52000), Just(xuu53000), app(ty_[], bda)) → new_ltEs3(xuu52000, xuu53000, bda)
new_compare2(Right(xuu5200), Right(xuu5300), False, bdc, app(app(ty_@2, bea), beb)) → new_ltEs1(xuu5200, xuu5300, bea, beb)
new_ltEs1(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), app(ty_[], baf), hg) → new_lt3(xuu52000, xuu53000, baf)
new_ltEs1(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), bag, app(ty_[], bbh)) → new_ltEs3(xuu52001, xuu53001, bbh)
new_primCompAux(xuu52000, xuu53000, xuu204, app(ty_[], bfe)) → new_compare(xuu52000, xuu53000, bfe)
new_ltEs3(:(xuu52000, xuu52001), :(xuu53000, xuu53001), bdb) → new_compare(xuu52001, xuu53001, bdb)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, eh), dg), app(app(ty_@2, gh), ha)), hd) → new_ltEs1(xuu52002, xuu53002, gh, ha)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, eh), dg), app(ty_[], hc)), hd) → new_ltEs3(xuu52002, xuu53002, hc)
new_ltEs2(Just(xuu52000), Just(xuu53000), app(app(app(ty_@3, bcc), bcd), bce)) → new_ltEs0(xuu52000, xuu53000, bcc, bcd, bce)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), app(ty_[], eg), dg, dh) → new_compare(xuu52000, xuu53000, eg)
new_ltEs(Left(xuu52000), Left(xuu53000), app(app(ty_@2, bf), bg), bb) → new_ltEs1(xuu52000, xuu53000, bf, bg)
new_ltEs3(:(xuu52000, xuu52001), :(xuu53000, xuu53001), bdb) → new_primCompAux(xuu52000, xuu53000, new_compare1(xuu52001, xuu53001, bdb), bdb)
new_lt0(xuu52000, xuu53000, ea, eb, ec) → new_compare20(xuu52000, xuu53000, new_esEs5(xuu52000, xuu53000, ea, eb, ec), ea, eb, ec)
new_compare2(Left(Just(xuu52000)), Left(Just(xuu53000)), False, app(ty_Maybe, app(ty_Maybe, bch)), hd) → new_ltEs2(xuu52000, xuu53000, bch)
new_lt1(xuu52000, xuu53000, ed, ee) → new_compare21(xuu52000, xuu53000, new_esEs6(xuu52000, xuu53000, ed, ee), ed, ee)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, eh), dg), app(app(app(ty_@3, ge), gf), gg)), hd) → new_ltEs0(xuu52002, xuu53002, ge, gf, gg)
new_ltEs(Right(xuu52000), Right(xuu53000), cb, app(ty_[], dd)) → new_ltEs3(xuu52000, xuu53000, dd)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), eh, app(app(ty_Either, fa), fb), dh) → new_lt(xuu52001, xuu53001, fa, fb)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), eh, dg, app(app(app(ty_@3, ge), gf), gg)) → new_ltEs0(xuu52002, xuu53002, ge, gf, gg)
new_compare2(Left(Right(xuu52000)), Left(Right(xuu53000)), False, app(app(ty_Either, cb), app(app(ty_@2, da), db)), hd) → new_ltEs1(xuu52000, xuu53000, da, db)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, eh), app(app(ty_Either, fa), fb)), dh), hd) → new_lt(xuu52001, xuu53001, fa, fb)
new_compare2(Left(@2(xuu52000, xuu52001)), Left(@2(xuu53000, xuu53001)), False, app(app(ty_@2, bag), app(app(app(ty_@3, bbb), bbc), bbd)), hd) → new_ltEs0(xuu52001, xuu53001, bbb, bbc, bbd)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), eh, app(app(ty_@2, fg), fh), dh) → new_lt1(xuu52001, xuu53001, fg, fh)
new_compare2(Right(xuu5200), Right(xuu5300), False, bdc, app(ty_[], bed)) → new_ltEs3(xuu5200, xuu5300, bed)
new_primCompAux(xuu52000, xuu53000, xuu204, app(app(app(ty_@3, beg), beh), bfa)) → new_compare3(xuu52000, xuu53000, beg, beh, bfa)
new_compare2(Left(Right(xuu52000)), Left(Right(xuu53000)), False, app(app(ty_Either, cb), app(app(app(ty_@3, ce), cf), cg)), hd) → new_ltEs0(xuu52000, xuu53000, ce, cf, cg)
new_compare2(Left(@2(xuu52000, xuu52001)), Left(@2(xuu53000, xuu53001)), False, app(app(ty_@2, app(app(ty_@2, bac), bad)), hg), hd) → new_lt1(xuu52000, xuu53000, bac, bad)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), eh, dg, app(app(ty_@2, gh), ha)) → new_ltEs1(xuu52002, xuu53002, gh, ha)
new_compare2(Left(:(xuu52000, xuu52001)), Left(:(xuu53000, xuu53001)), False, app(ty_[], bdb), hd) → new_compare(xuu52001, xuu53001, bdb)
new_compare2(Left(Just(xuu52000)), Left(Just(xuu53000)), False, app(ty_Maybe, app(ty_[], bda)), hd) → new_ltEs3(xuu52000, xuu53000, bda)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, eh), app(app(app(ty_@3, fc), fd), ff)), dh), hd) → new_lt0(xuu52001, xuu53001, fc, fd, ff)
new_compare0(xuu52000, xuu53000, de, df) → new_compare2(xuu52000, xuu53000, new_esEs4(xuu52000, xuu53000, de, df), de, df)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), eh, app(ty_Maybe, ga), dh) → new_lt2(xuu52001, xuu53001, ga)
new_ltEs(Left(xuu52000), Left(xuu53000), app(app(app(ty_@3, bc), bd), be), bb) → new_ltEs0(xuu52000, xuu53000, bc, bd, be)
new_compare20(xuu52000, xuu53000, False, ea, eb, ec) → new_ltEs0(xuu52000, xuu53000, ea, eb, ec)
new_compare4(xuu52000, xuu53000, ed, ee) → new_compare21(xuu52000, xuu53000, new_esEs6(xuu52000, xuu53000, ed, ee), ed, ee)
new_compare2(Left(Left(xuu52000)), Left(Left(xuu53000)), False, app(app(ty_Either, app(ty_Maybe, bh)), bb), hd) → new_ltEs2(xuu52000, xuu53000, bh)
new_ltEs(Left(xuu52000), Left(xuu53000), app(ty_Maybe, bh), bb) → new_ltEs2(xuu52000, xuu53000, bh)
new_ltEs2(Just(xuu52000), Just(xuu53000), app(app(ty_@2, bcf), bcg)) → new_ltEs1(xuu52000, xuu53000, bcf, bcg)
new_lt(xuu52000, xuu53000, de, df) → new_compare2(xuu52000, xuu53000, new_esEs4(xuu52000, xuu53000, de, df), de, df)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, eh), app(ty_[], gb)), dh), hd) → new_lt3(xuu52001, xuu53001, gb)
new_compare2(Left(@2(xuu52000, xuu52001)), Left(@2(xuu53000, xuu53001)), False, app(app(ty_@2, app(ty_[], baf)), hg), hd) → new_lt3(xuu52000, xuu53000, baf)
new_compare2(Left(Right(xuu52000)), Left(Right(xuu53000)), False, app(app(ty_Either, cb), app(ty_[], dd)), hd) → new_ltEs3(xuu52000, xuu53000, dd)
new_ltEs(Left(xuu52000), Left(xuu53000), app(app(ty_Either, h), ba), bb) → new_ltEs(xuu52000, xuu53000, h, ba)
new_compare2(Left(@2(xuu52000, xuu52001)), Left(@2(xuu53000, xuu53001)), False, app(app(ty_@2, bag), app(app(ty_@2, bbe), bbf)), hd) → new_ltEs1(xuu52001, xuu53001, bbe, bbf)
new_ltEs1(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), bag, app(app(app(ty_@3, bbb), bbc), bbd)) → new_ltEs0(xuu52001, xuu53001, bbb, bbc, bbd)
new_compare2(Left(Just(xuu52000)), Left(Just(xuu53000)), False, app(ty_Maybe, app(app(ty_@2, bcf), bcg)), hd) → new_ltEs1(xuu52000, xuu53000, bcf, bcg)
new_compare2(Left(@2(xuu52000, xuu52001)), Left(@2(xuu53000, xuu53001)), False, app(app(ty_@2, app(app(app(ty_@3, hh), baa), bab)), hg), hd) → new_lt0(xuu52000, xuu53000, hh, baa, bab)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), eh, dg, app(ty_[], hc)) → new_ltEs3(xuu52002, xuu53002, hc)
new_primCompAux(xuu52000, xuu53000, xuu204, app(app(ty_Either, bee), bef)) → new_compare0(xuu52000, xuu53000, bee, bef)
new_compare5(xuu52000, xuu53000, ef) → new_compare22(xuu52000, xuu53000, new_esEs7(xuu52000, xuu53000, ef), ef)
new_ltEs2(Just(xuu52000), Just(xuu53000), app(app(ty_Either, bca), bcb)) → new_ltEs(xuu52000, xuu53000, bca, bcb)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, app(ty_[], eg)), dg), dh), hd) → new_compare(xuu52000, xuu53000, eg)
new_ltEs1(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), app(app(ty_Either, he), hf), hg) → new_lt(xuu52000, xuu53000, he, hf)
new_compare2(Left(@2(xuu52000, xuu52001)), Left(@2(xuu53000, xuu53001)), False, app(app(ty_@2, app(app(ty_Either, he), hf)), hg), hd) → new_lt(xuu52000, xuu53000, he, hf)
new_compare2(Left(@2(xuu52000, xuu52001)), Left(@2(xuu53000, xuu53001)), False, app(app(ty_@2, bag), app(ty_[], bbh)), hd) → new_ltEs3(xuu52001, xuu53001, bbh)
new_compare2(Right(xuu5200), Right(xuu5300), False, bdc, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs0(xuu5200, xuu5300, bdf, bdg, bdh)
new_compare2(Left(Left(xuu52000)), Left(Left(xuu53000)), False, app(app(ty_Either, app(app(ty_@2, bf), bg)), bb), hd) → new_ltEs1(xuu52000, xuu53000, bf, bg)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), eh, app(app(app(ty_@3, fc), fd), ff), dh) → new_lt0(xuu52001, xuu53001, fc, fd, ff)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, app(app(ty_Either, de), df)), dg), dh), hd) → new_compare2(xuu52000, xuu53000, new_esEs4(xuu52000, xuu53000, de, df), de, df)
new_compare3(xuu52000, xuu53000, ea, eb, ec) → new_compare20(xuu52000, xuu53000, new_esEs5(xuu52000, xuu53000, ea, eb, ec), ea, eb, ec)
new_compare21(xuu52000, xuu53000, False, ed, ee) → new_ltEs1(xuu52000, xuu53000, ed, ee)
new_ltEs(Left(xuu52000), Left(xuu53000), app(ty_[], ca), bb) → new_ltEs3(xuu52000, xuu53000, ca)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), app(app(ty_Either, de), df), dg, dh) → new_compare2(xuu52000, xuu53000, new_esEs4(xuu52000, xuu53000, de, df), de, df)
new_compare2(Left(@2(xuu52000, xuu52001)), Left(@2(xuu53000, xuu53001)), False, app(app(ty_@2, app(ty_Maybe, bae)), hg), hd) → new_lt2(xuu52000, xuu53000, bae)
new_compare2(Left(Left(xuu52000)), Left(Left(xuu53000)), False, app(app(ty_Either, app(app(ty_Either, h), ba)), bb), hd) → new_ltEs(xuu52000, xuu53000, h, ba)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, eh), app(ty_Maybe, ga)), dh), hd) → new_lt2(xuu52001, xuu53001, ga)
new_lt2(xuu52000, xuu53000, ef) → new_compare22(xuu52000, xuu53000, new_esEs7(xuu52000, xuu53000, ef), ef)
new_compare2(Left(Left(xuu52000)), Left(Left(xuu53000)), False, app(app(ty_Either, app(ty_[], ca)), bb), hd) → new_ltEs3(xuu52000, xuu53000, ca)
new_compare2(Right(xuu5200), Right(xuu5300), False, bdc, app(app(ty_Either, bdd), bde)) → new_ltEs(xuu5200, xuu5300, bdd, bde)
new_ltEs1(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), app(app(ty_@2, bac), bad), hg) → new_lt1(xuu52000, xuu53000, bac, bad)
new_ltEs1(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), bag, app(app(ty_Either, bah), bba)) → new_ltEs(xuu52001, xuu53001, bah, bba)
new_compare22(xuu52000, xuu53000, False, ef) → new_ltEs2(xuu52000, xuu53000, ef)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, eh), dg), app(app(ty_Either, gc), gd)), hd) → new_ltEs(xuu52002, xuu53002, gc, gd)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), eh, dg, app(ty_Maybe, hb)) → new_ltEs2(xuu52002, xuu53002, hb)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, eh), dg), app(ty_Maybe, hb)), hd) → new_ltEs2(xuu52002, xuu53002, hb)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, app(app(app(ty_@3, ea), eb), ec)), dg), dh), hd) → new_compare20(xuu52000, xuu53000, new_esEs5(xuu52000, xuu53000, ea, eb, ec), ea, eb, ec)
new_ltEs2(Just(xuu52000), Just(xuu53000), app(ty_Maybe, bch)) → new_ltEs2(xuu52000, xuu53000, bch)
new_compare(:(xuu52000, xuu52001), :(xuu53000, xuu53001), bdb) → new_compare(xuu52001, xuu53001, bdb)
new_ltEs(Right(xuu52000), Right(xuu53000), cb, app(app(ty_@2, da), db)) → new_ltEs1(xuu52000, xuu53000, da, db)
new_ltEs1(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), app(app(app(ty_@3, hh), baa), bab), hg) → new_lt0(xuu52000, xuu53000, hh, baa, bab)
new_lt3(xuu52000, xuu53000, eg) → new_compare(xuu52000, xuu53000, eg)
new_primCompAux(xuu52000, xuu53000, xuu204, app(app(ty_@2, bfb), bfc)) → new_compare4(xuu52000, xuu53000, bfb, bfc)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), eh, dg, app(app(ty_Either, gc), gd)) → new_ltEs(xuu52002, xuu53002, gc, gd)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, app(app(ty_@2, ed), ee)), dg), dh), hd) → new_compare21(xuu52000, xuu53000, new_esEs6(xuu52000, xuu53000, ed, ee), ed, ee)
new_primCompAux(xuu52000, xuu53000, xuu204, app(ty_Maybe, bfd)) → new_compare5(xuu52000, xuu53000, bfd)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), eh, app(ty_[], gb), dh) → new_lt3(xuu52001, xuu53001, gb)
new_compare2(Left(Just(xuu52000)), Left(Just(xuu53000)), False, app(ty_Maybe, app(app(app(ty_@3, bcc), bcd), bce)), hd) → new_ltEs0(xuu52000, xuu53000, bcc, bcd, bce)
new_compare2(Right(xuu5200), Right(xuu5300), False, bdc, app(ty_Maybe, bec)) → new_ltEs2(xuu5200, xuu5300, bec)
new_compare2(Left(Right(xuu52000)), Left(Right(xuu53000)), False, app(app(ty_Either, cb), app(ty_Maybe, dc)), hd) → new_ltEs2(xuu52000, xuu53000, dc)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, eh), app(app(ty_@2, fg), fh)), dh), hd) → new_lt1(xuu52001, xuu53001, fg, fh)
new_compare2(Left(Just(xuu52000)), Left(Just(xuu53000)), False, app(ty_Maybe, app(app(ty_Either, bca), bcb)), hd) → new_ltEs(xuu52000, xuu53000, bca, bcb)
new_ltEs0(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), app(app(ty_@2, ed), ee), dg, dh) → new_compare21(xuu52000, xuu53000, new_esEs6(xuu52000, xuu53000, ed, ee), ed, ee)
new_ltEs1(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), app(ty_Maybe, bae), hg) → new_lt2(xuu52000, xuu53000, bae)
new_ltEs(Right(xuu52000), Right(xuu53000), cb, app(app(app(ty_@3, ce), cf), cg)) → new_ltEs0(xuu52000, xuu53000, ce, cf, cg)
new_compare2(Left(@2(xuu52000, xuu52001)), Left(@2(xuu53000, xuu53001)), False, app(app(ty_@2, bag), app(app(ty_Either, bah), bba)), hd) → new_ltEs(xuu52001, xuu53001, bah, bba)
new_compare2(Left(@3(xuu52000, xuu52001, xuu52002)), Left(@3(xuu53000, xuu53001, xuu53002)), False, app(app(app(ty_@3, app(ty_Maybe, ef)), dg), dh), hd) → new_compare22(xuu52000, xuu53000, new_esEs7(xuu52000, xuu53000, ef), ef)

The TRS R consists of the following rules:

new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Maybe, bhb)) → new_esEs7(xuu50000, xuu4000, bhb)
new_esEs20(xuu50000, xuu4000, app(ty_Maybe, cga)) → new_esEs7(xuu50000, xuu4000, cga)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_[], bgg)) → new_esEs15(xuu50000, xuu4000, bgg)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs21(xuu50002, xuu4002, app(app(ty_@2, chg), chh)) → new_esEs6(xuu50002, xuu4002, chg, chh)
new_ltEs16(GT, GT) → True
new_primCmpNat2(Zero, xuu5200) → LT
new_compare31(xuu52000, xuu53000, ty_Int) → new_compare6(xuu52000, xuu53000)
new_ltEs17(False, False) → True
new_esEs25(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_compare23(Left(xuu5200), Left(xuu5300), False, bdc, hd) → new_compare10(xuu5200, xuu5300, new_ltEs4(xuu5200, xuu5300, bdc), bdc, hd)
new_compare9(xuu52000, xuu53000, ef) → new_compare25(xuu52000, xuu53000, new_esEs7(xuu52000, xuu53000, ef), ef)
new_esEs18(xuu50000, xuu4000, app(app(ty_@2, cdd), cde)) → new_esEs6(xuu50000, xuu4000, cdd, cde)
new_compare1(:(xuu52000, xuu52001), :(xuu53000, xuu53001), bdb) → new_primCompAux1(xuu52000, xuu53000, new_compare1(xuu52001, xuu53001, bdb), bdb)
new_esEs24(xuu52001, xuu53001, app(app(app(ty_@3, fc), fd), ff)) → new_esEs5(xuu52001, xuu53001, fc, fd, ff)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Bool, bb) → new_ltEs17(xuu52000, xuu53000)
new_esEs18(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_ltEs20(xuu52002, xuu53002, app(ty_Ratio, dch)) → new_ltEs9(xuu52002, xuu53002, dch)
new_esEs17(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_esEs24(xuu52001, xuu53001, ty_Char) → new_esEs17(xuu52001, xuu53001)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_compare10(xuu167, xuu168, True, ddh, dea) → LT
new_compare31(xuu52000, xuu53000, app(ty_Maybe, bfd)) → new_compare9(xuu52000, xuu53000, bfd)
new_lt12(xuu52001, xuu53001, app(ty_[], gb)) → new_lt8(xuu52001, xuu53001, gb)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_ltEs16(LT, GT) → True
new_ltEs5(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_ltEs4(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_esEs21(xuu50002, xuu4002, ty_Int) → new_esEs14(xuu50002, xuu4002)
new_ltEs12(Nothing, Nothing, bfg) → True
new_esEs26(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_compare19(xuu52000, xuu53000, de, df) → new_compare23(xuu52000, xuu53000, new_esEs4(xuu52000, xuu53000, de, df), de, df)
new_primMulNat0(Zero, Zero) → Zero
new_lt20(xuu52000, xuu53000, app(ty_[], baf)) → new_lt8(xuu52000, xuu53000, baf)
new_esEs26(xuu52000, xuu53000, app(ty_Ratio, dda)) → new_esEs10(xuu52000, xuu53000, dda)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_esEs15(:(xuu50000, xuu50001), :(xuu4000, xuu4001), ccc) → new_asAs(new_esEs18(xuu50000, xuu4000, ccc), new_esEs15(xuu50001, xuu4001, ccc))
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_[], cab), bhe) → new_esEs15(xuu50000, xuu4000, cab)
new_compare25(xuu52000, xuu53000, True, ef) → EQ
new_ltEs5(xuu5200, xuu5300, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs10(xuu5200, xuu5300, bdf, bdg, bdh)
new_esEs22(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_compare24(xuu52000, xuu53000, False, ea, eb, ec) → new_compare12(xuu52000, xuu53000, new_ltEs10(xuu52000, xuu53000, ea, eb, ec), ea, eb, ec)
new_lt9(xuu52000, xuu53000, ea, eb, ec) → new_esEs8(new_compare8(xuu52000, xuu53000, ea, eb, ec), LT)
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, app(ty_[], chc)) → new_esEs15(xuu50002, xuu4002, chc)
new_ltEs4(xuu5200, xuu5300, app(app(app(ty_@3, eh), dg), dh)) → new_ltEs10(xuu5200, xuu5300, eh, dg, dh)
new_lt12(xuu52001, xuu53001, app(ty_Ratio, dcg)) → new_lt5(xuu52001, xuu53001, dcg)
new_lt14(xuu52000, xuu53000) → new_esEs8(new_compare27(xuu52000, xuu53000), LT)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, app(ty_[], cbe)) → new_esEs15(xuu50000, xuu4000, cbe)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_ltEs18(xuu5200, xuu5300) → new_fsEs(new_compare14(xuu5200, xuu5300))
new_compare1([], :(xuu53000, xuu53001), bdb) → LT
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_esEs20(xuu50000, xuu4000, app(app(ty_Either, cfg), cfh)) → new_esEs4(xuu50000, xuu4000, cfg, cfh)
new_lt11(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_esEs23(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_compare30(xuu52000, xuu53000) → new_compare28(xuu52000, xuu53000, new_esEs8(xuu52000, xuu53000))
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_@2, caf), cag), bhe) → new_esEs6(xuu50000, xuu4000, caf, cag)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_@2, bhc), bhd)) → new_esEs6(xuu50000, xuu4000, bhc, bhd)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Ratio, bhf), bhe) → new_esEs10(xuu50000, xuu4000, bhf)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs12(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, app(app(app(ty_@3, cea), ceb), cec)) → new_esEs5(xuu50001, xuu4001, cea, ceb, cec)
new_esEs20(xuu50000, xuu4000, app(app(ty_@2, cgb), cgc)) → new_esEs6(xuu50000, xuu4000, cgb, cgc)
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_compare31(xuu52000, xuu53000, ty_@0) → new_compare27(xuu52000, xuu53000)
new_primCmpNat1(xuu5200, Succ(xuu5300)) → new_primCmpNat0(xuu5200, xuu5300)
new_lt20(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_@0, bhe) → new_esEs11(xuu50000, xuu4000)
new_ltEs11(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), bag, hg) → new_pePe(new_lt20(xuu52000, xuu53000, bag), new_asAs(new_esEs26(xuu52000, xuu53000, bag), new_ltEs21(xuu52001, xuu53001, hg)))
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Ordering, bhe) → new_esEs8(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_compare25(xuu52000, xuu53000, False, ef) → new_compare18(xuu52000, xuu53000, new_ltEs12(xuu52000, xuu53000, ef), ef)
new_pePe(False, xuu194) → xuu194
new_esEs25(xuu52000, xuu53000, app(app(ty_Either, de), df)) → new_esEs4(xuu52000, xuu53000, de, df)
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Float) → new_compare32(xuu52000, xuu53000)
new_esEs22(xuu50001, xuu4001, app(app(ty_Either, daf), dag)) → new_esEs4(xuu50001, xuu4001, daf, dag)
new_esEs20(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_primCmpNat1(xuu5200, Zero) → GT
new_compare31(xuu52000, xuu53000, ty_Bool) → new_compare29(xuu52000, xuu53000)
new_compare15(Char(xuu52000), Char(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_ltEs21(xuu52001, xuu53001, ty_@0) → new_ltEs7(xuu52001, xuu53001)
new_lt11(xuu52000, xuu53000, app(app(app(ty_@3, ea), eb), ec)) → new_lt9(xuu52000, xuu53000, ea, eb, ec)
new_esEs24(xuu52001, xuu53001, app(ty_Maybe, ga)) → new_esEs7(xuu52001, xuu53001, ga)
new_esEs24(xuu52001, xuu53001, ty_@0) → new_esEs11(xuu52001, xuu53001)
new_ltEs16(EQ, GT) → True
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, app(ty_[], dd)) → new_ltEs14(xuu52000, xuu53000, dd)
new_esEs22(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs23(xuu50000, xuu4000, app(ty_Maybe, dcb)) → new_esEs7(xuu50000, xuu4000, dcb)
new_esEs22(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_ltEs4(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_esEs22(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_lt20(xuu52000, xuu53000, app(ty_Maybe, bae)) → new_lt16(xuu52000, xuu53000, bae)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, app(ty_Ratio, cba)) → new_esEs10(xuu50000, xuu4000, cba)
new_primCmpNat0(Zero, Succ(xuu53000)) → LT
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, app(app(ty_@2, da), db)) → new_ltEs11(xuu52000, xuu53000, da, db)
new_esEs25(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(app(ty_@2, ed), ee)) → new_esEs6(xuu52000, xuu53000, ed, ee)
new_lt11(xuu52000, xuu53000, app(app(ty_@2, ed), ee)) → new_lt15(xuu52000, xuu53000, ed, ee)
new_esEs8(LT, LT) → True
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Ratio, dde)) → new_ltEs9(xuu52000, xuu53000, dde)
new_esEs20(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs19(xuu50001, xuu4001, app(ty_Maybe, ceg)) → new_esEs7(xuu50001, xuu4001, ceg)
new_esEs23(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs16(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_ltEs21(xuu52001, xuu53001, ty_Char) → new_ltEs6(xuu52001, xuu53001)
new_pePe(True, xuu194) → True
new_esEs24(xuu52001, xuu53001, app(app(ty_@2, fg), fh)) → new_esEs6(xuu52001, xuu53001, fg, fh)
new_primEqNat0(Zero, Zero) → True
new_esEs23(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs26(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), cgd, cge, cgf) → new_asAs(new_esEs23(xuu50000, xuu4000, cgd), new_asAs(new_esEs22(xuu50001, xuu4001, cge), new_esEs21(xuu50002, xuu4002, cgf)))
new_primMulNat0(Succ(xuu5000100), Succ(xuu400100)) → new_primPlusNat1(new_primMulNat0(xuu5000100, Succ(xuu400100)), xuu400100)
new_compare111(xuu52000, xuu53000, False, ed, ee) → GT
new_ltEs20(xuu52002, xuu53002, ty_@0) → new_ltEs7(xuu52002, xuu53002)
new_esEs22(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_lt20(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_ltEs4(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_ltEs21(xuu52001, xuu53001, app(app(ty_Either, bah), bba)) → new_ltEs8(xuu52001, xuu53001, bah, bba)
new_ltEs16(EQ, LT) → False
new_lt12(xuu52001, xuu53001, ty_Ordering) → new_lt18(xuu52001, xuu53001)
new_esEs19(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_ltEs16(GT, EQ) → False
new_sr(xuu50001, xuu4001) → new_primMulInt(xuu50001, xuu4001)
new_compare12(xuu52000, xuu53000, True, ea, eb, ec) → LT
new_esEs18(xuu50000, xuu4000, app(app(app(ty_@3, cce), ccf), ccg)) → new_esEs5(xuu50000, xuu4000, cce, ccf, ccg)
new_esEs25(xuu52000, xuu53000, app(ty_[], eg)) → new_esEs15(xuu52000, xuu53000, eg)
new_esEs24(xuu52001, xuu53001, ty_Double) → new_esEs16(xuu52001, xuu53001)
new_esEs23(xuu50000, xuu4000, app(ty_[], dbg)) → new_esEs15(xuu50000, xuu4000, dbg)
new_lt15(xuu52000, xuu53000, ed, ee) → new_esEs8(new_compare17(xuu52000, xuu53000, ed, ee), LT)
new_esEs26(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_ltEs21(xuu52001, xuu53001, app(app(ty_@2, bbe), bbf)) → new_ltEs11(xuu52001, xuu53001, bbe, bbf)
new_ltEs20(xuu52002, xuu53002, ty_Int) → new_ltEs19(xuu52002, xuu53002)
new_esEs8(GT, GT) → True
new_esEs21(xuu50002, xuu4002, ty_Double) → new_esEs16(xuu50002, xuu4002)
new_lt12(xuu52001, xuu53001, app(ty_Maybe, ga)) → new_lt16(xuu52001, xuu53001, ga)
new_primCmpInt(Pos(Succ(xuu5200)), Pos(xuu530)) → new_primCmpNat1(xuu5200, xuu530)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_lt19(xuu52000, xuu53000) → new_esEs8(new_compare29(xuu52000, xuu53000), LT)
new_esEs26(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Integer) → new_compare14(new_sr0(xuu52000, xuu53001), new_sr0(xuu53000, xuu52001))
new_esEs26(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, app(app(ty_Either, cbf), cbg)) → new_esEs4(xuu50000, xuu4000, cbf, cbg)
new_compare24(xuu52000, xuu53000, True, ea, eb, ec) → EQ
new_ltEs5(xuu5200, xuu5300, app(app(ty_Either, bdd), bde)) → new_ltEs8(xuu5200, xuu5300, bdd, bde)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs4(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_esEs20(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_ltEs16(LT, EQ) → True
new_lt12(xuu52001, xuu53001, ty_Char) → new_lt13(xuu52001, xuu53001)
new_esEs23(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_Either, cac), cad), bhe) → new_esEs4(xuu50000, xuu4000, cac, cad)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, bhg), bhh), caa), bhe) → new_esEs5(xuu50000, xuu4000, bhg, bhh, caa)
new_esEs25(xuu52000, xuu53000, app(ty_Ratio, bga)) → new_esEs10(xuu52000, xuu53000, bga)
new_ltEs5(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Ratio, bgc)) → new_esEs10(xuu50000, xuu4000, bgc)
new_lt20(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_ltEs17(True, False) → False
new_compare16(xuu52000, xuu53000, True) → LT
new_ltEs5(xuu5200, xuu5300, app(ty_Ratio, bfh)) → new_ltEs9(xuu5200, xuu5300, bfh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt10(xuu52000, xuu53000, de, df) → new_esEs8(new_compare19(xuu52000, xuu53000, de, df), LT)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(app(ty_@3, bc), bd), be), bb) → new_ltEs10(xuu52000, xuu53000, bc, bd, be)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_primCmpNat2(Succ(xuu5300), xuu5200) → new_primCmpNat0(xuu5300, xuu5200)
new_esEs19(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primCompAux0(xuu218, GT) → GT
new_compare31(xuu52000, xuu53000, ty_Ordering) → new_compare30(xuu52000, xuu53000)
new_esEs8(EQ, EQ) → True
new_ltEs21(xuu52001, xuu53001, app(ty_[], bbh)) → new_ltEs14(xuu52001, xuu53001, bbh)
new_lt11(xuu52000, xuu53000, app(app(ty_Either, de), df)) → new_lt10(xuu52000, xuu53000, de, df)
new_compare26(xuu52000, xuu53000, True, ed, ee) → EQ
new_primPlusNat1(Zero, xuu400100) → Succ(xuu400100)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_[], ca), bb) → new_ltEs14(xuu52000, xuu53000, ca)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Char, bb) → new_ltEs6(xuu52000, xuu53000)
new_esEs22(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs21(xuu50002, xuu4002, app(app(ty_Either, chd), che)) → new_esEs4(xuu50002, xuu4002, chd, che)
new_compare29(xuu52000, xuu53000) → new_compare210(xuu52000, xuu53000, new_esEs9(xuu52000, xuu53000))
new_esEs22(xuu50001, xuu4001, app(app(app(ty_@3, dab), dac), dad)) → new_esEs5(xuu50001, xuu4001, dab, dac, dad)
new_esEs18(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_compare8(xuu52000, xuu53000, ea, eb, ec) → new_compare24(xuu52000, xuu53000, new_esEs5(xuu52000, xuu53000, ea, eb, ec), ea, eb, ec)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Char, bhe) → new_esEs17(xuu50000, xuu4000)
new_esEs26(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(xuu5200, xuu5300) → new_fsEs(new_compare6(xuu5200, xuu5300))
new_ltEs20(xuu52002, xuu53002, ty_Double) → new_ltEs15(xuu52002, xuu53002)
new_ltEs16(GT, LT) → False
new_compare6(xuu52, xuu53) → new_primCmpInt(xuu52, xuu53)
new_esEs19(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_ltEs4(xuu5200, xuu5300, app(app(ty_@2, bag), hg)) → new_ltEs11(xuu5200, xuu5300, bag, hg)
new_compare13(Double(xuu52000, xuu52001), Double(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_primCmpNat0(Succ(xuu52000), Succ(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_ltEs9(xuu5200, xuu5300, bff) → new_fsEs(new_compare7(xuu5200, xuu5300, bff))
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs5(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_compare10(xuu167, xuu168, False, ddh, dea) → GT
new_lt11(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_lt5(xuu52000, xuu53000, bga) → new_esEs8(new_compare7(xuu52000, xuu53000, bga), LT)
new_ltEs21(xuu52001, xuu53001, ty_Float) → new_ltEs13(xuu52001, xuu53001)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, app(app(app(ty_@3, ce), cf), cg)) → new_ltEs10(xuu52000, xuu53000, ce, cf, cg)
new_compare14(Integer(xuu52000), Integer(xuu53000)) → new_primCmpInt(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Float, bb) → new_ltEs13(xuu52000, xuu53000)
new_esEs19(xuu50001, xuu4001, app(app(ty_@2, ceh), cfa)) → new_esEs6(xuu50001, xuu4001, ceh, cfa)
new_ltEs5(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(ty_Maybe, bfg)) → new_ltEs12(xuu5200, xuu5300, bfg)
new_lt7(xuu52000, xuu53000) → new_esEs8(new_compare14(xuu52000, xuu53000), LT)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Bool, bhe) → new_esEs9(xuu50000, xuu4000)
new_esEs24(xuu52001, xuu53001, ty_Ordering) → new_esEs8(xuu52001, xuu53001)
new_esEs18(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_@2, bf), bg), bb) → new_ltEs11(xuu52000, xuu53000, bf, bg)
new_lt6(xuu52000, xuu53000) → new_esEs8(new_compare13(xuu52000, xuu53000), LT)
new_ltEs4(xuu5200, xuu5300, app(ty_[], bdb)) → new_ltEs14(xuu5200, xuu5300, bdb)
new_lt12(xuu52001, xuu53001, ty_@0) → new_lt14(xuu52001, xuu53001)
new_esEs7(Nothing, Nothing, bgb) → True
new_esEs15([], [], ccc) → True
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_lt20(xuu52000, xuu53000, app(ty_Ratio, dda)) → new_lt5(xuu52000, xuu53000, dda)
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_esEs18(xuu50000, xuu4000, app(ty_Maybe, cdc)) → new_esEs7(xuu50000, xuu4000, cdc)
new_lt4(xuu520, xuu530) → new_esEs8(new_compare6(xuu520, xuu530), LT)
new_ltEs20(xuu52002, xuu53002, app(ty_Maybe, hb)) → new_ltEs12(xuu52002, xuu53002, hb)
new_primPlusNat0(Succ(xuu55200), Zero) → Succ(xuu55200)
new_primPlusNat0(Zero, Succ(xuu13100)) → Succ(xuu13100)
new_compare31(xuu52000, xuu53000, ty_Integer) → new_compare14(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(app(app(ty_@3, beg), beh), bfa)) → new_compare8(xuu52000, xuu53000, beg, beh, bfa)
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_esEs19(xuu50001, xuu4001, app(ty_[], ced)) → new_esEs15(xuu50001, xuu4001, ced)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu52000), Zero) → GT
new_lt11(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, app(app(app(ty_@3, cbb), cbc), cbd)) → new_esEs5(xuu50000, xuu4000, cbb, cbc, cbd)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Maybe, bh), bb) → new_ltEs12(xuu52000, xuu53000, bh)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_[], bda)) → new_ltEs14(xuu52000, xuu53000, bda)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu5300))) → LT
new_compare11(xuu174, xuu175, True, dce, dcf) → LT
new_ltEs21(xuu52001, xuu53001, ty_Ordering) → new_ltEs16(xuu52001, xuu53001)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_esEs23(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_lt20(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_sr0(Integer(xuu530000), Integer(xuu520010)) → Integer(new_primMulInt(xuu530000, xuu520010))
new_ltEs5(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_ltEs20(xuu52002, xuu53002, app(ty_[], hc)) → new_ltEs14(xuu52002, xuu53002, hc)
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_esEs7(Nothing, Just(xuu4000), bgb) → False
new_esEs7(Just(xuu50000), Nothing, bgb) → False
new_esEs13(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Maybe, bch)) → new_ltEs12(xuu52000, xuu53000, bch)
new_esEs24(xuu52001, xuu53001, ty_Int) → new_esEs14(xuu52001, xuu53001)
new_ltEs4(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_esEs22(xuu50001, xuu4001, app(app(ty_@2, dba), dbb)) → new_esEs6(xuu50001, xuu4001, dba, dbb)
new_ltEs20(xuu52002, xuu53002, ty_Integer) → new_ltEs18(xuu52002, xuu53002)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_Either, bca), bcb)) → new_ltEs8(xuu52000, xuu53000, bca, bcb)
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_esEs18(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_ltEs20(xuu52002, xuu53002, app(app(ty_@2, gh), ha)) → new_ltEs11(xuu52002, xuu53002, gh, ha)
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, app(ty_Maybe, dc)) → new_ltEs12(xuu52000, xuu53000, dc)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_@0, bb) → new_ltEs7(xuu52000, xuu53000)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Ratio, dbc)) → new_esEs10(xuu50000, xuu4000, dbc)
new_esEs6(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), cdf, cdg) → new_asAs(new_esEs20(xuu50000, xuu4000, cdf), new_esEs19(xuu50001, xuu4001, cdg))
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Integer, bhe) → new_esEs12(xuu50000, xuu4000)
new_lt20(xuu52000, xuu53000, app(app(app(ty_@3, hh), baa), bab)) → new_lt9(xuu52000, xuu53000, hh, baa, bab)
new_ltEs16(EQ, EQ) → True
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Double, bhe) → new_esEs16(xuu50000, xuu4000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Ratio, ddf), bb) → new_ltEs9(xuu52000, xuu53000, ddf)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_compare31(xuu52000, xuu53000, app(app(ty_Either, bee), bef)) → new_compare19(xuu52000, xuu53000, bee, bef)
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_lt12(xuu52001, xuu53001, app(app(ty_@2, fg), fh)) → new_lt15(xuu52001, xuu53001, fg, fh)
new_primCompAux0(xuu218, LT) → LT
new_lt20(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_not(False) → True
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, app(app(ty_Either, cc), cd)) → new_ltEs8(xuu52000, xuu53000, cc, cd)
new_esEs20(xuu50000, xuu4000, app(ty_Ratio, cfb)) → new_esEs10(xuu50000, xuu4000, cfb)
new_compare12(xuu52000, xuu53000, False, ea, eb, ec) → GT
new_esEs23(xuu50000, xuu4000, app(app(ty_@2, dcc), dcd)) → new_esEs6(xuu50000, xuu4000, dcc, dcd)
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(app(ty_@2, bfb), bfc)) → new_compare17(xuu52000, xuu53000, bfb, bfc)
new_lt11(xuu52000, xuu53000, app(ty_[], eg)) → new_lt8(xuu52000, xuu53000, eg)
new_esEs19(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_ltEs21(xuu52001, xuu53001, ty_Int) → new_ltEs19(xuu52001, xuu53001)
new_ltEs10(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), eh, dg, dh) → new_pePe(new_lt11(xuu52000, xuu53000, eh), new_asAs(new_esEs25(xuu52000, xuu53000, eh), new_pePe(new_lt12(xuu52001, xuu53001, dg), new_asAs(new_esEs24(xuu52001, xuu53001, dg), new_ltEs20(xuu52002, xuu53002, dh)))))
new_ltEs5(xuu5200, xuu5300, app(app(ty_@2, bea), beb)) → new_ltEs11(xuu5200, xuu5300, bea, beb)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_@2, bcf), bcg)) → new_ltEs11(xuu52000, xuu53000, bcf, bcg)
new_esEs24(xuu52001, xuu53001, ty_Integer) → new_esEs12(xuu52001, xuu53001)
new_lt20(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_compare28(xuu52000, xuu53000, True) → EQ
new_lt20(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_lt12(xuu52001, xuu53001, ty_Double) → new_lt6(xuu52001, xuu53001)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, app(app(ty_@2, cca), ccb)) → new_esEs6(xuu50000, xuu4000, cca, ccb)
new_lt11(xuu52000, xuu53000, app(ty_Ratio, bga)) → new_lt5(xuu52000, xuu53000, bga)
new_esEs18(xuu50000, xuu4000, app(app(ty_Either, cda), cdb)) → new_esEs4(xuu50000, xuu4000, cda, cdb)
new_esEs9(True, True) → True
new_compare11(xuu174, xuu175, False, dce, dcf) → GT
new_lt11(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_esEs20(xuu50000, xuu4000, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs5(xuu50000, xuu4000, cfc, cfd, cfe)
new_primCmpInt(Pos(Succ(xuu5200)), Neg(xuu530)) → GT
new_lt8(xuu52000, xuu53000, eg) → new_esEs8(new_compare1(xuu52000, xuu53000, eg), LT)
new_esEs21(xuu50002, xuu4002, app(app(app(ty_@3, cgh), cha), chb)) → new_esEs5(xuu50002, xuu4002, cgh, cha, chb)
new_esEs21(xuu50002, xuu4002, app(ty_Maybe, chf)) → new_esEs7(xuu50002, xuu4002, chf)
new_ltEs4(xuu5200, xuu5300, app(ty_Ratio, bff)) → new_ltEs9(xuu5200, xuu5300, bff)
new_primMulInt(Pos(xuu500010), Pos(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_lt12(xuu52001, xuu53001, app(app(app(ty_@3, fc), fd), ff)) → new_lt9(xuu52001, xuu53001, fc, fd, ff)
new_esEs18(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(app(ty_Either, dbh), dca)) → new_esEs4(xuu50000, xuu4000, dbh, dca)
new_ltEs20(xuu52002, xuu53002, ty_Bool) → new_ltEs17(xuu52002, xuu53002)
new_lt20(xuu52000, xuu53000, app(app(ty_Either, he), hf)) → new_lt10(xuu52000, xuu53000, he, hf)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Maybe, cae), bhe) → new_esEs7(xuu50000, xuu4000, cae)
new_compare23(Right(xuu5200), Left(xuu5300), False, bdc, hd) → GT
new_primMulInt(Neg(xuu500010), Neg(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_ltEs5(xuu5200, xuu5300, app(ty_Maybe, bec)) → new_ltEs12(xuu5200, xuu5300, bec)
new_compare110(xuu52000, xuu53000, True) → LT
new_esEs21(xuu50002, xuu4002, app(ty_Ratio, cgg)) → new_esEs10(xuu50002, xuu4002, cgg)
new_lt20(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_primEqNat0(Succ(xuu500000), Zero) → False
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_Either, h), ba), bb) → new_ltEs8(xuu52000, xuu53000, h, ba)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(app(ty_@3, bcc), bcd), bce)) → new_ltEs10(xuu52000, xuu53000, bcc, bcd, bce)
new_compare110(xuu52000, xuu53000, False) → GT
new_ltEs6(xuu5200, xuu5300) → new_fsEs(new_compare15(xuu5200, xuu5300))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(xuu52001, xuu53001, app(app(ty_Either, fa), fb)) → new_esEs4(xuu52001, xuu53001, fa, fb)
new_compare17(xuu52000, xuu53000, ed, ee) → new_compare26(xuu52000, xuu53000, new_esEs6(xuu52000, xuu53000, ed, ee), ed, ee)
new_ltEs21(xuu52001, xuu53001, app(ty_Ratio, ddb)) → new_ltEs9(xuu52001, xuu53001, ddb)
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Ordering, bb) → new_ltEs16(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, ty_Bool) → new_esEs9(xuu50002, xuu4002)
new_esEs11(@0, @0) → True
new_compare210(xuu52000, xuu53000, True) → EQ
new_esEs25(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs10(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), ddc) → new_asAs(new_esEs28(xuu50000, xuu4000, ddc), new_esEs27(xuu50001, xuu4001, ddc))
new_ltEs20(xuu52002, xuu53002, ty_Ordering) → new_ltEs16(xuu52002, xuu53002)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Int, bhe) → new_esEs14(xuu50000, xuu4000)
new_compare31(xuu52000, xuu53000, ty_Char) → new_compare15(xuu52000, xuu53000)
new_primPlusNat1(Succ(xuu1400), xuu400100) → Succ(Succ(new_primPlusNat0(xuu1400, xuu400100)))
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_esEs22(xuu50001, xuu4001, app(ty_[], dae)) → new_esEs15(xuu50001, xuu4001, dae)
new_esEs21(xuu50002, xuu4002, ty_Char) → new_esEs17(xuu50002, xuu4002)
new_ltEs4(xuu5200, xuu5300, app(app(ty_Either, cb), bb)) → new_ltEs8(xuu5200, xuu5300, cb, bb)
new_esEs18(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_compare23(xuu520, xuu530, True, bdc, hd) → EQ
new_lt20(xuu52000, xuu53000, app(app(ty_@2, bac), bad)) → new_lt15(xuu52000, xuu53000, bac, bad)
new_esEs20(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu5300))) → GT
new_ltEs20(xuu52002, xuu53002, ty_Float) → new_ltEs13(xuu52002, xuu53002)
new_compare31(xuu52000, xuu53000, app(ty_Ratio, ddd)) → new_compare7(xuu52000, xuu53000, ddd)
new_esEs15(:(xuu50000, xuu50001), [], ccc) → False
new_esEs15([], :(xuu4000, xuu4001), ccc) → False
new_ltEs21(xuu52001, xuu53001, app(ty_Maybe, bbg)) → new_ltEs12(xuu52001, xuu53001, bbg)
new_esEs18(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(ty_Maybe, ef)) → new_esEs7(xuu52000, xuu53000, ef)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs5(xuu50000, xuu4000, bgd, bge, bgf)
new_esEs9(False, True) → False
new_esEs9(True, False) → False
new_lt12(xuu52001, xuu53001, app(app(ty_Either, fa), fb)) → new_lt10(xuu52001, xuu53001, fa, fb)
new_compare32(Float(xuu52000, xuu52001), Float(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_ltEs7(xuu5200, xuu5300) → new_fsEs(new_compare27(xuu5200, xuu5300))
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_compare31(xuu52000, xuu53000, ty_Double) → new_compare13(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, ty_Float) → new_esEs13(xuu50002, xuu4002)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCompAux1(xuu52000, xuu53000, xuu204, bdb) → new_primCompAux0(xuu204, new_compare31(xuu52000, xuu53000, bdb))
new_esEs7(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs26(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_esEs19(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_asAs(False, xuu162) → False
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_ltEs13(xuu5200, xuu5300) → new_fsEs(new_compare32(xuu5200, xuu5300))
new_primMulInt(Pos(xuu500010), Neg(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Neg(xuu500010), Pos(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_compare23(Left(xuu5200), Right(xuu5300), False, bdc, hd) → LT
new_primCmpInt(Neg(Succ(xuu5200)), Neg(xuu530)) → new_primCmpNat2(xuu530, xuu5200)
new_primMulNat0(Succ(xuu5000100), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu400100)) → Zero
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Int, bb) → new_ltEs19(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, ty_Ordering) → new_esEs8(xuu50002, xuu4002)
new_compare26(xuu52000, xuu53000, False, ed, ee) → new_compare111(xuu52000, xuu53000, new_ltEs11(xuu52000, xuu53000, ed, ee), ed, ee)
new_esEs26(xuu52000, xuu53000, app(ty_Maybe, bae)) → new_esEs7(xuu52000, xuu53000, bae)
new_lt18(xuu52000, xuu53000) → new_esEs8(new_compare30(xuu52000, xuu53000), LT)
new_ltEs21(xuu52001, xuu53001, ty_Double) → new_ltEs15(xuu52001, xuu53001)
new_ltEs8(Right(xuu52000), Left(xuu53000), cb, bb) → False
new_esEs18(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, app(ty_[], cff)) → new_esEs15(xuu50000, xuu4000, cff)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, app(ty_Maybe, cbh)) → new_esEs7(xuu50000, xuu4000, cbh)
new_ltEs17(True, True) → True
new_ltEs14(xuu5200, xuu5300, bdb) → new_fsEs(new_compare1(xuu5200, xuu5300, bdb))
new_lt11(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_compare18(xuu52000, xuu53000, True, ef) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(xuu5300))) → new_primCmpNat2(Zero, xuu5300)
new_lt13(xuu52000, xuu53000) → new_esEs8(new_compare15(xuu52000, xuu53000), LT)
new_esEs24(xuu52001, xuu53001, app(ty_Ratio, dcg)) → new_esEs10(xuu52001, xuu53001, dcg)
new_ltEs12(Nothing, Just(xuu53000), bfg) → True
new_esEs23(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Double, bb) → new_ltEs15(xuu52000, xuu53000)
new_ltEs5(xuu5200, xuu5300, app(ty_[], bed)) → new_ltEs14(xuu5200, xuu5300, bed)
new_ltEs4(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_compare210(xuu52000, xuu53000, False) → new_compare16(xuu52000, xuu53000, new_ltEs17(xuu52000, xuu53000))
new_esEs20(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_compare18(xuu52000, xuu53000, False, ef) → GT
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_Either, bgh), bha)) → new_esEs4(xuu50000, xuu4000, bgh, bha)
new_esEs9(False, False) → True
new_esEs22(xuu50001, xuu4001, app(ty_Ratio, daa)) → new_esEs10(xuu50001, xuu4001, daa)
new_esEs26(xuu52000, xuu53000, app(ty_[], baf)) → new_esEs15(xuu52000, xuu53000, baf)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Float, bhe) → new_esEs13(xuu50000, xuu4000)
new_ltEs5(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_esEs14(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs17(xuu50000, xuu4000)
new_lt12(xuu52001, xuu53001, ty_Int) → new_lt4(xuu52001, xuu53001)
new_lt11(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Integer, bb) → new_ltEs18(xuu52000, xuu53000)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, app(ty_Ratio, cdh)) → new_esEs10(xuu50001, xuu4001, cdh)
new_esEs20(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_ltEs17(False, True) → True
new_esEs25(xuu52000, xuu53000, app(app(app(ty_@3, ea), eb), ec)) → new_esEs5(xuu52000, xuu53000, ea, eb, ec)
new_ltEs21(xuu52001, xuu53001, ty_Bool) → new_ltEs17(xuu52001, xuu53001)
new_ltEs4(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs13(xuu50000, xuu4000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu5300))) → new_primCmpNat1(xuu5300, Zero)
new_ltEs21(xuu52001, xuu53001, app(app(app(ty_@3, bbb), bbc), bbd)) → new_ltEs10(xuu52001, xuu53001, bbb, bbc, bbd)
new_esEs22(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs14(xuu50000, xuu4000)
new_compare31(xuu52000, xuu53000, app(ty_[], bfe)) → new_compare1(xuu52000, xuu53000, bfe)
new_esEs22(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs24(xuu52001, xuu53001, ty_Bool) → new_esEs9(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Float) → new_lt17(xuu52001, xuu53001)
new_ltEs20(xuu52002, xuu53002, ty_Char) → new_ltEs6(xuu52002, xuu53002)
new_esEs20(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_primPlusNat0(Succ(xuu55200), Succ(xuu13100)) → Succ(Succ(new_primPlusNat0(xuu55200, xuu13100)))
new_ltEs4(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_ltEs21(xuu52001, xuu53001, ty_Integer) → new_ltEs18(xuu52001, xuu53001)
new_compare23(Right(xuu5200), Right(xuu5300), False, bdc, hd) → new_compare11(xuu5200, xuu5300, new_ltEs5(xuu5200, xuu5300, hd), bdc, hd)
new_esEs21(xuu50002, xuu4002, ty_@0) → new_esEs11(xuu50002, xuu4002)
new_compare111(xuu52000, xuu53000, True, ed, ee) → LT
new_ltEs8(Right(xuu52000), Right(xuu53000), cb, app(ty_Ratio, ddg)) → new_ltEs9(xuu52000, xuu53000, ddg)
new_esEs26(xuu52000, xuu53000, app(app(ty_Either, he), hf)) → new_esEs4(xuu52000, xuu53000, he, hf)
new_asAs(True, xuu162) → xuu162
new_compare27(@0, @0) → EQ
new_esEs19(xuu50001, xuu4001, app(app(ty_Either, cee), cef)) → new_esEs4(xuu50001, xuu4001, cee, cef)
new_esEs26(xuu52000, xuu53000, app(app(app(ty_@3, hh), baa), bab)) → new_esEs5(xuu52000, xuu53000, hh, baa, bab)
new_lt12(xuu52001, xuu53001, ty_Bool) → new_lt19(xuu52001, xuu53001)
new_esEs19(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs4(Right(xuu50000), Left(xuu4000), cah, bhe) → False
new_esEs4(Left(xuu50000), Right(xuu4000), cah, bhe) → False
new_ltEs5(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_ltEs20(xuu52002, xuu53002, app(app(ty_Either, gc), gd)) → new_ltEs8(xuu52002, xuu53002, gc, gd)
new_ltEs16(LT, LT) → True
new_ltEs12(Just(xuu52000), Nothing, bfg) → False
new_compare1(:(xuu52000, xuu52001), [], bdb) → GT
new_lt16(xuu52000, xuu53000, ef) → new_esEs8(new_compare9(xuu52000, xuu53000, ef), LT)
new_fsEs(xuu177) → new_not(new_esEs8(xuu177, GT))
new_esEs24(xuu52001, xuu53001, ty_Float) → new_esEs13(xuu52001, xuu53001)
new_esEs26(xuu52000, xuu53000, app(app(ty_@2, bac), bad)) → new_esEs6(xuu52000, xuu53000, bac, bad)
new_esEs23(xuu50000, xuu4000, app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs5(xuu50000, xuu4000, dbd, dbe, dbf)
new_esEs4(Right(xuu50000), Right(xuu4000), cah, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs26(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_ltEs20(xuu52002, xuu53002, app(app(app(ty_@3, ge), gf), gg)) → new_ltEs10(xuu52002, xuu53002, ge, gf, gg)
new_ltEs8(Left(xuu52000), Right(xuu53000), cb, bb) → True
new_esEs21(xuu50002, xuu4002, ty_Integer) → new_esEs12(xuu50002, xuu4002)
new_lt17(xuu52000, xuu53000) → new_esEs8(new_compare32(xuu52000, xuu53000), LT)
new_lt11(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, app(ty_Maybe, ef)) → new_lt16(xuu52000, xuu53000, ef)
new_ltEs5(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_lt12(xuu52001, xuu53001, ty_Integer) → new_lt7(xuu52001, xuu53001)
new_ltEs15(xuu5200, xuu5300) → new_fsEs(new_compare13(xuu5200, xuu5300))
new_esEs18(xuu50000, xuu4000, app(ty_[], cch)) → new_esEs15(xuu50000, xuu4000, cch)
new_compare28(xuu52000, xuu53000, False) → new_compare110(xuu52000, xuu53000, new_ltEs16(xuu52000, xuu53000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(xuu218, EQ) → xuu218
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Int) → new_compare6(new_sr(xuu52000, xuu53001), new_sr(xuu53000, xuu52001))
new_esEs24(xuu52001, xuu53001, app(ty_[], gb)) → new_esEs15(xuu52001, xuu53001, gb)
new_esEs18(xuu50000, xuu4000, app(ty_Ratio, ccd)) → new_esEs10(xuu50000, xuu4000, ccd)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs16(xuu50000, xuu4000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(xuu50001, xuu4001, app(ty_Maybe, dah)) → new_esEs7(xuu50001, xuu4001, dah)
new_primCmpInt(Neg(Succ(xuu5200)), Pos(xuu530)) → LT
new_not(True) → False
new_compare16(xuu52000, xuu53000, False) → GT
new_compare1([], [], bdb) → EQ

The set Q consists of the following terms:

new_compare1([], [], x0)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primCompAux0(x0, EQ)
new_ltEs5(x0, x1, ty_Float)
new_ltEs4(x0, x1, ty_Bool)
new_compare29(x0, x1)
new_fsEs(x0)
new_primCompAux0(x0, GT)
new_esEs19(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_@0)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_compare10(x0, x1, False, x2, x3)
new_compare16(x0, x1, False)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare18(x0, x1, False, x2)
new_ltEs11(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs13(x0, x1)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Char)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs25(x0, x1, ty_Float)
new_compare110(x0, x1, False)
new_ltEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_ltEs9(x0, x1, x2)
new_lt19(x0, x1)
new_esEs20(x0, x1, ty_Bool)
new_compare1([], :(x0, x1), x2)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt12(x0, x1, app(ty_Ratio, x2))
new_ltEs4(x0, x1, ty_Char)
new_lt10(x0, x1, x2, x3)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Float)
new_lt5(x0, x1, x2)
new_esEs11(@0, @0)
new_ltEs20(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_esEs7(Nothing, Nothing, x0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs4(x0, x1, ty_Int)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs8(GT, GT)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs5(x0, x1, ty_Double)
new_lt9(x0, x1, x2, x3, x4)
new_primCmpNat1(x0, Zero)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs4(x0, x1, ty_Integer)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs4(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(LT, LT)
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Nothing, Just(x0), x1)
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_esEs21(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Ordering)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt11(x0, x1, ty_Integer)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Float)
new_ltEs17(False, False)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_primCompAux1(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_ltEs4(x0, x1, ty_Double)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_primEqNat0(Zero, Zero)
new_esEs19(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_[], x2))
new_lt11(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs21(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs9(True, True)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt14(x0, x1)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_primCmpNat1(x0, Succ(x1))
new_primMulNat0(Zero, Zero)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_compare31(x0, x1, ty_Integer)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_ltEs20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs18(x0, x1)
new_esEs27(x0, x1, ty_Integer)
new_compare26(x0, x1, True, x2, x3)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs17(True, True)
new_esEs26(x0, x1, ty_Char)
new_compare8(x0, x1, x2, x3, x4)
new_primMulNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt12(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare12(x0, x1, False, x2, x3, x4)
new_compare14(Integer(x0), Integer(x1))
new_primCmpNat0(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Zero)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Integer)
new_pePe(False, x0)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1, x2, x3)
new_ltEs21(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_compare24(x0, x1, False, x2, x3, x4)
new_ltEs6(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Bool)
new_compare32(Float(x0, x1), Float(x2, x3))
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(Left(x0), Right(x1), False, x2, x3)
new_compare23(Right(x0), Left(x1), False, x2, x3)
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_compare11(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_Float)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_lt12(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17(Char(x0), Char(x1))
new_esEs19(x0, x1, ty_Char)
new_primPlusNat0(Zero, Zero)
new_ltEs16(EQ, EQ)
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, ty_Int)
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Succ(x0), Zero)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs4(x0, x1, ty_@0)
new_ltEs5(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare25(x0, x1, False, x2)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_ltEs14(x0, x1, x2)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, ty_Double)
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_esEs19(x0, x1, ty_Int)
new_ltEs4(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Double)
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, False)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Float)
new_compare16(x0, x1, True)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Float)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs18(x0, x1, ty_Int)
new_ltEs16(LT, GT)
new_ltEs16(GT, LT)
new_esEs25(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_lt7(x0, x1)
new_primPlusNat1(Succ(x0), x1)
new_pePe(True, x0)
new_lt11(x0, x1, ty_@0)
new_lt11(x0, x1, ty_Ordering)
new_primCompAux0(x0, LT)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_esEs21(x0, x1, ty_Int)
new_compare31(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_[], x2))
new_compare30(x0, x1)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_compare25(x0, x1, True, x2)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs22(x0, x1, ty_Bool)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Zero, Succ(x0))
new_lt8(x0, x1, x2)
new_ltEs15(x0, x1)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare31(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_asAs(True, x0)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Char)
new_compare210(x0, x1, False)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, app(ty_[], x2))
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs20(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Bool)
new_ltEs16(GT, GT)
new_ltEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Double)
new_compare1(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs15([], [], x0)
new_esEs22(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs13(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs5(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_primCmpNat2(Succ(x0), x1)
new_esEs7(Just(x0), Nothing, x1)
new_esEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, False, x2, x3)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs14(x0, x1)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_compare13(Double(x0, x1), Double(x2, x3))
new_primPlusNat1(Zero, x0)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_compare31(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_compare15(Char(x0), Char(x1))
new_esEs15([], :(x0, x1), x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Nothing, Just(x0), x1)
new_compare9(x0, x1, x2)
new_primCmpNat0(Zero, Zero)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Char)
new_compare19(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(False, False)
new_esEs15(:(x0, x1), [], x2)
new_esEs25(x0, x1, ty_Int)
new_ltEs12(Just(x0), Nothing, x1)
new_esEs23(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt18(x0, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Bool)
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_ltEs21(x0, x1, ty_@0)
new_ltEs21(x0, x1, app(ty_[], x2))
new_compare6(x0, x1)
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(Left(x0), Left(x1), False, x2, x3)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_compare31(x0, x1, ty_Ordering)
new_ltEs4(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(x0, x1, False, x2, x3)
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_esEs22(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Float)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_not(True)
new_ltEs19(x0, x1)
new_esEs20(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs21(x0, x1, ty_Float)
new_lt11(x0, x1, ty_Int)
new_ltEs5(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt4(x0, x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_primCmpNat2(Zero, x0)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_compare31(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs17(False, True)
new_ltEs17(True, False)
new_ltEs20(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt12(x0, x1, ty_Integer)
new_compare210(x0, x1, True)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt6(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Char)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(Nothing, Nothing, x0)
new_ltEs5(x0, x1, ty_Int)
new_compare28(x0, x1, True)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Char)
new_compare10(x0, x1, True, x2, x3)
new_compare31(x0, x1, app(ty_[], x2))
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_compare23(Right(x0), Right(x1), False, x2, x3)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Double)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2)
new_esEs23(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare27(@0, @0)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_lt11(x0, x1, ty_Double)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt11(x0, x1, ty_Bool)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs20(x0, x1, ty_Double)
new_lt12(x0, x1, ty_Ordering)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Double)
new_ltEs4(x0, x1, app(ty_[], x2))
new_ltEs4(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(x0, x1, ty_Double)
new_compare18(x0, x1, True, x2)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr(x0, x1)
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, 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
                                  ↳ QDP

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

new_addToFM_C2(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, h, ba, bb) → new_addToFM_C(xuu16, xuu20, Left(xuu22), xuu23, h, ba, bb)
new_addToFM_C(xuu3, Branch(Left(xuu400), xuu41, xuu42, xuu43, xuu44), Right(xuu5000), xuu501, bc, bd, be) → new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Right(xuu5000), Left(xuu400), False, bc, bd), LT), bc, bd, be)
new_addToFM_C20(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu43, Left(xuu5000), xuu501, bc, bd, be)
new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, False, bc, bd, be) → new_addToFM_C11(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Right(xuu5000), Left(xuu400), False, bc, bd), GT), bc, bd, be)
new_addToFM_C1(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, h, ba, bb) → new_addToFM_C(xuu16, xuu21, Left(xuu22), xuu23, h, ba, bb)
new_addToFM_C(xuu3, Branch(Right(xuu400), xuu41, xuu42, xuu43, xuu44), Right(xuu5000), xuu501, bc, bd, be) → new_addToFM_C22(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Right(xuu5000), Right(xuu400), new_esEs31(xuu5000, xuu400, bd), bc, bd), LT), bc, bd, be)
new_addToFM_C2(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, False, h, ba, bb) → new_addToFM_C1(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, new_esEs8(new_compare23(Left(xuu22), Left(xuu17), new_esEs29(xuu22, xuu17, h), h, ba), GT), h, ba, bb)
new_addToFM_C22(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, True, bf, bg, bh) → new_addToFM_C(xuu35, xuu39, Right(xuu41), xuu42, bf, bg, bh)
new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu43, Right(xuu5000), xuu501, bc, bd, be)
new_addToFM_C11(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu44, Right(xuu5000), xuu501, bc, bd, be)
new_addToFM_C20(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, False, bc, bd, be) → new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Left(xuu5000), Right(xuu400), False, bc, bd), GT), bc, bd, be)
new_addToFM_C(xuu3, Branch(Right(xuu400), xuu41, xuu42, xuu43, xuu44), Left(xuu5000), xuu501, bc, bd, be) → new_addToFM_C20(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Left(xuu5000), Right(xuu400), False, bc, bd), LT), bc, bd, be)
new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu44, Left(xuu5000), xuu501, bc, bd, be)
new_addToFM_C(xuu3, Branch(Left(xuu400), xuu41, xuu42, xuu43, xuu44), Left(xuu5000), xuu501, bc, bd, be) → new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Left(xuu5000), Left(xuu400), new_esEs30(xuu5000, xuu400, bc), bc, bd), LT), bc, bd, be)
new_addToFM_C22(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, False, bf, bg, bh) → new_addToFM_C12(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, new_esEs8(new_compare23(Right(xuu41), Right(xuu36), new_esEs32(xuu41, xuu36, bg), bf, bg), GT), bf, bg, bh)
new_addToFM_C12(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, True, bf, bg, bh) → new_addToFM_C(xuu35, xuu40, Right(xuu41), xuu42, bf, bg, bh)

The TRS R consists of the following rules:

new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Maybe, hh)) → new_esEs7(xuu50000, xuu4000, hh)
new_esEs20(xuu50000, xuu4000, app(ty_Maybe, bhd)) → new_esEs7(xuu50000, xuu4000, bhd)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_[], he)) → new_esEs15(xuu50000, xuu4000, he)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs21(xuu50002, xuu4002, app(app(ty_@2, cbb), cbc)) → new_esEs6(xuu50002, xuu4002, cbb, cbc)
new_ltEs16(GT, GT) → True
new_primCmpNat2(Zero, xuu5200) → LT
new_compare31(xuu52000, xuu53000, ty_Int) → new_compare6(xuu52000, xuu53000)
new_ltEs17(False, False) → True
new_esEs31(xuu5000, xuu400, ty_@0) → new_esEs11(xuu5000, xuu400)
new_esEs25(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_compare9(xuu52000, xuu53000, gg) → new_compare25(xuu52000, xuu53000, new_esEs7(xuu52000, xuu53000, gg), gg)
new_compare23(Left(xuu5200), Left(xuu5300), False, ca, cb) → new_compare10(xuu5200, xuu5300, new_ltEs4(xuu5200, xuu5300, ca), ca, cb)
new_esEs18(xuu50000, xuu4000, app(app(ty_@2, beg), beh)) → new_esEs6(xuu50000, xuu4000, beg, beh)
new_compare1(:(xuu52000, xuu52001), :(xuu53000, xuu53001), de) → new_primCompAux1(xuu52000, xuu53000, new_compare1(xuu52001, xuu53001, de), de)
new_esEs24(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs5(xuu52001, xuu53001, cee, cef, ceg)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Bool, cd) → new_ltEs17(xuu52000, xuu53000)
new_esEs18(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_ltEs20(xuu52002, xuu53002, app(ty_Ratio, cff)) → new_ltEs9(xuu52002, xuu53002, cff)
new_esEs17(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_esEs31(xuu5000, xuu400, ty_Ordering) → new_esEs8(xuu5000, xuu400)
new_esEs24(xuu52001, xuu53001, ty_Char) → new_esEs17(xuu52001, xuu53001)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_compare10(xuu167, xuu168, True, dhe, dhf) → LT
new_compare31(xuu52000, xuu53000, app(ty_Maybe, dde)) → new_compare9(xuu52000, xuu53000, dde)
new_lt12(xuu52001, xuu53001, app(ty_[], cfc)) → new_lt8(xuu52001, xuu53001, cfc)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_ltEs16(LT, GT) → True
new_ltEs5(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs31(xuu5000, xuu400, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs5(xuu5000, xuu400, cgg, cgh, cha)
new_ltEs4(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_esEs21(xuu50002, xuu4002, ty_Int) → new_esEs14(xuu50002, xuu4002)
new_ltEs12(Nothing, Nothing, dd) → True
new_esEs26(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_compare19(xuu52000, xuu53000, bdd, bde) → new_compare23(xuu52000, xuu53000, new_esEs4(xuu52000, xuu53000, bdd, bde), bdd, bde)
new_primMulNat0(Zero, Zero) → Zero
new_lt20(xuu52000, xuu53000, app(ty_[], dba)) → new_lt8(xuu52000, xuu53000, dba)
new_esEs26(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_esEs10(xuu52000, xuu53000, dab)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_esEs15(:(xuu50000, xuu50001), :(xuu4000, xuu4001), bdf) → new_asAs(new_esEs18(xuu50000, xuu4000, bdf), new_esEs15(xuu50001, xuu4001, bdf))
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_[], bbc), baf) → new_esEs15(xuu50000, xuu4000, bbc)
new_compare25(xuu52000, xuu53000, True, gg) → EQ
new_ltEs5(xuu5200, xuu5300, app(app(app(ty_@3, ea), eb), ec)) → new_ltEs10(xuu5200, xuu5300, ea, eb, ec)
new_esEs22(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_compare24(xuu52000, xuu53000, False, fa, fb, fc) → new_compare12(xuu52000, xuu53000, new_ltEs10(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_lt9(xuu52000, xuu53000, fa, fb, fc) → new_esEs8(new_compare8(xuu52000, xuu53000, fa, fb, fc), LT)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, app(ty_[], caf)) → new_esEs15(xuu50002, xuu4002, caf)
new_ltEs4(xuu5200, xuu5300, app(app(app(ty_@3, cf), cg), da)) → new_ltEs10(xuu5200, xuu5300, cf, cg, da)
new_lt12(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_lt5(xuu52001, xuu53001, ced)
new_lt14(xuu52000, xuu53000) → new_esEs8(new_compare27(xuu52000, xuu53000), LT)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_[], bcf)) → new_esEs15(xuu50000, xuu4000, bcf)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs29(xuu22, xuu17, app(app(ty_Either, ead), eae)) → new_esEs4(xuu22, xuu17, ead, eae)
new_ltEs18(xuu5200, xuu5300) → new_fsEs(new_compare14(xuu5200, xuu5300))
new_compare1([], :(xuu53000, xuu53001), de) → LT
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_esEs29(xuu22, xuu17, app(ty_Maybe, eaf)) → new_esEs7(xuu22, xuu17, eaf)
new_esEs20(xuu50000, xuu4000, app(app(ty_Either, bhb), bhc)) → new_esEs4(xuu50000, xuu4000, bhb, bhc)
new_lt11(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_esEs23(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_compare30(xuu52000, xuu53000) → new_compare28(xuu52000, xuu53000, new_esEs8(xuu52000, xuu53000))
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_@2, bbg), bbh), baf) → new_esEs6(xuu50000, xuu4000, bbg, bbh)
new_esEs31(xuu5000, xuu400, ty_Char) → new_esEs17(xuu5000, xuu400)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_@2, baa), bab)) → new_esEs6(xuu50000, xuu4000, baa, bab)
new_esEs30(xuu5000, xuu400, ty_Bool) → new_esEs9(xuu5000, xuu400)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Ratio, bag), baf) → new_esEs10(xuu50000, xuu4000, bag)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs29(xuu22, xuu17, ty_Bool) → new_esEs9(xuu22, xuu17)
new_esEs12(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs5(xuu50001, xuu4001, bfd, bfe, bff)
new_esEs20(xuu50000, xuu4000, app(app(ty_@2, bhe), bhf)) → new_esEs6(xuu50000, xuu4000, bhe, bhf)
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_compare31(xuu52000, xuu53000, ty_@0) → new_compare27(xuu52000, xuu53000)
new_primCmpNat1(xuu5200, Succ(xuu5300)) → new_primCmpNat0(xuu5200, xuu5300)
new_lt20(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_@0, baf) → new_esEs11(xuu50000, xuu4000)
new_ltEs11(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), db, dc) → new_pePe(new_lt20(xuu52000, xuu53000, db), new_asAs(new_esEs26(xuu52000, xuu53000, db), new_ltEs21(xuu52001, xuu53001, dc)))
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Ordering, baf) → new_esEs8(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_esEs32(xuu41, xuu36, app(app(ty_@2, ge), gf)) → new_esEs6(xuu41, xuu36, ge, gf)
new_compare25(xuu52000, xuu53000, False, gg) → new_compare18(xuu52000, xuu53000, new_ltEs12(xuu52000, xuu53000, gg), gg)
new_pePe(False, xuu194) → xuu194
new_esEs29(xuu22, xuu17, ty_Double) → new_esEs16(xuu22, xuu17)
new_esEs25(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_esEs4(xuu52000, xuu53000, bdd, bde)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_esEs31(xuu5000, xuu400, ty_Bool) → new_esEs9(xuu5000, xuu400)
new_compare31(xuu52000, xuu53000, ty_Float) → new_compare32(xuu52000, xuu53000)
new_esEs22(xuu50001, xuu4001, app(app(ty_Either, cca), ccb)) → new_esEs4(xuu50001, xuu4001, cca, ccb)
new_esEs20(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_primCmpNat1(xuu5200, Zero) → GT
new_compare31(xuu52000, xuu53000, ty_Bool) → new_compare29(xuu52000, xuu53000)
new_compare15(Char(xuu52000), Char(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_ltEs21(xuu52001, xuu53001, ty_@0) → new_ltEs7(xuu52001, xuu53001)
new_lt11(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_lt9(xuu52000, xuu53000, fa, fb, fc)
new_esEs32(xuu41, xuu36, app(ty_Maybe, gd)) → new_esEs7(xuu41, xuu36, gd)
new_esEs24(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_esEs7(xuu52001, xuu53001, cfb)
new_esEs24(xuu52001, xuu53001, ty_@0) → new_esEs11(xuu52001, xuu53001)
new_ltEs16(EQ, GT) → True
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_[], dhd)) → new_ltEs14(xuu52000, xuu53000, dhd)
new_esEs22(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs23(xuu50000, xuu4000, app(ty_Maybe, cde)) → new_esEs7(xuu50000, xuu4000, cde)
new_esEs22(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_ltEs4(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_esEs22(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_lt20(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_lt16(xuu52000, xuu53000, dah)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Ratio, bcb)) → new_esEs10(xuu50000, xuu4000, bcb)
new_primCmpNat0(Zero, Succ(xuu53000)) → LT
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_@2, dha), dhb)) → new_ltEs11(xuu52000, xuu53000, dha, dhb)
new_esEs25(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_esEs6(xuu52000, xuu53000, bad, bae)
new_lt11(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_lt15(xuu52000, xuu53000, bad, bae)
new_esEs8(LT, LT) → True
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Ratio, dea)) → new_ltEs9(xuu52000, xuu53000, dea)
new_esEs20(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs19(xuu50001, xuu4001, app(ty_Maybe, bgb)) → new_esEs7(xuu50001, xuu4001, bgb)
new_esEs23(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs16(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_ltEs21(xuu52001, xuu53001, ty_Char) → new_ltEs6(xuu52001, xuu53001)
new_pePe(True, xuu194) → True
new_esEs24(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_esEs6(xuu52001, xuu53001, ceh, cfa)
new_primEqNat0(Zero, Zero) → True
new_esEs23(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs26(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), bhg, bhh, caa) → new_asAs(new_esEs23(xuu50000, xuu4000, bhg), new_asAs(new_esEs22(xuu50001, xuu4001, bhh), new_esEs21(xuu50002, xuu4002, caa)))
new_primMulNat0(Succ(xuu5000100), Succ(xuu400100)) → new_primPlusNat1(new_primMulNat0(xuu5000100, Succ(xuu400100)), xuu400100)
new_compare111(xuu52000, xuu53000, False, bad, bae) → GT
new_ltEs20(xuu52002, xuu53002, ty_@0) → new_ltEs7(xuu52002, xuu53002)
new_esEs22(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs31(xuu5000, xuu400, ty_Integer) → new_esEs12(xuu5000, xuu400)
new_esEs29(xuu22, xuu17, ty_Int) → new_esEs14(xuu22, xuu17)
new_lt20(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_ltEs4(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_ltEs21(xuu52001, xuu53001, app(app(ty_Either, dbb), dbc)) → new_ltEs8(xuu52001, xuu53001, dbb, dbc)
new_ltEs16(EQ, LT) → False
new_lt12(xuu52001, xuu53001, ty_Ordering) → new_lt18(xuu52001, xuu53001)
new_esEs19(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_ltEs16(GT, EQ) → False
new_sr(xuu50001, xuu4001) → new_primMulInt(xuu50001, xuu4001)
new_compare12(xuu52000, xuu53000, True, fa, fb, fc) → LT
new_esEs32(xuu41, xuu36, ty_Bool) → new_esEs9(xuu41, xuu36)
new_esEs18(xuu50000, xuu4000, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs5(xuu50000, xuu4000, bdh, bea, beb)
new_esEs25(xuu52000, xuu53000, app(ty_[], bac)) → new_esEs15(xuu52000, xuu53000, bac)
new_esEs24(xuu52001, xuu53001, ty_Double) → new_esEs16(xuu52001, xuu53001)
new_esEs23(xuu50000, xuu4000, app(ty_[], cdb)) → new_esEs15(xuu50000, xuu4000, cdb)
new_lt15(xuu52000, xuu53000, bad, bae) → new_esEs8(new_compare17(xuu52000, xuu53000, bad, bae), LT)
new_ltEs21(xuu52001, xuu53001, app(app(ty_@2, dbh), dca)) → new_ltEs11(xuu52001, xuu53001, dbh, dca)
new_ltEs20(xuu52002, xuu53002, ty_Int) → new_ltEs19(xuu52002, xuu53002)
new_esEs26(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs8(GT, GT) → True
new_esEs21(xuu50002, xuu4002, ty_Double) → new_esEs16(xuu50002, xuu4002)
new_esEs31(xuu5000, xuu400, app(ty_[], chb)) → new_esEs15(xuu5000, xuu400, chb)
new_lt12(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_lt16(xuu52001, xuu53001, cfb)
new_primCmpInt(Pos(Succ(xuu5200)), Pos(xuu530)) → new_primCmpNat1(xuu5200, xuu530)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_lt19(xuu52000, xuu53000) → new_esEs8(new_compare29(xuu52000, xuu53000), LT)
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Integer) → new_compare14(new_sr0(xuu52000, xuu53001), new_sr0(xuu53000, xuu52001))
new_esEs26(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_esEs32(xuu41, xuu36, ty_Int) → new_esEs14(xuu41, xuu36)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_Either, bcg), bch)) → new_esEs4(xuu50000, xuu4000, bcg, bch)
new_compare24(xuu52000, xuu53000, True, fa, fb, fc) → EQ
new_ltEs5(xuu5200, xuu5300, app(app(ty_Either, df), dg)) → new_ltEs8(xuu5200, xuu5300, df, dg)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs4(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_esEs20(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_ltEs16(LT, EQ) → True
new_esEs31(xuu5000, xuu400, app(app(ty_Either, chc), chd)) → new_esEs4(xuu5000, xuu400, chc, chd)
new_lt12(xuu52001, xuu53001, ty_Char) → new_lt13(xuu52001, xuu53001)
new_esEs23(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_Either, bbd), bbe), baf) → new_esEs4(xuu50000, xuu4000, bbd, bbe)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs5(xuu50000, xuu4000, bah, bba, bbb)
new_esEs25(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_esEs10(xuu52000, xuu53000, eh)
new_ltEs5(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Ratio, ha)) → new_esEs10(xuu50000, xuu4000, ha)
new_lt20(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_ltEs17(True, False) → False
new_compare16(xuu52000, xuu53000, True) → LT
new_ltEs5(xuu5200, xuu5300, app(ty_Ratio, dh)) → new_ltEs9(xuu5200, xuu5300, dh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt10(xuu52000, xuu53000, bdd, bde) → new_esEs8(new_compare19(xuu52000, xuu53000, bdd, bde), LT)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(app(ty_@3, dfd), dfe), dff), cd) → new_ltEs10(xuu52000, xuu53000, dfd, dfe, dff)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs32(xuu41, xuu36, app(app(app(ty_@3, ff), fg), fh)) → new_esEs5(xuu41, xuu36, ff, fg, fh)
new_primCmpNat2(Succ(xuu5300), xuu5200) → new_primCmpNat0(xuu5300, xuu5200)
new_esEs32(xuu41, xuu36, ty_@0) → new_esEs11(xuu41, xuu36)
new_esEs19(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primCompAux0(xuu218, GT) → GT
new_compare31(xuu52000, xuu53000, ty_Ordering) → new_compare30(xuu52000, xuu53000)
new_ltEs21(xuu52001, xuu53001, app(ty_[], dcc)) → new_ltEs14(xuu52001, xuu53001, dcc)
new_lt11(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_lt10(xuu52000, xuu53000, bdd, bde)
new_esEs8(EQ, EQ) → True
new_compare26(xuu52000, xuu53000, True, bad, bae) → EQ
new_primPlusNat1(Zero, xuu400100) → Succ(xuu400100)
new_esEs32(xuu41, xuu36, app(ty_Ratio, fd)) → new_esEs10(xuu41, xuu36, fd)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_[], dgb), cd) → new_ltEs14(xuu52000, xuu53000, dgb)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Char, cd) → new_ltEs6(xuu52000, xuu53000)
new_esEs22(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs21(xuu50002, xuu4002, app(app(ty_Either, cag), cah)) → new_esEs4(xuu50002, xuu4002, cag, cah)
new_compare29(xuu52000, xuu53000) → new_compare210(xuu52000, xuu53000, new_esEs9(xuu52000, xuu53000))
new_esEs32(xuu41, xuu36, ty_Char) → new_esEs17(xuu41, xuu36)
new_esEs22(xuu50001, xuu4001, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs5(xuu50001, xuu4001, cbe, cbf, cbg)
new_esEs18(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_compare8(xuu52000, xuu53000, fa, fb, fc) → new_compare24(xuu52000, xuu53000, new_esEs5(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Char, baf) → new_esEs17(xuu50000, xuu4000)
new_esEs26(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, ty_Float) → new_esEs13(xuu5000, xuu400)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(xuu5200, xuu5300) → new_fsEs(new_compare6(xuu5200, xuu5300))
new_ltEs20(xuu52002, xuu53002, ty_Double) → new_ltEs15(xuu52002, xuu53002)
new_ltEs16(GT, LT) → False
new_compare6(xuu52, xuu53) → new_primCmpInt(xuu52, xuu53)
new_esEs19(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_ltEs4(xuu5200, xuu5300, app(app(ty_@2, db), dc)) → new_ltEs11(xuu5200, xuu5300, db, dc)
new_esEs29(xuu22, xuu17, ty_Float) → new_esEs13(xuu22, xuu17)
new_compare13(Double(xuu52000, xuu52001), Double(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_primCmpNat0(Succ(xuu52000), Succ(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_ltEs9(xuu5200, xuu5300, ce) → new_fsEs(new_compare7(xuu5200, xuu5300, ce))
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs5(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_compare10(xuu167, xuu168, False, dhe, dhf) → GT
new_lt11(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_lt5(xuu52000, xuu53000, eh) → new_esEs8(new_compare7(xuu52000, xuu53000, eh), LT)
new_ltEs21(xuu52001, xuu53001, ty_Float) → new_ltEs13(xuu52001, xuu53001)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(app(ty_@3, dgf), dgg), dgh)) → new_ltEs10(xuu52000, xuu53000, dgf, dgg, dgh)
new_compare14(Integer(xuu52000), Integer(xuu53000)) → new_primCmpInt(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Float, cd) → new_ltEs13(xuu52000, xuu53000)
new_esEs19(xuu50001, xuu4001, app(app(ty_@2, bgc), bgd)) → new_esEs6(xuu50001, xuu4001, bgc, bgd)
new_ltEs5(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(ty_Maybe, dd)) → new_ltEs12(xuu5200, xuu5300, dd)
new_lt7(xuu52000, xuu53000) → new_esEs8(new_compare14(xuu52000, xuu53000), LT)
new_esEs30(xuu5000, xuu400, ty_Int) → new_esEs14(xuu5000, xuu400)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Bool, baf) → new_esEs9(xuu50000, xuu4000)
new_esEs24(xuu52001, xuu53001, ty_Ordering) → new_esEs8(xuu52001, xuu53001)
new_esEs18(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_@2, dfg), dfh), cd) → new_ltEs11(xuu52000, xuu53000, dfg, dfh)
new_lt6(xuu52000, xuu53000) → new_esEs8(new_compare13(xuu52000, xuu53000), LT)
new_ltEs4(xuu5200, xuu5300, app(ty_[], de)) → new_ltEs14(xuu5200, xuu5300, de)
new_lt12(xuu52001, xuu53001, ty_@0) → new_lt14(xuu52001, xuu53001)
new_esEs7(Nothing, Nothing, gh) → True
new_esEs15([], [], bdf) → True
new_lt20(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_lt5(xuu52000, xuu53000, dab)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_esEs18(xuu50000, xuu4000, app(ty_Maybe, bef)) → new_esEs7(xuu50000, xuu4000, bef)
new_lt4(xuu520, xuu530) → new_esEs8(new_compare6(xuu520, xuu530), LT)
new_ltEs20(xuu52002, xuu53002, app(ty_Maybe, cgd)) → new_ltEs12(xuu52002, xuu53002, cgd)
new_primPlusNat0(Succ(xuu55200), Zero) → Succ(xuu55200)
new_primPlusNat0(Zero, Succ(xuu13100)) → Succ(xuu13100)
new_compare31(xuu52000, xuu53000, ty_Integer) → new_compare14(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(app(app(ty_@3, dch), dda), ddb)) → new_compare8(xuu52000, xuu53000, dch, dda, ddb)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_esEs19(xuu50001, xuu4001, app(ty_[], bfg)) → new_esEs15(xuu50001, xuu4001, bfg)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu52000), Zero) → GT
new_lt11(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs5(xuu50000, xuu4000, bcc, bcd, bce)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Maybe, dga), cd) → new_ltEs12(xuu52000, xuu53000, dga)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_[], deh)) → new_ltEs14(xuu52000, xuu53000, deh)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu5300))) → LT
new_compare11(xuu174, xuu175, True, cdh, cea) → LT
new_ltEs21(xuu52001, xuu53001, ty_Ordering) → new_ltEs16(xuu52001, xuu53001)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_esEs23(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_lt20(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_sr0(Integer(xuu530000), Integer(xuu520010)) → Integer(new_primMulInt(xuu530000, xuu520010))
new_esEs31(xuu5000, xuu400, ty_Int) → new_esEs14(xuu5000, xuu400)
new_ltEs5(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_esEs31(xuu5000, xuu400, app(ty_Ratio, cgf)) → new_esEs10(xuu5000, xuu400, cgf)
new_ltEs20(xuu52002, xuu53002, app(ty_[], cge)) → new_ltEs14(xuu52002, xuu53002, cge)
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_esEs7(Just(xuu50000), Nothing, gh) → False
new_esEs7(Nothing, Just(xuu4000), gh) → False
new_esEs13(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Maybe, deg)) → new_ltEs12(xuu52000, xuu53000, deg)
new_esEs24(xuu52001, xuu53001, ty_Int) → new_esEs14(xuu52001, xuu53001)
new_ltEs4(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_esEs30(xuu5000, xuu400, ty_Integer) → new_esEs12(xuu5000, xuu400)
new_esEs22(xuu50001, xuu4001, app(app(ty_@2, ccd), cce)) → new_esEs6(xuu50001, xuu4001, ccd, cce)
new_ltEs20(xuu52002, xuu53002, ty_Integer) → new_ltEs18(xuu52002, xuu53002)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_Either, ddg), ddh)) → new_ltEs8(xuu52000, xuu53000, ddg, ddh)
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_esEs18(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_ltEs20(xuu52002, xuu53002, app(app(ty_@2, cgb), cgc)) → new_ltEs11(xuu52002, xuu53002, cgb, cgc)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Maybe, dhc)) → new_ltEs12(xuu52000, xuu53000, dhc)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_@0, cd) → new_ltEs7(xuu52000, xuu53000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Ratio, ccf)) → new_esEs10(xuu50000, xuu4000, ccf)
new_esEs6(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), bfa, bfb) → new_asAs(new_esEs20(xuu50000, xuu4000, bfa), new_esEs19(xuu50001, xuu4001, bfb))
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Integer, baf) → new_esEs12(xuu50000, xuu4000)
new_lt20(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_lt9(xuu52000, xuu53000, dac, dad, dae)
new_ltEs16(EQ, EQ) → True
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Double, baf) → new_esEs16(xuu50000, xuu4000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Ratio, dfc), cd) → new_ltEs9(xuu52000, xuu53000, dfc)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_compare31(xuu52000, xuu53000, app(app(ty_Either, dce), dcf)) → new_compare19(xuu52000, xuu53000, dce, dcf)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_lt12(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_lt15(xuu52001, xuu53001, ceh, cfa)
new_primCompAux0(xuu218, LT) → LT
new_lt20(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, app(ty_Ratio, dcd)) → new_esEs10(xuu5000, xuu400, dcd)
new_not(False) → True
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_Either, dgc), dgd)) → new_ltEs8(xuu52000, xuu53000, dgc, dgd)
new_esEs20(xuu50000, xuu4000, app(ty_Ratio, bge)) → new_esEs10(xuu50000, xuu4000, bge)
new_esEs29(xuu22, xuu17, ty_Integer) → new_esEs12(xuu22, xuu17)
new_compare12(xuu52000, xuu53000, False, fa, fb, fc) → GT
new_esEs23(xuu50000, xuu4000, app(app(ty_@2, cdf), cdg)) → new_esEs6(xuu50000, xuu4000, cdf, cdg)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(app(ty_@2, ddc), ddd)) → new_compare17(xuu52000, xuu53000, ddc, ddd)
new_lt11(xuu52000, xuu53000, app(ty_[], bac)) → new_lt8(xuu52000, xuu53000, bac)
new_esEs30(xuu5000, xuu400, app(app(ty_Either, bca), baf)) → new_esEs4(xuu5000, xuu400, bca, baf)
new_esEs19(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_esEs32(xuu41, xuu36, ty_Ordering) → new_esEs8(xuu41, xuu36)
new_ltEs21(xuu52001, xuu53001, ty_Int) → new_ltEs19(xuu52001, xuu53001)
new_ltEs10(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), cf, cg, da) → new_pePe(new_lt11(xuu52000, xuu53000, cf), new_asAs(new_esEs25(xuu52000, xuu53000, cf), new_pePe(new_lt12(xuu52001, xuu53001, cg), new_asAs(new_esEs24(xuu52001, xuu53001, cg), new_ltEs20(xuu52002, xuu53002, da)))))
new_ltEs5(xuu5200, xuu5300, app(app(ty_@2, ed), ee)) → new_ltEs11(xuu5200, xuu5300, ed, ee)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_@2, dee), def)) → new_ltEs11(xuu52000, xuu53000, dee, def)
new_esEs24(xuu52001, xuu53001, ty_Integer) → new_esEs12(xuu52001, xuu53001)
new_esEs32(xuu41, xuu36, app(ty_[], ga)) → new_esEs15(xuu41, xuu36, ga)
new_lt20(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_compare28(xuu52000, xuu53000, True) → EQ
new_lt20(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_lt12(xuu52001, xuu53001, ty_Double) → new_lt6(xuu52001, xuu53001)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_@2, bdb), bdc)) → new_esEs6(xuu50000, xuu4000, bdb, bdc)
new_lt11(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_lt5(xuu52000, xuu53000, eh)
new_esEs18(xuu50000, xuu4000, app(app(ty_Either, bed), bee)) → new_esEs4(xuu50000, xuu4000, bed, bee)
new_esEs9(True, True) → True
new_compare11(xuu174, xuu175, False, cdh, cea) → GT
new_lt11(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_esEs20(xuu50000, xuu4000, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs5(xuu50000, xuu4000, bgf, bgg, bgh)
new_primCmpInt(Pos(Succ(xuu5200)), Neg(xuu530)) → GT
new_lt8(xuu52000, xuu53000, bac) → new_esEs8(new_compare1(xuu52000, xuu53000, bac), LT)
new_esEs30(xuu5000, xuu400, ty_@0) → new_esEs11(xuu5000, xuu400)
new_esEs21(xuu50002, xuu4002, app(app(app(ty_@3, cac), cad), cae)) → new_esEs5(xuu50002, xuu4002, cac, cad, cae)
new_esEs21(xuu50002, xuu4002, app(ty_Maybe, cba)) → new_esEs7(xuu50002, xuu4002, cba)
new_ltEs4(xuu5200, xuu5300, app(ty_Ratio, ce)) → new_ltEs9(xuu5200, xuu5300, ce)
new_primMulInt(Pos(xuu500010), Pos(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_lt12(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_lt9(xuu52001, xuu53001, cee, cef, ceg)
new_esEs18(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(app(ty_Either, cdc), cdd)) → new_esEs4(xuu50000, xuu4000, cdc, cdd)
new_ltEs20(xuu52002, xuu53002, ty_Bool) → new_ltEs17(xuu52002, xuu53002)
new_lt20(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_lt10(xuu52000, xuu53000, chh, daa)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Maybe, bbf), baf) → new_esEs7(xuu50000, xuu4000, bbf)
new_compare23(Right(xuu5200), Left(xuu5300), False, ca, cb) → GT
new_primMulInt(Neg(xuu500010), Neg(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_ltEs5(xuu5200, xuu5300, app(ty_Maybe, ef)) → new_ltEs12(xuu5200, xuu5300, ef)
new_compare110(xuu52000, xuu53000, True) → LT
new_esEs29(xuu22, xuu17, app(app(ty_@2, eag), eah)) → new_esEs6(xuu22, xuu17, eag, eah)
new_esEs21(xuu50002, xuu4002, app(ty_Ratio, cab)) → new_esEs10(xuu50002, xuu4002, cab)
new_lt20(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, app(ty_Maybe, gh)) → new_esEs7(xuu5000, xuu400, gh)
new_primEqNat0(Succ(xuu500000), Zero) → False
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_Either, dfa), dfb), cd) → new_ltEs8(xuu52000, xuu53000, dfa, dfb)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(app(ty_@3, deb), dec), ded)) → new_ltEs10(xuu52000, xuu53000, deb, dec, ded)
new_compare110(xuu52000, xuu53000, False) → GT
new_ltEs6(xuu5200, xuu5300) → new_fsEs(new_compare15(xuu5200, xuu5300))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_esEs4(xuu52001, xuu53001, ceb, cec)
new_compare17(xuu52000, xuu53000, bad, bae) → new_compare26(xuu52000, xuu53000, new_esEs6(xuu52000, xuu53000, bad, bae), bad, bae)
new_ltEs21(xuu52001, xuu53001, app(ty_Ratio, dbd)) → new_ltEs9(xuu52001, xuu53001, dbd)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Ordering, cd) → new_ltEs16(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, ty_Bool) → new_esEs9(xuu50002, xuu4002)
new_esEs11(@0, @0) → True
new_compare210(xuu52000, xuu53000, True) → EQ
new_esEs25(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs10(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), dcd) → new_asAs(new_esEs28(xuu50000, xuu4000, dcd), new_esEs27(xuu50001, xuu4001, dcd))
new_ltEs20(xuu52002, xuu53002, ty_Ordering) → new_ltEs16(xuu52002, xuu53002)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Int, baf) → new_esEs14(xuu50000, xuu4000)
new_compare31(xuu52000, xuu53000, ty_Char) → new_compare15(xuu52000, xuu53000)
new_primPlusNat1(Succ(xuu1400), xuu400100) → Succ(Succ(new_primPlusNat0(xuu1400, xuu400100)))
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_esEs29(xuu22, xuu17, app(app(app(ty_@3, dhh), eaa), eab)) → new_esEs5(xuu22, xuu17, dhh, eaa, eab)
new_esEs22(xuu50001, xuu4001, app(ty_[], cbh)) → new_esEs15(xuu50001, xuu4001, cbh)
new_esEs21(xuu50002, xuu4002, ty_Char) → new_esEs17(xuu50002, xuu4002)
new_ltEs4(xuu5200, xuu5300, app(app(ty_Either, cc), cd)) → new_ltEs8(xuu5200, xuu5300, cc, cd)
new_esEs18(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_compare23(xuu520, xuu530, True, ca, cb) → EQ
new_lt20(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_lt15(xuu52000, xuu53000, daf, dag)
new_esEs20(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu5300))) → GT
new_esEs32(xuu41, xuu36, ty_Float) → new_esEs13(xuu41, xuu36)
new_ltEs20(xuu52002, xuu53002, ty_Float) → new_ltEs13(xuu52002, xuu53002)
new_compare31(xuu52000, xuu53000, app(ty_Ratio, dcg)) → new_compare7(xuu52000, xuu53000, dcg)
new_esEs15(:(xuu50000, xuu50001), [], bdf) → False
new_esEs15([], :(xuu4000, xuu4001), bdf) → False
new_ltEs21(xuu52001, xuu53001, app(ty_Maybe, dcb)) → new_ltEs12(xuu52001, xuu53001, dcb)
new_esEs18(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_esEs7(xuu52000, xuu53000, gg)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, hb), hc), hd)) → new_esEs5(xuu50000, xuu4000, hb, hc, hd)
new_esEs9(False, True) → False
new_esEs9(True, False) → False
new_lt12(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_lt10(xuu52001, xuu53001, ceb, cec)
new_compare32(Float(xuu52000, xuu52001), Float(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_ltEs7(xuu5200, xuu5300) → new_fsEs(new_compare27(xuu5200, xuu5300))
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_compare31(xuu52000, xuu53000, ty_Double) → new_compare13(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, ty_Float) → new_esEs13(xuu50002, xuu4002)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCompAux1(xuu52000, xuu53000, xuu204, de) → new_primCompAux0(xuu204, new_compare31(xuu52000, xuu53000, de))
new_esEs7(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs26(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_asAs(False, xuu162) → False
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_ltEs13(xuu5200, xuu5300) → new_fsEs(new_compare32(xuu5200, xuu5300))
new_primMulInt(Pos(xuu500010), Neg(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Neg(xuu500010), Pos(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_compare23(Left(xuu5200), Right(xuu5300), False, ca, cb) → LT
new_primCmpInt(Neg(Succ(xuu5200)), Neg(xuu530)) → new_primCmpNat2(xuu530, xuu5200)
new_primMulNat0(Succ(xuu5000100), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu400100)) → Zero
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Int, cd) → new_ltEs19(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, ty_Ordering) → new_esEs8(xuu50002, xuu4002)
new_compare26(xuu52000, xuu53000, False, bad, bae) → new_compare111(xuu52000, xuu53000, new_ltEs11(xuu52000, xuu53000, bad, bae), bad, bae)
new_esEs31(xuu5000, xuu400, ty_Double) → new_esEs16(xuu5000, xuu400)
new_esEs26(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_esEs7(xuu52000, xuu53000, dah)
new_esEs29(xuu22, xuu17, ty_Char) → new_esEs17(xuu22, xuu17)
new_lt18(xuu52000, xuu53000) → new_esEs8(new_compare30(xuu52000, xuu53000), LT)
new_ltEs21(xuu52001, xuu53001, ty_Double) → new_ltEs15(xuu52001, xuu53001)
new_ltEs8(Right(xuu52000), Left(xuu53000), cc, cd) → False
new_esEs18(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, app(ty_[], bha)) → new_esEs15(xuu50000, xuu4000, bha)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Maybe, bda)) → new_esEs7(xuu50000, xuu4000, bda)
new_ltEs17(True, True) → True
new_ltEs14(xuu5200, xuu5300, de) → new_fsEs(new_compare1(xuu5200, xuu5300, de))
new_lt11(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_compare18(xuu52000, xuu53000, True, gg) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(xuu5300))) → new_primCmpNat2(Zero, xuu5300)
new_esEs29(xuu22, xuu17, app(ty_Ratio, dhg)) → new_esEs10(xuu22, xuu17, dhg)
new_lt13(xuu52000, xuu53000) → new_esEs8(new_compare15(xuu52000, xuu53000), LT)
new_esEs24(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_esEs10(xuu52001, xuu53001, ced)
new_ltEs12(Nothing, Just(xuu53000), dd) → True
new_esEs23(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Double, cd) → new_ltEs15(xuu52000, xuu53000)
new_ltEs5(xuu5200, xuu5300, app(ty_[], eg)) → new_ltEs14(xuu5200, xuu5300, eg)
new_ltEs4(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_compare210(xuu52000, xuu53000, False) → new_compare16(xuu52000, xuu53000, new_ltEs17(xuu52000, xuu53000))
new_esEs20(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_compare18(xuu52000, xuu53000, False, gg) → GT
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_Either, hf), hg)) → new_esEs4(xuu50000, xuu4000, hf, hg)
new_esEs9(False, False) → True
new_esEs22(xuu50001, xuu4001, app(ty_Ratio, cbd)) → new_esEs10(xuu50001, xuu4001, cbd)
new_esEs26(xuu52000, xuu53000, app(ty_[], dba)) → new_esEs15(xuu52000, xuu53000, dba)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Float, baf) → new_esEs13(xuu50000, xuu4000)
new_ltEs5(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_esEs14(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs17(xuu50000, xuu4000)
new_lt12(xuu52001, xuu53001, ty_Int) → new_lt4(xuu52001, xuu53001)
new_lt11(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Integer, cd) → new_ltEs18(xuu52000, xuu53000)
new_esEs32(xuu41, xuu36, app(app(ty_Either, gb), gc)) → new_esEs4(xuu41, xuu36, gb, gc)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, app(ty_Ratio, bfc)) → new_esEs10(xuu50001, xuu4001, bfc)
new_esEs30(xuu5000, xuu400, app(app(ty_@2, bfa), bfb)) → new_esEs6(xuu5000, xuu400, bfa, bfb)
new_esEs31(xuu5000, xuu400, ty_Float) → new_esEs13(xuu5000, xuu400)
new_esEs20(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_ltEs17(False, True) → True
new_esEs25(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_esEs5(xuu52000, xuu53000, fa, fb, fc)
new_ltEs21(xuu52001, xuu53001, ty_Bool) → new_ltEs17(xuu52001, xuu53001)
new_ltEs4(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_esEs29(xuu22, xuu17, ty_@0) → new_esEs11(xuu22, xuu17)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs13(xuu50000, xuu4000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, ty_Char) → new_esEs17(xuu5000, xuu400)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu5300))) → new_primCmpNat1(xuu5300, Zero)
new_ltEs21(xuu52001, xuu53001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_ltEs10(xuu52001, xuu53001, dbe, dbf, dbg)
new_esEs30(xuu5000, xuu400, ty_Ordering) → new_esEs8(xuu5000, xuu400)
new_esEs22(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs14(xuu50000, xuu4000)
new_compare31(xuu52000, xuu53000, app(ty_[], ddf)) → new_compare1(xuu52000, xuu53000, ddf)
new_esEs22(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs24(xuu52001, xuu53001, ty_Bool) → new_esEs9(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Float) → new_lt17(xuu52001, xuu53001)
new_ltEs20(xuu52002, xuu53002, ty_Char) → new_ltEs6(xuu52002, xuu53002)
new_esEs20(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_primPlusNat0(Succ(xuu55200), Succ(xuu13100)) → Succ(Succ(new_primPlusNat0(xuu55200, xuu13100)))
new_ltEs4(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_ltEs21(xuu52001, xuu53001, ty_Integer) → new_ltEs18(xuu52001, xuu53001)
new_compare23(Right(xuu5200), Right(xuu5300), False, ca, cb) → new_compare11(xuu5200, xuu5300, new_ltEs5(xuu5200, xuu5300, cb), ca, cb)
new_esEs21(xuu50002, xuu4002, ty_@0) → new_esEs11(xuu50002, xuu4002)
new_compare111(xuu52000, xuu53000, True, bad, bae) → LT
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Ratio, dge)) → new_ltEs9(xuu52000, xuu53000, dge)
new_esEs26(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_esEs4(xuu52000, xuu53000, chh, daa)
new_asAs(True, xuu162) → xuu162
new_esEs19(xuu50001, xuu4001, app(app(ty_Either, bfh), bga)) → new_esEs4(xuu50001, xuu4001, bfh, bga)
new_esEs32(xuu41, xuu36, ty_Integer) → new_esEs12(xuu41, xuu36)
new_compare27(@0, @0) → EQ
new_lt12(xuu52001, xuu53001, ty_Bool) → new_lt19(xuu52001, xuu53001)
new_esEs19(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs26(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_esEs5(xuu52000, xuu53000, dac, dad, dae)
new_esEs4(Left(xuu50000), Right(xuu4000), bca, baf) → False
new_esEs4(Right(xuu50000), Left(xuu4000), bca, baf) → False
new_esEs31(xuu5000, xuu400, app(ty_Maybe, che)) → new_esEs7(xuu5000, xuu400, che)
new_ltEs5(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_ltEs20(xuu52002, xuu53002, app(app(ty_Either, cfd), cfe)) → new_ltEs8(xuu52002, xuu53002, cfd, cfe)
new_esEs32(xuu41, xuu36, ty_Double) → new_esEs16(xuu41, xuu36)
new_ltEs16(LT, LT) → True
new_ltEs12(Just(xuu52000), Nothing, dd) → False
new_compare1(:(xuu52000, xuu52001), [], de) → GT
new_lt16(xuu52000, xuu53000, gg) → new_esEs8(new_compare9(xuu52000, xuu53000, gg), LT)
new_fsEs(xuu177) → new_not(new_esEs8(xuu177, GT))
new_esEs24(xuu52001, xuu53001, ty_Float) → new_esEs13(xuu52001, xuu53001)
new_esEs26(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_esEs6(xuu52000, xuu53000, daf, dag)
new_esEs23(xuu50000, xuu4000, app(app(app(ty_@3, ccg), cch), cda)) → new_esEs5(xuu50000, xuu4000, ccg, cch, cda)
new_esEs19(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs26(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_esEs29(xuu22, xuu17, app(ty_[], eac)) → new_esEs15(xuu22, xuu17, eac)
new_ltEs20(xuu52002, xuu53002, app(app(app(ty_@3, cfg), cfh), cga)) → new_ltEs10(xuu52002, xuu53002, cfg, cfh, cga)
new_esEs30(xuu5000, xuu400, ty_Double) → new_esEs16(xuu5000, xuu400)
new_ltEs8(Left(xuu52000), Right(xuu53000), cc, cd) → True
new_esEs21(xuu50002, xuu4002, ty_Integer) → new_esEs12(xuu50002, xuu4002)
new_lt17(xuu52000, xuu53000) → new_esEs8(new_compare32(xuu52000, xuu53000), LT)
new_esEs30(xuu5000, xuu400, app(app(app(ty_@3, bhg), bhh), caa)) → new_esEs5(xuu5000, xuu400, bhg, bhh, caa)
new_lt11(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, app(ty_[], bdf)) → new_esEs15(xuu5000, xuu400, bdf)
new_lt11(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_lt16(xuu52000, xuu53000, gg)
new_ltEs5(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_lt12(xuu52001, xuu53001, ty_Integer) → new_lt7(xuu52001, xuu53001)
new_esEs31(xuu5000, xuu400, app(app(ty_@2, chf), chg)) → new_esEs6(xuu5000, xuu400, chf, chg)
new_ltEs15(xuu5200, xuu5300) → new_fsEs(new_compare13(xuu5200, xuu5300))
new_esEs18(xuu50000, xuu4000, app(ty_[], bec)) → new_esEs15(xuu50000, xuu4000, bec)
new_compare28(xuu52000, xuu53000, False) → new_compare110(xuu52000, xuu53000, new_ltEs16(xuu52000, xuu53000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(xuu218, EQ) → xuu218
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Int) → new_compare6(new_sr(xuu52000, xuu53001), new_sr(xuu53000, xuu52001))
new_esEs29(xuu22, xuu17, ty_Ordering) → new_esEs8(xuu22, xuu17)
new_esEs24(xuu52001, xuu53001, app(ty_[], cfc)) → new_esEs15(xuu52001, xuu53001, cfc)
new_esEs18(xuu50000, xuu4000, app(ty_Ratio, bdg)) → new_esEs10(xuu50000, xuu4000, bdg)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs16(xuu50000, xuu4000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(xuu50001, xuu4001, app(ty_Maybe, ccc)) → new_esEs7(xuu50001, xuu4001, ccc)
new_primCmpInt(Neg(Succ(xuu5200)), Pos(xuu530)) → LT
new_not(True) → False
new_compare16(xuu52000, xuu53000, False) → GT
new_compare1([], [], de) → EQ

The set Q consists of the following terms:

new_primCompAux0(x0, EQ)
new_ltEs4(x0, x1, ty_Bool)
new_ltEs5(x0, x1, ty_Float)
new_compare29(x0, x1)
new_fsEs(x0)
new_primCompAux0(x0, GT)
new_esEs19(x0, x1, ty_Bool)
new_esEs18(x0, x1, ty_@0)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3)
new_compare16(x0, x1, False)
new_esEs32(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_compare9(x0, x1, x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, False)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Char)
new_compare8(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Double)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare23(x0, x1, True, x2, x3)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1)
new_compare17(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs31(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Float)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs11(@0, @0)
new_compare10(x0, x1, True, x2, x3)
new_compare111(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_ltEs4(x0, x1, ty_Int)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs8(GT, GT)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_primCmpNat1(x0, Zero)
new_ltEs21(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs4(x0, x1, ty_Integer)
new_esEs7(Nothing, Just(x0), x1)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_ltEs4(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(LT, LT)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, x2)
new_esEs21(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Ordering)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_@0)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Int)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, ty_Integer)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs7(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(False, False)
new_esEs7(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Integer)
new_ltEs4(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(ty_[], x2))
new_compare1(:(x0, x1), [], x2)
new_compare24(x0, x1, False, x2, x3, x4)
new_primEqNat0(Zero, Zero)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs9(True, True)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs29(x0, x1, ty_Double)
new_lt10(x0, x1, x2, x3)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(x0, Succ(x1))
new_primMulNat0(Zero, Zero)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs18(x0, x1)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Integer)
new_ltEs17(True, True)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(Left(x0), Left(x1), False, x2, x3)
new_esEs29(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_lt12(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare14(Integer(x0), Integer(x1))
new_primCmpNat0(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Zero)
new_compare23(Right(x0), Right(x1), False, x2, x3)
new_esEs24(x0, x1, ty_Bool)
new_primCompAux1(x0, x1, x2, x3)
new_esEs7(Nothing, Nothing, x0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1)
new_ltEs4(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(x0, x1, ty_Integer)
new_pePe(False, x0)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_compare1([], :(x0, x1), x2)
new_ltEs21(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_ltEs6(x0, x1)
new_ltEs12(Just(x0), Nothing, x1)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(Float(x0, x1), Float(x2, x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs30(x0, x1, ty_Float)
new_lt12(x0, x1, ty_Int)
new_esEs17(Char(x0), Char(x1))
new_esEs19(x0, x1, ty_Char)
new_primPlusNat0(Zero, Zero)
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs16(EQ, EQ)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Zero)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare25(x0, x1, True, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_esEs19(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_compare28(x0, x1, False)
new_esEs18(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Float)
new_compare16(x0, x1, True)
new_esEs23(x0, x1, ty_Float)
new_esEs18(x0, x1, ty_Int)
new_ltEs16(LT, GT)
new_ltEs16(GT, LT)
new_esEs25(x0, x1, ty_@0)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1)
new_primPlusNat1(Succ(x0), x1)
new_pePe(True, x0)
new_lt11(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt11(x0, x1, ty_Ordering)
new_primCompAux0(x0, LT)
new_esEs25(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_lt12(x0, x1, ty_Bool)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1)
new_compare10(x0, x1, False, x2, x3)
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1, x2)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Bool)
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt15(x0, x1, x2, x3)
new_primPlusNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare31(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_asAs(True, x0)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare26(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs32(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare31(x0, x1, ty_Char)
new_compare210(x0, x1, False)
new_ltEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Integer)
new_ltEs16(GT, GT)
new_esEs18(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_@0)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Double)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs13(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs5(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_primCmpNat2(Succ(x0), x1)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs14(x0, x1)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_compare18(x0, x1, True, x2)
new_esEs30(x0, x1, ty_Integer)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_compare13(Double(x0, x1), Double(x2, x3))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, x0)
new_compare31(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare15(Char(x0), Char(x1))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCmpNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare23(Left(x0), Right(x1), False, x2, x3)
new_compare23(Right(x0), Left(x1), False, x2, x3)
new_ltEs12(Nothing, Nothing, x0)
new_esEs18(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Char)
new_ltEs12(Nothing, Just(x0), x1)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Int)
new_esEs9(False, False)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs18(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_compare6(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Bool)
new_compare31(x0, x1, ty_Ordering)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs4(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_ltEs4(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Double)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_compare18(x0, x1, False, x2)
new_compare26(x0, x1, False, x2, x3)
new_esEs30(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_not(True)
new_ltEs19(x0, x1)
new_esEs20(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs21(x0, x1, ty_Float)
new_lt11(x0, x1, ty_Int)
new_lt9(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, x0)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_lt11(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_ltEs17(False, True)
new_ltEs17(True, False)
new_ltEs20(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_lt12(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, True)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt6(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Int)
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_compare28(x0, x1, True)
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs9(False, True)
new_esEs9(True, False)
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_ltEs20(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare31(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs15([], :(x0, x1), x2)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs15(:(x0, x1), [], x2)
new_esEs21(x0, x1, ty_Bool)
new_ltEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_compare27(@0, @0)
new_lt11(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs30(x0, x1, ty_@0)
new_lt11(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Integer)
new_ltEs9(x0, x1, x2)
new_compare25(x0, x1, False, x2)
new_esEs30(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt8(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs32(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs20(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_esEs29(x0, x1, ty_Int)
new_esEs15([], [], x0)
new_lt12(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_sr(x0, x1)
new_esEs31(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)

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
                                          ↳ UsableRulesProof
                                        ↳ QDP
                                  ↳ QDP

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

new_addToFM_C(xuu3, Branch(Left(xuu400), xuu41, xuu42, xuu43, xuu44), Right(xuu5000), xuu501, bc, bd, be) → new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Right(xuu5000), Left(xuu400), False, bc, bd), LT), bc, bd, be)
new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, False, bc, bd, be) → new_addToFM_C11(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Right(xuu5000), Left(xuu400), False, bc, bd), GT), bc, bd, be)
new_addToFM_C11(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu44, Right(xuu5000), xuu501, bc, bd, be)
new_addToFM_C(xuu3, Branch(Right(xuu400), xuu41, xuu42, xuu43, xuu44), Right(xuu5000), xuu501, bc, bd, be) → new_addToFM_C22(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Right(xuu5000), Right(xuu400), new_esEs31(xuu5000, xuu400, bd), bc, bd), LT), bc, bd, be)
new_addToFM_C12(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, True, bf, bg, bh) → new_addToFM_C(xuu35, xuu40, Right(xuu41), xuu42, bf, bg, bh)
new_addToFM_C22(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, False, bf, bg, bh) → new_addToFM_C12(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, new_esEs8(new_compare23(Right(xuu41), Right(xuu36), new_esEs32(xuu41, xuu36, bg), bf, bg), GT), bf, bg, bh)
new_addToFM_C22(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, True, bf, bg, bh) → new_addToFM_C(xuu35, xuu39, Right(xuu41), xuu42, bf, bg, bh)
new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu43, Right(xuu5000), xuu501, bc, bd, be)

The TRS R consists of the following rules:

new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Maybe, hh)) → new_esEs7(xuu50000, xuu4000, hh)
new_esEs20(xuu50000, xuu4000, app(ty_Maybe, bhd)) → new_esEs7(xuu50000, xuu4000, bhd)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_[], he)) → new_esEs15(xuu50000, xuu4000, he)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs21(xuu50002, xuu4002, app(app(ty_@2, cbb), cbc)) → new_esEs6(xuu50002, xuu4002, cbb, cbc)
new_ltEs16(GT, GT) → True
new_primCmpNat2(Zero, xuu5200) → LT
new_compare31(xuu52000, xuu53000, ty_Int) → new_compare6(xuu52000, xuu53000)
new_ltEs17(False, False) → True
new_esEs31(xuu5000, xuu400, ty_@0) → new_esEs11(xuu5000, xuu400)
new_esEs25(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_compare9(xuu52000, xuu53000, gg) → new_compare25(xuu52000, xuu53000, new_esEs7(xuu52000, xuu53000, gg), gg)
new_compare23(Left(xuu5200), Left(xuu5300), False, ca, cb) → new_compare10(xuu5200, xuu5300, new_ltEs4(xuu5200, xuu5300, ca), ca, cb)
new_esEs18(xuu50000, xuu4000, app(app(ty_@2, beg), beh)) → new_esEs6(xuu50000, xuu4000, beg, beh)
new_compare1(:(xuu52000, xuu52001), :(xuu53000, xuu53001), de) → new_primCompAux1(xuu52000, xuu53000, new_compare1(xuu52001, xuu53001, de), de)
new_esEs24(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs5(xuu52001, xuu53001, cee, cef, ceg)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Bool, cd) → new_ltEs17(xuu52000, xuu53000)
new_esEs18(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_ltEs20(xuu52002, xuu53002, app(ty_Ratio, cff)) → new_ltEs9(xuu52002, xuu53002, cff)
new_esEs17(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_esEs31(xuu5000, xuu400, ty_Ordering) → new_esEs8(xuu5000, xuu400)
new_esEs24(xuu52001, xuu53001, ty_Char) → new_esEs17(xuu52001, xuu53001)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_compare10(xuu167, xuu168, True, dhe, dhf) → LT
new_compare31(xuu52000, xuu53000, app(ty_Maybe, dde)) → new_compare9(xuu52000, xuu53000, dde)
new_lt12(xuu52001, xuu53001, app(ty_[], cfc)) → new_lt8(xuu52001, xuu53001, cfc)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_ltEs16(LT, GT) → True
new_ltEs5(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs31(xuu5000, xuu400, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs5(xuu5000, xuu400, cgg, cgh, cha)
new_ltEs4(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_esEs21(xuu50002, xuu4002, ty_Int) → new_esEs14(xuu50002, xuu4002)
new_ltEs12(Nothing, Nothing, dd) → True
new_esEs26(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_compare19(xuu52000, xuu53000, bdd, bde) → new_compare23(xuu52000, xuu53000, new_esEs4(xuu52000, xuu53000, bdd, bde), bdd, bde)
new_primMulNat0(Zero, Zero) → Zero
new_lt20(xuu52000, xuu53000, app(ty_[], dba)) → new_lt8(xuu52000, xuu53000, dba)
new_esEs26(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_esEs10(xuu52000, xuu53000, dab)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_esEs15(:(xuu50000, xuu50001), :(xuu4000, xuu4001), bdf) → new_asAs(new_esEs18(xuu50000, xuu4000, bdf), new_esEs15(xuu50001, xuu4001, bdf))
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_[], bbc), baf) → new_esEs15(xuu50000, xuu4000, bbc)
new_compare25(xuu52000, xuu53000, True, gg) → EQ
new_ltEs5(xuu5200, xuu5300, app(app(app(ty_@3, ea), eb), ec)) → new_ltEs10(xuu5200, xuu5300, ea, eb, ec)
new_esEs22(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_compare24(xuu52000, xuu53000, False, fa, fb, fc) → new_compare12(xuu52000, xuu53000, new_ltEs10(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_lt9(xuu52000, xuu53000, fa, fb, fc) → new_esEs8(new_compare8(xuu52000, xuu53000, fa, fb, fc), LT)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, app(ty_[], caf)) → new_esEs15(xuu50002, xuu4002, caf)
new_ltEs4(xuu5200, xuu5300, app(app(app(ty_@3, cf), cg), da)) → new_ltEs10(xuu5200, xuu5300, cf, cg, da)
new_lt12(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_lt5(xuu52001, xuu53001, ced)
new_lt14(xuu52000, xuu53000) → new_esEs8(new_compare27(xuu52000, xuu53000), LT)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_[], bcf)) → new_esEs15(xuu50000, xuu4000, bcf)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs29(xuu22, xuu17, app(app(ty_Either, ead), eae)) → new_esEs4(xuu22, xuu17, ead, eae)
new_ltEs18(xuu5200, xuu5300) → new_fsEs(new_compare14(xuu5200, xuu5300))
new_compare1([], :(xuu53000, xuu53001), de) → LT
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_esEs29(xuu22, xuu17, app(ty_Maybe, eaf)) → new_esEs7(xuu22, xuu17, eaf)
new_esEs20(xuu50000, xuu4000, app(app(ty_Either, bhb), bhc)) → new_esEs4(xuu50000, xuu4000, bhb, bhc)
new_lt11(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_esEs23(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_compare30(xuu52000, xuu53000) → new_compare28(xuu52000, xuu53000, new_esEs8(xuu52000, xuu53000))
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_@2, bbg), bbh), baf) → new_esEs6(xuu50000, xuu4000, bbg, bbh)
new_esEs31(xuu5000, xuu400, ty_Char) → new_esEs17(xuu5000, xuu400)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_@2, baa), bab)) → new_esEs6(xuu50000, xuu4000, baa, bab)
new_esEs30(xuu5000, xuu400, ty_Bool) → new_esEs9(xuu5000, xuu400)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Ratio, bag), baf) → new_esEs10(xuu50000, xuu4000, bag)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs29(xuu22, xuu17, ty_Bool) → new_esEs9(xuu22, xuu17)
new_esEs12(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs5(xuu50001, xuu4001, bfd, bfe, bff)
new_esEs20(xuu50000, xuu4000, app(app(ty_@2, bhe), bhf)) → new_esEs6(xuu50000, xuu4000, bhe, bhf)
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_compare31(xuu52000, xuu53000, ty_@0) → new_compare27(xuu52000, xuu53000)
new_primCmpNat1(xuu5200, Succ(xuu5300)) → new_primCmpNat0(xuu5200, xuu5300)
new_lt20(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_@0, baf) → new_esEs11(xuu50000, xuu4000)
new_ltEs11(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), db, dc) → new_pePe(new_lt20(xuu52000, xuu53000, db), new_asAs(new_esEs26(xuu52000, xuu53000, db), new_ltEs21(xuu52001, xuu53001, dc)))
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Ordering, baf) → new_esEs8(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_esEs32(xuu41, xuu36, app(app(ty_@2, ge), gf)) → new_esEs6(xuu41, xuu36, ge, gf)
new_compare25(xuu52000, xuu53000, False, gg) → new_compare18(xuu52000, xuu53000, new_ltEs12(xuu52000, xuu53000, gg), gg)
new_pePe(False, xuu194) → xuu194
new_esEs29(xuu22, xuu17, ty_Double) → new_esEs16(xuu22, xuu17)
new_esEs25(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_esEs4(xuu52000, xuu53000, bdd, bde)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_esEs31(xuu5000, xuu400, ty_Bool) → new_esEs9(xuu5000, xuu400)
new_compare31(xuu52000, xuu53000, ty_Float) → new_compare32(xuu52000, xuu53000)
new_esEs22(xuu50001, xuu4001, app(app(ty_Either, cca), ccb)) → new_esEs4(xuu50001, xuu4001, cca, ccb)
new_esEs20(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_primCmpNat1(xuu5200, Zero) → GT
new_compare31(xuu52000, xuu53000, ty_Bool) → new_compare29(xuu52000, xuu53000)
new_compare15(Char(xuu52000), Char(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_ltEs21(xuu52001, xuu53001, ty_@0) → new_ltEs7(xuu52001, xuu53001)
new_lt11(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_lt9(xuu52000, xuu53000, fa, fb, fc)
new_esEs32(xuu41, xuu36, app(ty_Maybe, gd)) → new_esEs7(xuu41, xuu36, gd)
new_esEs24(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_esEs7(xuu52001, xuu53001, cfb)
new_esEs24(xuu52001, xuu53001, ty_@0) → new_esEs11(xuu52001, xuu53001)
new_ltEs16(EQ, GT) → True
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_[], dhd)) → new_ltEs14(xuu52000, xuu53000, dhd)
new_esEs22(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs23(xuu50000, xuu4000, app(ty_Maybe, cde)) → new_esEs7(xuu50000, xuu4000, cde)
new_esEs22(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_ltEs4(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_esEs22(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_lt20(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_lt16(xuu52000, xuu53000, dah)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Ratio, bcb)) → new_esEs10(xuu50000, xuu4000, bcb)
new_primCmpNat0(Zero, Succ(xuu53000)) → LT
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_@2, dha), dhb)) → new_ltEs11(xuu52000, xuu53000, dha, dhb)
new_esEs25(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_esEs6(xuu52000, xuu53000, bad, bae)
new_lt11(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_lt15(xuu52000, xuu53000, bad, bae)
new_esEs8(LT, LT) → True
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Ratio, dea)) → new_ltEs9(xuu52000, xuu53000, dea)
new_esEs20(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs19(xuu50001, xuu4001, app(ty_Maybe, bgb)) → new_esEs7(xuu50001, xuu4001, bgb)
new_esEs23(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs16(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_ltEs21(xuu52001, xuu53001, ty_Char) → new_ltEs6(xuu52001, xuu53001)
new_pePe(True, xuu194) → True
new_esEs24(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_esEs6(xuu52001, xuu53001, ceh, cfa)
new_primEqNat0(Zero, Zero) → True
new_esEs23(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs26(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), bhg, bhh, caa) → new_asAs(new_esEs23(xuu50000, xuu4000, bhg), new_asAs(new_esEs22(xuu50001, xuu4001, bhh), new_esEs21(xuu50002, xuu4002, caa)))
new_primMulNat0(Succ(xuu5000100), Succ(xuu400100)) → new_primPlusNat1(new_primMulNat0(xuu5000100, Succ(xuu400100)), xuu400100)
new_compare111(xuu52000, xuu53000, False, bad, bae) → GT
new_ltEs20(xuu52002, xuu53002, ty_@0) → new_ltEs7(xuu52002, xuu53002)
new_esEs22(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs31(xuu5000, xuu400, ty_Integer) → new_esEs12(xuu5000, xuu400)
new_esEs29(xuu22, xuu17, ty_Int) → new_esEs14(xuu22, xuu17)
new_lt20(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_ltEs4(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_ltEs21(xuu52001, xuu53001, app(app(ty_Either, dbb), dbc)) → new_ltEs8(xuu52001, xuu53001, dbb, dbc)
new_ltEs16(EQ, LT) → False
new_lt12(xuu52001, xuu53001, ty_Ordering) → new_lt18(xuu52001, xuu53001)
new_esEs19(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_ltEs16(GT, EQ) → False
new_sr(xuu50001, xuu4001) → new_primMulInt(xuu50001, xuu4001)
new_compare12(xuu52000, xuu53000, True, fa, fb, fc) → LT
new_esEs32(xuu41, xuu36, ty_Bool) → new_esEs9(xuu41, xuu36)
new_esEs18(xuu50000, xuu4000, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs5(xuu50000, xuu4000, bdh, bea, beb)
new_esEs25(xuu52000, xuu53000, app(ty_[], bac)) → new_esEs15(xuu52000, xuu53000, bac)
new_esEs24(xuu52001, xuu53001, ty_Double) → new_esEs16(xuu52001, xuu53001)
new_esEs23(xuu50000, xuu4000, app(ty_[], cdb)) → new_esEs15(xuu50000, xuu4000, cdb)
new_lt15(xuu52000, xuu53000, bad, bae) → new_esEs8(new_compare17(xuu52000, xuu53000, bad, bae), LT)
new_ltEs21(xuu52001, xuu53001, app(app(ty_@2, dbh), dca)) → new_ltEs11(xuu52001, xuu53001, dbh, dca)
new_ltEs20(xuu52002, xuu53002, ty_Int) → new_ltEs19(xuu52002, xuu53002)
new_esEs26(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs8(GT, GT) → True
new_esEs21(xuu50002, xuu4002, ty_Double) → new_esEs16(xuu50002, xuu4002)
new_esEs31(xuu5000, xuu400, app(ty_[], chb)) → new_esEs15(xuu5000, xuu400, chb)
new_lt12(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_lt16(xuu52001, xuu53001, cfb)
new_primCmpInt(Pos(Succ(xuu5200)), Pos(xuu530)) → new_primCmpNat1(xuu5200, xuu530)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_lt19(xuu52000, xuu53000) → new_esEs8(new_compare29(xuu52000, xuu53000), LT)
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Integer) → new_compare14(new_sr0(xuu52000, xuu53001), new_sr0(xuu53000, xuu52001))
new_esEs26(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_esEs32(xuu41, xuu36, ty_Int) → new_esEs14(xuu41, xuu36)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_Either, bcg), bch)) → new_esEs4(xuu50000, xuu4000, bcg, bch)
new_compare24(xuu52000, xuu53000, True, fa, fb, fc) → EQ
new_ltEs5(xuu5200, xuu5300, app(app(ty_Either, df), dg)) → new_ltEs8(xuu5200, xuu5300, df, dg)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs4(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_esEs20(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_ltEs16(LT, EQ) → True
new_esEs31(xuu5000, xuu400, app(app(ty_Either, chc), chd)) → new_esEs4(xuu5000, xuu400, chc, chd)
new_lt12(xuu52001, xuu53001, ty_Char) → new_lt13(xuu52001, xuu53001)
new_esEs23(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_Either, bbd), bbe), baf) → new_esEs4(xuu50000, xuu4000, bbd, bbe)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs5(xuu50000, xuu4000, bah, bba, bbb)
new_esEs25(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_esEs10(xuu52000, xuu53000, eh)
new_ltEs5(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Ratio, ha)) → new_esEs10(xuu50000, xuu4000, ha)
new_lt20(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_ltEs17(True, False) → False
new_compare16(xuu52000, xuu53000, True) → LT
new_ltEs5(xuu5200, xuu5300, app(ty_Ratio, dh)) → new_ltEs9(xuu5200, xuu5300, dh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt10(xuu52000, xuu53000, bdd, bde) → new_esEs8(new_compare19(xuu52000, xuu53000, bdd, bde), LT)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(app(ty_@3, dfd), dfe), dff), cd) → new_ltEs10(xuu52000, xuu53000, dfd, dfe, dff)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs32(xuu41, xuu36, app(app(app(ty_@3, ff), fg), fh)) → new_esEs5(xuu41, xuu36, ff, fg, fh)
new_primCmpNat2(Succ(xuu5300), xuu5200) → new_primCmpNat0(xuu5300, xuu5200)
new_esEs32(xuu41, xuu36, ty_@0) → new_esEs11(xuu41, xuu36)
new_esEs19(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primCompAux0(xuu218, GT) → GT
new_compare31(xuu52000, xuu53000, ty_Ordering) → new_compare30(xuu52000, xuu53000)
new_ltEs21(xuu52001, xuu53001, app(ty_[], dcc)) → new_ltEs14(xuu52001, xuu53001, dcc)
new_lt11(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_lt10(xuu52000, xuu53000, bdd, bde)
new_esEs8(EQ, EQ) → True
new_compare26(xuu52000, xuu53000, True, bad, bae) → EQ
new_primPlusNat1(Zero, xuu400100) → Succ(xuu400100)
new_esEs32(xuu41, xuu36, app(ty_Ratio, fd)) → new_esEs10(xuu41, xuu36, fd)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_[], dgb), cd) → new_ltEs14(xuu52000, xuu53000, dgb)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Char, cd) → new_ltEs6(xuu52000, xuu53000)
new_esEs22(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs21(xuu50002, xuu4002, app(app(ty_Either, cag), cah)) → new_esEs4(xuu50002, xuu4002, cag, cah)
new_compare29(xuu52000, xuu53000) → new_compare210(xuu52000, xuu53000, new_esEs9(xuu52000, xuu53000))
new_esEs32(xuu41, xuu36, ty_Char) → new_esEs17(xuu41, xuu36)
new_esEs22(xuu50001, xuu4001, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs5(xuu50001, xuu4001, cbe, cbf, cbg)
new_esEs18(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_compare8(xuu52000, xuu53000, fa, fb, fc) → new_compare24(xuu52000, xuu53000, new_esEs5(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Char, baf) → new_esEs17(xuu50000, xuu4000)
new_esEs26(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, ty_Float) → new_esEs13(xuu5000, xuu400)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(xuu5200, xuu5300) → new_fsEs(new_compare6(xuu5200, xuu5300))
new_ltEs20(xuu52002, xuu53002, ty_Double) → new_ltEs15(xuu52002, xuu53002)
new_ltEs16(GT, LT) → False
new_compare6(xuu52, xuu53) → new_primCmpInt(xuu52, xuu53)
new_esEs19(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_ltEs4(xuu5200, xuu5300, app(app(ty_@2, db), dc)) → new_ltEs11(xuu5200, xuu5300, db, dc)
new_esEs29(xuu22, xuu17, ty_Float) → new_esEs13(xuu22, xuu17)
new_compare13(Double(xuu52000, xuu52001), Double(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_primCmpNat0(Succ(xuu52000), Succ(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_ltEs9(xuu5200, xuu5300, ce) → new_fsEs(new_compare7(xuu5200, xuu5300, ce))
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs5(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_compare10(xuu167, xuu168, False, dhe, dhf) → GT
new_lt11(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_lt5(xuu52000, xuu53000, eh) → new_esEs8(new_compare7(xuu52000, xuu53000, eh), LT)
new_ltEs21(xuu52001, xuu53001, ty_Float) → new_ltEs13(xuu52001, xuu53001)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(app(ty_@3, dgf), dgg), dgh)) → new_ltEs10(xuu52000, xuu53000, dgf, dgg, dgh)
new_compare14(Integer(xuu52000), Integer(xuu53000)) → new_primCmpInt(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Float, cd) → new_ltEs13(xuu52000, xuu53000)
new_esEs19(xuu50001, xuu4001, app(app(ty_@2, bgc), bgd)) → new_esEs6(xuu50001, xuu4001, bgc, bgd)
new_ltEs5(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(ty_Maybe, dd)) → new_ltEs12(xuu5200, xuu5300, dd)
new_lt7(xuu52000, xuu53000) → new_esEs8(new_compare14(xuu52000, xuu53000), LT)
new_esEs30(xuu5000, xuu400, ty_Int) → new_esEs14(xuu5000, xuu400)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Bool, baf) → new_esEs9(xuu50000, xuu4000)
new_esEs24(xuu52001, xuu53001, ty_Ordering) → new_esEs8(xuu52001, xuu53001)
new_esEs18(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_@2, dfg), dfh), cd) → new_ltEs11(xuu52000, xuu53000, dfg, dfh)
new_lt6(xuu52000, xuu53000) → new_esEs8(new_compare13(xuu52000, xuu53000), LT)
new_ltEs4(xuu5200, xuu5300, app(ty_[], de)) → new_ltEs14(xuu5200, xuu5300, de)
new_lt12(xuu52001, xuu53001, ty_@0) → new_lt14(xuu52001, xuu53001)
new_esEs7(Nothing, Nothing, gh) → True
new_esEs15([], [], bdf) → True
new_lt20(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_lt5(xuu52000, xuu53000, dab)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_esEs18(xuu50000, xuu4000, app(ty_Maybe, bef)) → new_esEs7(xuu50000, xuu4000, bef)
new_lt4(xuu520, xuu530) → new_esEs8(new_compare6(xuu520, xuu530), LT)
new_ltEs20(xuu52002, xuu53002, app(ty_Maybe, cgd)) → new_ltEs12(xuu52002, xuu53002, cgd)
new_primPlusNat0(Succ(xuu55200), Zero) → Succ(xuu55200)
new_primPlusNat0(Zero, Succ(xuu13100)) → Succ(xuu13100)
new_compare31(xuu52000, xuu53000, ty_Integer) → new_compare14(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(app(app(ty_@3, dch), dda), ddb)) → new_compare8(xuu52000, xuu53000, dch, dda, ddb)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_esEs19(xuu50001, xuu4001, app(ty_[], bfg)) → new_esEs15(xuu50001, xuu4001, bfg)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu52000), Zero) → GT
new_lt11(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs5(xuu50000, xuu4000, bcc, bcd, bce)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Maybe, dga), cd) → new_ltEs12(xuu52000, xuu53000, dga)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_[], deh)) → new_ltEs14(xuu52000, xuu53000, deh)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu5300))) → LT
new_compare11(xuu174, xuu175, True, cdh, cea) → LT
new_ltEs21(xuu52001, xuu53001, ty_Ordering) → new_ltEs16(xuu52001, xuu53001)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_esEs23(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_lt20(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_sr0(Integer(xuu530000), Integer(xuu520010)) → Integer(new_primMulInt(xuu530000, xuu520010))
new_esEs31(xuu5000, xuu400, ty_Int) → new_esEs14(xuu5000, xuu400)
new_ltEs5(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_esEs31(xuu5000, xuu400, app(ty_Ratio, cgf)) → new_esEs10(xuu5000, xuu400, cgf)
new_ltEs20(xuu52002, xuu53002, app(ty_[], cge)) → new_ltEs14(xuu52002, xuu53002, cge)
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_esEs7(Just(xuu50000), Nothing, gh) → False
new_esEs7(Nothing, Just(xuu4000), gh) → False
new_esEs13(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Maybe, deg)) → new_ltEs12(xuu52000, xuu53000, deg)
new_esEs24(xuu52001, xuu53001, ty_Int) → new_esEs14(xuu52001, xuu53001)
new_ltEs4(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_esEs30(xuu5000, xuu400, ty_Integer) → new_esEs12(xuu5000, xuu400)
new_esEs22(xuu50001, xuu4001, app(app(ty_@2, ccd), cce)) → new_esEs6(xuu50001, xuu4001, ccd, cce)
new_ltEs20(xuu52002, xuu53002, ty_Integer) → new_ltEs18(xuu52002, xuu53002)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_Either, ddg), ddh)) → new_ltEs8(xuu52000, xuu53000, ddg, ddh)
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_esEs18(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_ltEs20(xuu52002, xuu53002, app(app(ty_@2, cgb), cgc)) → new_ltEs11(xuu52002, xuu53002, cgb, cgc)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Maybe, dhc)) → new_ltEs12(xuu52000, xuu53000, dhc)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_@0, cd) → new_ltEs7(xuu52000, xuu53000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Ratio, ccf)) → new_esEs10(xuu50000, xuu4000, ccf)
new_esEs6(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), bfa, bfb) → new_asAs(new_esEs20(xuu50000, xuu4000, bfa), new_esEs19(xuu50001, xuu4001, bfb))
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Integer, baf) → new_esEs12(xuu50000, xuu4000)
new_lt20(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_lt9(xuu52000, xuu53000, dac, dad, dae)
new_ltEs16(EQ, EQ) → True
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Double, baf) → new_esEs16(xuu50000, xuu4000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Ratio, dfc), cd) → new_ltEs9(xuu52000, xuu53000, dfc)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_compare31(xuu52000, xuu53000, app(app(ty_Either, dce), dcf)) → new_compare19(xuu52000, xuu53000, dce, dcf)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_lt12(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_lt15(xuu52001, xuu53001, ceh, cfa)
new_primCompAux0(xuu218, LT) → LT
new_lt20(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, app(ty_Ratio, dcd)) → new_esEs10(xuu5000, xuu400, dcd)
new_not(False) → True
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_Either, dgc), dgd)) → new_ltEs8(xuu52000, xuu53000, dgc, dgd)
new_esEs20(xuu50000, xuu4000, app(ty_Ratio, bge)) → new_esEs10(xuu50000, xuu4000, bge)
new_esEs29(xuu22, xuu17, ty_Integer) → new_esEs12(xuu22, xuu17)
new_compare12(xuu52000, xuu53000, False, fa, fb, fc) → GT
new_esEs23(xuu50000, xuu4000, app(app(ty_@2, cdf), cdg)) → new_esEs6(xuu50000, xuu4000, cdf, cdg)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(app(ty_@2, ddc), ddd)) → new_compare17(xuu52000, xuu53000, ddc, ddd)
new_lt11(xuu52000, xuu53000, app(ty_[], bac)) → new_lt8(xuu52000, xuu53000, bac)
new_esEs30(xuu5000, xuu400, app(app(ty_Either, bca), baf)) → new_esEs4(xuu5000, xuu400, bca, baf)
new_esEs19(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_esEs32(xuu41, xuu36, ty_Ordering) → new_esEs8(xuu41, xuu36)
new_ltEs21(xuu52001, xuu53001, ty_Int) → new_ltEs19(xuu52001, xuu53001)
new_ltEs10(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), cf, cg, da) → new_pePe(new_lt11(xuu52000, xuu53000, cf), new_asAs(new_esEs25(xuu52000, xuu53000, cf), new_pePe(new_lt12(xuu52001, xuu53001, cg), new_asAs(new_esEs24(xuu52001, xuu53001, cg), new_ltEs20(xuu52002, xuu53002, da)))))
new_ltEs5(xuu5200, xuu5300, app(app(ty_@2, ed), ee)) → new_ltEs11(xuu5200, xuu5300, ed, ee)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_@2, dee), def)) → new_ltEs11(xuu52000, xuu53000, dee, def)
new_esEs24(xuu52001, xuu53001, ty_Integer) → new_esEs12(xuu52001, xuu53001)
new_esEs32(xuu41, xuu36, app(ty_[], ga)) → new_esEs15(xuu41, xuu36, ga)
new_lt20(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_compare28(xuu52000, xuu53000, True) → EQ
new_lt20(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_lt12(xuu52001, xuu53001, ty_Double) → new_lt6(xuu52001, xuu53001)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_@2, bdb), bdc)) → new_esEs6(xuu50000, xuu4000, bdb, bdc)
new_lt11(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_lt5(xuu52000, xuu53000, eh)
new_esEs18(xuu50000, xuu4000, app(app(ty_Either, bed), bee)) → new_esEs4(xuu50000, xuu4000, bed, bee)
new_esEs9(True, True) → True
new_compare11(xuu174, xuu175, False, cdh, cea) → GT
new_lt11(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_esEs20(xuu50000, xuu4000, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs5(xuu50000, xuu4000, bgf, bgg, bgh)
new_primCmpInt(Pos(Succ(xuu5200)), Neg(xuu530)) → GT
new_lt8(xuu52000, xuu53000, bac) → new_esEs8(new_compare1(xuu52000, xuu53000, bac), LT)
new_esEs30(xuu5000, xuu400, ty_@0) → new_esEs11(xuu5000, xuu400)
new_esEs21(xuu50002, xuu4002, app(app(app(ty_@3, cac), cad), cae)) → new_esEs5(xuu50002, xuu4002, cac, cad, cae)
new_esEs21(xuu50002, xuu4002, app(ty_Maybe, cba)) → new_esEs7(xuu50002, xuu4002, cba)
new_ltEs4(xuu5200, xuu5300, app(ty_Ratio, ce)) → new_ltEs9(xuu5200, xuu5300, ce)
new_primMulInt(Pos(xuu500010), Pos(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_lt12(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_lt9(xuu52001, xuu53001, cee, cef, ceg)
new_esEs18(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(app(ty_Either, cdc), cdd)) → new_esEs4(xuu50000, xuu4000, cdc, cdd)
new_ltEs20(xuu52002, xuu53002, ty_Bool) → new_ltEs17(xuu52002, xuu53002)
new_lt20(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_lt10(xuu52000, xuu53000, chh, daa)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Maybe, bbf), baf) → new_esEs7(xuu50000, xuu4000, bbf)
new_compare23(Right(xuu5200), Left(xuu5300), False, ca, cb) → GT
new_primMulInt(Neg(xuu500010), Neg(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_ltEs5(xuu5200, xuu5300, app(ty_Maybe, ef)) → new_ltEs12(xuu5200, xuu5300, ef)
new_compare110(xuu52000, xuu53000, True) → LT
new_esEs29(xuu22, xuu17, app(app(ty_@2, eag), eah)) → new_esEs6(xuu22, xuu17, eag, eah)
new_esEs21(xuu50002, xuu4002, app(ty_Ratio, cab)) → new_esEs10(xuu50002, xuu4002, cab)
new_lt20(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, app(ty_Maybe, gh)) → new_esEs7(xuu5000, xuu400, gh)
new_primEqNat0(Succ(xuu500000), Zero) → False
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_Either, dfa), dfb), cd) → new_ltEs8(xuu52000, xuu53000, dfa, dfb)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(app(ty_@3, deb), dec), ded)) → new_ltEs10(xuu52000, xuu53000, deb, dec, ded)
new_compare110(xuu52000, xuu53000, False) → GT
new_ltEs6(xuu5200, xuu5300) → new_fsEs(new_compare15(xuu5200, xuu5300))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_esEs4(xuu52001, xuu53001, ceb, cec)
new_compare17(xuu52000, xuu53000, bad, bae) → new_compare26(xuu52000, xuu53000, new_esEs6(xuu52000, xuu53000, bad, bae), bad, bae)
new_ltEs21(xuu52001, xuu53001, app(ty_Ratio, dbd)) → new_ltEs9(xuu52001, xuu53001, dbd)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Ordering, cd) → new_ltEs16(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, ty_Bool) → new_esEs9(xuu50002, xuu4002)
new_esEs11(@0, @0) → True
new_compare210(xuu52000, xuu53000, True) → EQ
new_esEs25(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs10(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), dcd) → new_asAs(new_esEs28(xuu50000, xuu4000, dcd), new_esEs27(xuu50001, xuu4001, dcd))
new_ltEs20(xuu52002, xuu53002, ty_Ordering) → new_ltEs16(xuu52002, xuu53002)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Int, baf) → new_esEs14(xuu50000, xuu4000)
new_compare31(xuu52000, xuu53000, ty_Char) → new_compare15(xuu52000, xuu53000)
new_primPlusNat1(Succ(xuu1400), xuu400100) → Succ(Succ(new_primPlusNat0(xuu1400, xuu400100)))
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_esEs29(xuu22, xuu17, app(app(app(ty_@3, dhh), eaa), eab)) → new_esEs5(xuu22, xuu17, dhh, eaa, eab)
new_esEs22(xuu50001, xuu4001, app(ty_[], cbh)) → new_esEs15(xuu50001, xuu4001, cbh)
new_esEs21(xuu50002, xuu4002, ty_Char) → new_esEs17(xuu50002, xuu4002)
new_ltEs4(xuu5200, xuu5300, app(app(ty_Either, cc), cd)) → new_ltEs8(xuu5200, xuu5300, cc, cd)
new_esEs18(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_compare23(xuu520, xuu530, True, ca, cb) → EQ
new_lt20(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_lt15(xuu52000, xuu53000, daf, dag)
new_esEs20(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu5300))) → GT
new_esEs32(xuu41, xuu36, ty_Float) → new_esEs13(xuu41, xuu36)
new_ltEs20(xuu52002, xuu53002, ty_Float) → new_ltEs13(xuu52002, xuu53002)
new_compare31(xuu52000, xuu53000, app(ty_Ratio, dcg)) → new_compare7(xuu52000, xuu53000, dcg)
new_esEs15(:(xuu50000, xuu50001), [], bdf) → False
new_esEs15([], :(xuu4000, xuu4001), bdf) → False
new_ltEs21(xuu52001, xuu53001, app(ty_Maybe, dcb)) → new_ltEs12(xuu52001, xuu53001, dcb)
new_esEs18(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_esEs7(xuu52000, xuu53000, gg)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, hb), hc), hd)) → new_esEs5(xuu50000, xuu4000, hb, hc, hd)
new_esEs9(False, True) → False
new_esEs9(True, False) → False
new_lt12(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_lt10(xuu52001, xuu53001, ceb, cec)
new_compare32(Float(xuu52000, xuu52001), Float(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_ltEs7(xuu5200, xuu5300) → new_fsEs(new_compare27(xuu5200, xuu5300))
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_compare31(xuu52000, xuu53000, ty_Double) → new_compare13(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, ty_Float) → new_esEs13(xuu50002, xuu4002)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCompAux1(xuu52000, xuu53000, xuu204, de) → new_primCompAux0(xuu204, new_compare31(xuu52000, xuu53000, de))
new_esEs7(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs26(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_asAs(False, xuu162) → False
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_ltEs13(xuu5200, xuu5300) → new_fsEs(new_compare32(xuu5200, xuu5300))
new_primMulInt(Pos(xuu500010), Neg(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Neg(xuu500010), Pos(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_compare23(Left(xuu5200), Right(xuu5300), False, ca, cb) → LT
new_primCmpInt(Neg(Succ(xuu5200)), Neg(xuu530)) → new_primCmpNat2(xuu530, xuu5200)
new_primMulNat0(Succ(xuu5000100), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu400100)) → Zero
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Int, cd) → new_ltEs19(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, ty_Ordering) → new_esEs8(xuu50002, xuu4002)
new_compare26(xuu52000, xuu53000, False, bad, bae) → new_compare111(xuu52000, xuu53000, new_ltEs11(xuu52000, xuu53000, bad, bae), bad, bae)
new_esEs31(xuu5000, xuu400, ty_Double) → new_esEs16(xuu5000, xuu400)
new_esEs26(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_esEs7(xuu52000, xuu53000, dah)
new_esEs29(xuu22, xuu17, ty_Char) → new_esEs17(xuu22, xuu17)
new_lt18(xuu52000, xuu53000) → new_esEs8(new_compare30(xuu52000, xuu53000), LT)
new_ltEs21(xuu52001, xuu53001, ty_Double) → new_ltEs15(xuu52001, xuu53001)
new_ltEs8(Right(xuu52000), Left(xuu53000), cc, cd) → False
new_esEs18(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, app(ty_[], bha)) → new_esEs15(xuu50000, xuu4000, bha)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Maybe, bda)) → new_esEs7(xuu50000, xuu4000, bda)
new_ltEs17(True, True) → True
new_ltEs14(xuu5200, xuu5300, de) → new_fsEs(new_compare1(xuu5200, xuu5300, de))
new_lt11(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_compare18(xuu52000, xuu53000, True, gg) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(xuu5300))) → new_primCmpNat2(Zero, xuu5300)
new_esEs29(xuu22, xuu17, app(ty_Ratio, dhg)) → new_esEs10(xuu22, xuu17, dhg)
new_lt13(xuu52000, xuu53000) → new_esEs8(new_compare15(xuu52000, xuu53000), LT)
new_esEs24(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_esEs10(xuu52001, xuu53001, ced)
new_ltEs12(Nothing, Just(xuu53000), dd) → True
new_esEs23(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Double, cd) → new_ltEs15(xuu52000, xuu53000)
new_ltEs5(xuu5200, xuu5300, app(ty_[], eg)) → new_ltEs14(xuu5200, xuu5300, eg)
new_ltEs4(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_compare210(xuu52000, xuu53000, False) → new_compare16(xuu52000, xuu53000, new_ltEs17(xuu52000, xuu53000))
new_esEs20(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_compare18(xuu52000, xuu53000, False, gg) → GT
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_Either, hf), hg)) → new_esEs4(xuu50000, xuu4000, hf, hg)
new_esEs9(False, False) → True
new_esEs22(xuu50001, xuu4001, app(ty_Ratio, cbd)) → new_esEs10(xuu50001, xuu4001, cbd)
new_esEs26(xuu52000, xuu53000, app(ty_[], dba)) → new_esEs15(xuu52000, xuu53000, dba)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Float, baf) → new_esEs13(xuu50000, xuu4000)
new_ltEs5(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_esEs14(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs17(xuu50000, xuu4000)
new_lt12(xuu52001, xuu53001, ty_Int) → new_lt4(xuu52001, xuu53001)
new_lt11(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Integer, cd) → new_ltEs18(xuu52000, xuu53000)
new_esEs32(xuu41, xuu36, app(app(ty_Either, gb), gc)) → new_esEs4(xuu41, xuu36, gb, gc)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, app(ty_Ratio, bfc)) → new_esEs10(xuu50001, xuu4001, bfc)
new_esEs30(xuu5000, xuu400, app(app(ty_@2, bfa), bfb)) → new_esEs6(xuu5000, xuu400, bfa, bfb)
new_esEs31(xuu5000, xuu400, ty_Float) → new_esEs13(xuu5000, xuu400)
new_esEs20(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_ltEs17(False, True) → True
new_esEs25(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_esEs5(xuu52000, xuu53000, fa, fb, fc)
new_ltEs21(xuu52001, xuu53001, ty_Bool) → new_ltEs17(xuu52001, xuu53001)
new_ltEs4(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_esEs29(xuu22, xuu17, ty_@0) → new_esEs11(xuu22, xuu17)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs13(xuu50000, xuu4000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, ty_Char) → new_esEs17(xuu5000, xuu400)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu5300))) → new_primCmpNat1(xuu5300, Zero)
new_ltEs21(xuu52001, xuu53001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_ltEs10(xuu52001, xuu53001, dbe, dbf, dbg)
new_esEs30(xuu5000, xuu400, ty_Ordering) → new_esEs8(xuu5000, xuu400)
new_esEs22(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs14(xuu50000, xuu4000)
new_compare31(xuu52000, xuu53000, app(ty_[], ddf)) → new_compare1(xuu52000, xuu53000, ddf)
new_esEs22(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs24(xuu52001, xuu53001, ty_Bool) → new_esEs9(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Float) → new_lt17(xuu52001, xuu53001)
new_ltEs20(xuu52002, xuu53002, ty_Char) → new_ltEs6(xuu52002, xuu53002)
new_esEs20(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_primPlusNat0(Succ(xuu55200), Succ(xuu13100)) → Succ(Succ(new_primPlusNat0(xuu55200, xuu13100)))
new_ltEs4(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_ltEs21(xuu52001, xuu53001, ty_Integer) → new_ltEs18(xuu52001, xuu53001)
new_compare23(Right(xuu5200), Right(xuu5300), False, ca, cb) → new_compare11(xuu5200, xuu5300, new_ltEs5(xuu5200, xuu5300, cb), ca, cb)
new_esEs21(xuu50002, xuu4002, ty_@0) → new_esEs11(xuu50002, xuu4002)
new_compare111(xuu52000, xuu53000, True, bad, bae) → LT
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Ratio, dge)) → new_ltEs9(xuu52000, xuu53000, dge)
new_esEs26(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_esEs4(xuu52000, xuu53000, chh, daa)
new_asAs(True, xuu162) → xuu162
new_esEs19(xuu50001, xuu4001, app(app(ty_Either, bfh), bga)) → new_esEs4(xuu50001, xuu4001, bfh, bga)
new_esEs32(xuu41, xuu36, ty_Integer) → new_esEs12(xuu41, xuu36)
new_compare27(@0, @0) → EQ
new_lt12(xuu52001, xuu53001, ty_Bool) → new_lt19(xuu52001, xuu53001)
new_esEs19(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs26(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_esEs5(xuu52000, xuu53000, dac, dad, dae)
new_esEs4(Left(xuu50000), Right(xuu4000), bca, baf) → False
new_esEs4(Right(xuu50000), Left(xuu4000), bca, baf) → False
new_esEs31(xuu5000, xuu400, app(ty_Maybe, che)) → new_esEs7(xuu5000, xuu400, che)
new_ltEs5(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_ltEs20(xuu52002, xuu53002, app(app(ty_Either, cfd), cfe)) → new_ltEs8(xuu52002, xuu53002, cfd, cfe)
new_esEs32(xuu41, xuu36, ty_Double) → new_esEs16(xuu41, xuu36)
new_ltEs16(LT, LT) → True
new_ltEs12(Just(xuu52000), Nothing, dd) → False
new_compare1(:(xuu52000, xuu52001), [], de) → GT
new_lt16(xuu52000, xuu53000, gg) → new_esEs8(new_compare9(xuu52000, xuu53000, gg), LT)
new_fsEs(xuu177) → new_not(new_esEs8(xuu177, GT))
new_esEs24(xuu52001, xuu53001, ty_Float) → new_esEs13(xuu52001, xuu53001)
new_esEs26(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_esEs6(xuu52000, xuu53000, daf, dag)
new_esEs23(xuu50000, xuu4000, app(app(app(ty_@3, ccg), cch), cda)) → new_esEs5(xuu50000, xuu4000, ccg, cch, cda)
new_esEs19(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs26(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_esEs29(xuu22, xuu17, app(ty_[], eac)) → new_esEs15(xuu22, xuu17, eac)
new_ltEs20(xuu52002, xuu53002, app(app(app(ty_@3, cfg), cfh), cga)) → new_ltEs10(xuu52002, xuu53002, cfg, cfh, cga)
new_esEs30(xuu5000, xuu400, ty_Double) → new_esEs16(xuu5000, xuu400)
new_ltEs8(Left(xuu52000), Right(xuu53000), cc, cd) → True
new_esEs21(xuu50002, xuu4002, ty_Integer) → new_esEs12(xuu50002, xuu4002)
new_lt17(xuu52000, xuu53000) → new_esEs8(new_compare32(xuu52000, xuu53000), LT)
new_esEs30(xuu5000, xuu400, app(app(app(ty_@3, bhg), bhh), caa)) → new_esEs5(xuu5000, xuu400, bhg, bhh, caa)
new_lt11(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, app(ty_[], bdf)) → new_esEs15(xuu5000, xuu400, bdf)
new_lt11(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_lt16(xuu52000, xuu53000, gg)
new_ltEs5(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_lt12(xuu52001, xuu53001, ty_Integer) → new_lt7(xuu52001, xuu53001)
new_esEs31(xuu5000, xuu400, app(app(ty_@2, chf), chg)) → new_esEs6(xuu5000, xuu400, chf, chg)
new_ltEs15(xuu5200, xuu5300) → new_fsEs(new_compare13(xuu5200, xuu5300))
new_esEs18(xuu50000, xuu4000, app(ty_[], bec)) → new_esEs15(xuu50000, xuu4000, bec)
new_compare28(xuu52000, xuu53000, False) → new_compare110(xuu52000, xuu53000, new_ltEs16(xuu52000, xuu53000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(xuu218, EQ) → xuu218
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Int) → new_compare6(new_sr(xuu52000, xuu53001), new_sr(xuu53000, xuu52001))
new_esEs29(xuu22, xuu17, ty_Ordering) → new_esEs8(xuu22, xuu17)
new_esEs24(xuu52001, xuu53001, app(ty_[], cfc)) → new_esEs15(xuu52001, xuu53001, cfc)
new_esEs18(xuu50000, xuu4000, app(ty_Ratio, bdg)) → new_esEs10(xuu50000, xuu4000, bdg)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs16(xuu50000, xuu4000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(xuu50001, xuu4001, app(ty_Maybe, ccc)) → new_esEs7(xuu50001, xuu4001, ccc)
new_primCmpInt(Neg(Succ(xuu5200)), Pos(xuu530)) → LT
new_not(True) → False
new_compare16(xuu52000, xuu53000, False) → GT
new_compare1([], [], de) → EQ

The set Q consists of the following terms:

new_primCompAux0(x0, EQ)
new_ltEs4(x0, x1, ty_Bool)
new_ltEs5(x0, x1, ty_Float)
new_compare29(x0, x1)
new_fsEs(x0)
new_primCompAux0(x0, GT)
new_esEs19(x0, x1, ty_Bool)
new_esEs18(x0, x1, ty_@0)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3)
new_compare16(x0, x1, False)
new_esEs32(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_compare9(x0, x1, x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, False)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Char)
new_compare8(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Double)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare23(x0, x1, True, x2, x3)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1)
new_compare17(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs31(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Float)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs11(@0, @0)
new_compare10(x0, x1, True, x2, x3)
new_compare111(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_ltEs4(x0, x1, ty_Int)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs8(GT, GT)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_primCmpNat1(x0, Zero)
new_ltEs21(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs4(x0, x1, ty_Integer)
new_esEs7(Nothing, Just(x0), x1)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_ltEs4(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(LT, LT)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, x2)
new_esEs21(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Ordering)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_@0)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Int)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, ty_Integer)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs7(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(False, False)
new_esEs7(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Integer)
new_ltEs4(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(ty_[], x2))
new_compare1(:(x0, x1), [], x2)
new_compare24(x0, x1, False, x2, x3, x4)
new_primEqNat0(Zero, Zero)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs9(True, True)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs29(x0, x1, ty_Double)
new_lt10(x0, x1, x2, x3)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(x0, Succ(x1))
new_primMulNat0(Zero, Zero)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs18(x0, x1)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Integer)
new_ltEs17(True, True)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(Left(x0), Left(x1), False, x2, x3)
new_esEs29(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_lt12(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare14(Integer(x0), Integer(x1))
new_primCmpNat0(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Zero)
new_compare23(Right(x0), Right(x1), False, x2, x3)
new_esEs24(x0, x1, ty_Bool)
new_primCompAux1(x0, x1, x2, x3)
new_esEs7(Nothing, Nothing, x0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1)
new_ltEs4(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(x0, x1, ty_Integer)
new_pePe(False, x0)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_compare1([], :(x0, x1), x2)
new_ltEs21(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_ltEs6(x0, x1)
new_ltEs12(Just(x0), Nothing, x1)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(Float(x0, x1), Float(x2, x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs30(x0, x1, ty_Float)
new_lt12(x0, x1, ty_Int)
new_esEs17(Char(x0), Char(x1))
new_esEs19(x0, x1, ty_Char)
new_primPlusNat0(Zero, Zero)
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs16(EQ, EQ)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Zero)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare25(x0, x1, True, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_esEs19(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_compare28(x0, x1, False)
new_esEs18(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Float)
new_compare16(x0, x1, True)
new_esEs23(x0, x1, ty_Float)
new_esEs18(x0, x1, ty_Int)
new_ltEs16(LT, GT)
new_ltEs16(GT, LT)
new_esEs25(x0, x1, ty_@0)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1)
new_primPlusNat1(Succ(x0), x1)
new_pePe(True, x0)
new_lt11(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt11(x0, x1, ty_Ordering)
new_primCompAux0(x0, LT)
new_esEs25(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_lt12(x0, x1, ty_Bool)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1)
new_compare10(x0, x1, False, x2, x3)
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1, x2)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Bool)
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt15(x0, x1, x2, x3)
new_primPlusNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare31(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_asAs(True, x0)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare26(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs32(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare31(x0, x1, ty_Char)
new_compare210(x0, x1, False)
new_ltEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Integer)
new_ltEs16(GT, GT)
new_esEs18(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_@0)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Double)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs13(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs5(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_primCmpNat2(Succ(x0), x1)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs14(x0, x1)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_compare18(x0, x1, True, x2)
new_esEs30(x0, x1, ty_Integer)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_compare13(Double(x0, x1), Double(x2, x3))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, x0)
new_compare31(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare15(Char(x0), Char(x1))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCmpNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare23(Left(x0), Right(x1), False, x2, x3)
new_compare23(Right(x0), Left(x1), False, x2, x3)
new_ltEs12(Nothing, Nothing, x0)
new_esEs18(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Char)
new_ltEs12(Nothing, Just(x0), x1)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Int)
new_esEs9(False, False)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs18(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_compare6(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Bool)
new_compare31(x0, x1, ty_Ordering)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs4(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_ltEs4(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Double)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_compare18(x0, x1, False, x2)
new_compare26(x0, x1, False, x2, x3)
new_esEs30(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_not(True)
new_ltEs19(x0, x1)
new_esEs20(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs21(x0, x1, ty_Float)
new_lt11(x0, x1, ty_Int)
new_lt9(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, x0)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_lt11(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_ltEs17(False, True)
new_ltEs17(True, False)
new_ltEs20(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_lt12(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, True)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt6(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Int)
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_compare28(x0, x1, True)
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs9(False, True)
new_esEs9(True, False)
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_ltEs20(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare31(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs15([], :(x0, x1), x2)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs15(:(x0, x1), [], x2)
new_esEs21(x0, x1, ty_Bool)
new_ltEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_compare27(@0, @0)
new_lt11(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs30(x0, x1, ty_@0)
new_lt11(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Integer)
new_ltEs9(x0, x1, x2)
new_compare25(x0, x1, False, x2)
new_esEs30(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt8(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs32(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs20(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_esEs29(x0, x1, ty_Int)
new_esEs15([], [], x0)
new_lt12(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_sr(x0, x1)
new_esEs31(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)

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
                                          ↳ UsableRulesProof
QDP
                                              ↳ QReductionProof
                                        ↳ QDP
                                  ↳ QDP

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

new_addToFM_C(xuu3, Branch(Left(xuu400), xuu41, xuu42, xuu43, xuu44), Right(xuu5000), xuu501, bc, bd, be) → new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Right(xuu5000), Left(xuu400), False, bc, bd), LT), bc, bd, be)
new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, False, bc, bd, be) → new_addToFM_C11(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Right(xuu5000), Left(xuu400), False, bc, bd), GT), bc, bd, be)
new_addToFM_C11(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu44, Right(xuu5000), xuu501, bc, bd, be)
new_addToFM_C(xuu3, Branch(Right(xuu400), xuu41, xuu42, xuu43, xuu44), Right(xuu5000), xuu501, bc, bd, be) → new_addToFM_C22(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Right(xuu5000), Right(xuu400), new_esEs31(xuu5000, xuu400, bd), bc, bd), LT), bc, bd, be)
new_addToFM_C12(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, True, bf, bg, bh) → new_addToFM_C(xuu35, xuu40, Right(xuu41), xuu42, bf, bg, bh)
new_addToFM_C22(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, False, bf, bg, bh) → new_addToFM_C12(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, new_esEs8(new_compare23(Right(xuu41), Right(xuu36), new_esEs32(xuu41, xuu36, bg), bf, bg), GT), bf, bg, bh)
new_addToFM_C22(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, True, bf, bg, bh) → new_addToFM_C(xuu35, xuu39, Right(xuu41), xuu42, bf, bg, bh)
new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu43, Right(xuu5000), xuu501, bc, bd, be)

The TRS R consists of the following rules:

new_esEs32(xuu41, xuu36, app(app(ty_@2, ge), gf)) → new_esEs6(xuu41, xuu36, ge, gf)
new_esEs32(xuu41, xuu36, app(ty_Maybe, gd)) → new_esEs7(xuu41, xuu36, gd)
new_esEs32(xuu41, xuu36, ty_Bool) → new_esEs9(xuu41, xuu36)
new_esEs32(xuu41, xuu36, ty_Int) → new_esEs14(xuu41, xuu36)
new_esEs32(xuu41, xuu36, app(app(app(ty_@3, ff), fg), fh)) → new_esEs5(xuu41, xuu36, ff, fg, fh)
new_esEs32(xuu41, xuu36, ty_@0) → new_esEs11(xuu41, xuu36)
new_esEs32(xuu41, xuu36, app(ty_Ratio, fd)) → new_esEs10(xuu41, xuu36, fd)
new_esEs32(xuu41, xuu36, ty_Char) → new_esEs17(xuu41, xuu36)
new_esEs32(xuu41, xuu36, ty_Ordering) → new_esEs8(xuu41, xuu36)
new_esEs32(xuu41, xuu36, app(ty_[], ga)) → new_esEs15(xuu41, xuu36, ga)
new_esEs32(xuu41, xuu36, ty_Float) → new_esEs13(xuu41, xuu36)
new_esEs32(xuu41, xuu36, app(app(ty_Either, gb), gc)) → new_esEs4(xuu41, xuu36, gb, gc)
new_esEs32(xuu41, xuu36, ty_Integer) → new_esEs12(xuu41, xuu36)
new_esEs32(xuu41, xuu36, ty_Double) → new_esEs16(xuu41, xuu36)
new_compare23(xuu520, xuu530, True, ca, cb) → EQ
new_compare23(Right(xuu5200), Right(xuu5300), False, ca, cb) → new_compare11(xuu5200, xuu5300, new_ltEs5(xuu5200, xuu5300, cb), ca, cb)
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_ltEs5(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, app(app(app(ty_@3, ea), eb), ec)) → new_ltEs10(xuu5200, xuu5300, ea, eb, ec)
new_ltEs5(xuu5200, xuu5300, app(app(ty_Either, df), dg)) → new_ltEs8(xuu5200, xuu5300, df, dg)
new_ltEs5(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, app(ty_Ratio, dh)) → new_ltEs9(xuu5200, xuu5300, dh)
new_ltEs5(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, app(app(ty_@2, ed), ee)) → new_ltEs11(xuu5200, xuu5300, ed, ee)
new_ltEs5(xuu5200, xuu5300, app(ty_Maybe, ef)) → new_ltEs12(xuu5200, xuu5300, ef)
new_ltEs5(xuu5200, xuu5300, app(ty_[], eg)) → new_ltEs14(xuu5200, xuu5300, eg)
new_ltEs5(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_compare11(xuu174, xuu175, True, cdh, cea) → LT
new_compare11(xuu174, xuu175, False, cdh, cea) → GT
new_ltEs19(xuu5200, xuu5300) → new_fsEs(new_compare6(xuu5200, xuu5300))
new_compare6(xuu52, xuu53) → new_primCmpInt(xuu52, xuu53)
new_fsEs(xuu177) → new_not(new_esEs8(xuu177, GT))
new_not(False) → True
new_not(True) → False
new_primCmpInt(Pos(Succ(xuu5200)), Pos(xuu530)) → new_primCmpNat1(xuu5200, xuu530)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(xuu5300))) → LT
new_primCmpInt(Pos(Succ(xuu5200)), Neg(xuu530)) → GT
new_primCmpInt(Pos(Zero), Neg(Succ(xuu5300))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(xuu5200)), Neg(xuu530)) → new_primCmpNat2(xuu530, xuu5200)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu5300))) → new_primCmpNat2(Zero, xuu5300)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu5300))) → new_primCmpNat1(xuu5300, Zero)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(xuu5200)), Pos(xuu530)) → LT
new_primCmpNat1(xuu5200, Zero) → GT
new_primCmpNat2(Zero, xuu5200) → LT
new_primCmpNat2(Succ(xuu5300), xuu5200) → new_primCmpNat0(xuu5300, xuu5200)
new_primCmpNat0(Zero, Succ(xuu53000)) → LT
new_primCmpNat0(Succ(xuu52000), Succ(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu52000), Zero) → GT
new_primCmpNat1(xuu5200, Succ(xuu5300)) → new_primCmpNat0(xuu5200, xuu5300)
new_ltEs18(xuu5200, xuu5300) → new_fsEs(new_compare14(xuu5200, xuu5300))
new_compare14(Integer(xuu52000), Integer(xuu53000)) → new_primCmpInt(xuu52000, xuu53000)
new_ltEs6(xuu5200, xuu5300) → new_fsEs(new_compare15(xuu5200, xuu5300))
new_compare15(Char(xuu52000), Char(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_ltEs14(xuu5200, xuu5300, de) → new_fsEs(new_compare1(xuu5200, xuu5300, de))
new_compare1(:(xuu52000, xuu52001), :(xuu53000, xuu53001), de) → new_primCompAux1(xuu52000, xuu53000, new_compare1(xuu52001, xuu53001, de), de)
new_compare1([], :(xuu53000, xuu53001), de) → LT
new_compare1(:(xuu52000, xuu52001), [], de) → GT
new_compare1([], [], de) → EQ
new_primCompAux1(xuu52000, xuu53000, xuu204, de) → new_primCompAux0(xuu204, new_compare31(xuu52000, xuu53000, de))
new_compare31(xuu52000, xuu53000, ty_Int) → new_compare6(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(ty_Maybe, dde)) → new_compare9(xuu52000, xuu53000, dde)
new_compare31(xuu52000, xuu53000, ty_@0) → new_compare27(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Float) → new_compare32(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Bool) → new_compare29(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Ordering) → new_compare30(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Integer) → new_compare14(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(app(app(ty_@3, dch), dda), ddb)) → new_compare8(xuu52000, xuu53000, dch, dda, ddb)
new_compare31(xuu52000, xuu53000, app(app(ty_Either, dce), dcf)) → new_compare19(xuu52000, xuu53000, dce, dcf)
new_compare31(xuu52000, xuu53000, app(app(ty_@2, ddc), ddd)) → new_compare17(xuu52000, xuu53000, ddc, ddd)
new_compare31(xuu52000, xuu53000, ty_Char) → new_compare15(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(ty_Ratio, dcg)) → new_compare7(xuu52000, xuu53000, dcg)
new_compare31(xuu52000, xuu53000, ty_Double) → new_compare13(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(ty_[], ddf)) → new_compare1(xuu52000, xuu53000, ddf)
new_primCompAux0(xuu218, GT) → GT
new_primCompAux0(xuu218, LT) → LT
new_primCompAux0(xuu218, EQ) → xuu218
new_compare13(Double(xuu52000, xuu52001), Double(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_sr(xuu50001, xuu4001) → new_primMulInt(xuu50001, xuu4001)
new_primMulInt(Pos(xuu500010), Pos(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Neg(xuu500010), Neg(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Pos(xuu500010), Neg(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Neg(xuu500010), Pos(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(xuu5000100), Succ(xuu400100)) → new_primPlusNat1(new_primMulNat0(xuu5000100, Succ(xuu400100)), xuu400100)
new_primMulNat0(Succ(xuu5000100), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu400100)) → Zero
new_primPlusNat1(Zero, xuu400100) → Succ(xuu400100)
new_primPlusNat1(Succ(xuu1400), xuu400100) → Succ(Succ(new_primPlusNat0(xuu1400, xuu400100)))
new_primPlusNat0(Succ(xuu55200), Zero) → Succ(xuu55200)
new_primPlusNat0(Zero, Succ(xuu13100)) → Succ(xuu13100)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(xuu55200), Succ(xuu13100)) → Succ(Succ(new_primPlusNat0(xuu55200, xuu13100)))
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Integer) → new_compare14(new_sr0(xuu52000, xuu53001), new_sr0(xuu53000, xuu52001))
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Int) → new_compare6(new_sr(xuu52000, xuu53001), new_sr(xuu53000, xuu52001))
new_sr0(Integer(xuu530000), Integer(xuu520010)) → Integer(new_primMulInt(xuu530000, xuu520010))
new_compare17(xuu52000, xuu53000, bad, bae) → new_compare26(xuu52000, xuu53000, new_esEs6(xuu52000, xuu53000, bad, bae), bad, bae)
new_esEs6(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), bfa, bfb) → new_asAs(new_esEs20(xuu50000, xuu4000, bfa), new_esEs19(xuu50001, xuu4001, bfb))
new_compare26(xuu52000, xuu53000, True, bad, bae) → EQ
new_compare26(xuu52000, xuu53000, False, bad, bae) → new_compare111(xuu52000, xuu53000, new_ltEs11(xuu52000, xuu53000, bad, bae), bad, bae)
new_ltEs11(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), db, dc) → new_pePe(new_lt20(xuu52000, xuu53000, db), new_asAs(new_esEs26(xuu52000, xuu53000, db), new_ltEs21(xuu52001, xuu53001, dc)))
new_compare111(xuu52000, xuu53000, False, bad, bae) → GT
new_compare111(xuu52000, xuu53000, True, bad, bae) → LT
new_lt20(xuu52000, xuu53000, app(ty_[], dba)) → new_lt8(xuu52000, xuu53000, dba)
new_lt20(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_lt16(xuu52000, xuu53000, dah)
new_lt20(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_lt5(xuu52000, xuu53000, dab)
new_lt20(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_lt9(xuu52000, xuu53000, dac, dad, dae)
new_lt20(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_lt10(xuu52000, xuu53000, chh, daa)
new_lt20(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_lt15(xuu52000, xuu53000, daf, dag)
new_esEs26(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_esEs10(xuu52000, xuu53000, dab)
new_esEs26(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_esEs7(xuu52000, xuu53000, dah)
new_esEs26(xuu52000, xuu53000, app(ty_[], dba)) → new_esEs15(xuu52000, xuu53000, dba)
new_esEs26(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_esEs4(xuu52000, xuu53000, chh, daa)
new_esEs26(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_esEs5(xuu52000, xuu53000, dac, dad, dae)
new_esEs26(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_esEs6(xuu52000, xuu53000, daf, dag)
new_esEs26(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_ltEs21(xuu52001, xuu53001, ty_@0) → new_ltEs7(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Char) → new_ltEs6(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, app(app(ty_Either, dbb), dbc)) → new_ltEs8(xuu52001, xuu53001, dbb, dbc)
new_ltEs21(xuu52001, xuu53001, app(app(ty_@2, dbh), dca)) → new_ltEs11(xuu52001, xuu53001, dbh, dca)
new_ltEs21(xuu52001, xuu53001, app(ty_[], dcc)) → new_ltEs14(xuu52001, xuu53001, dcc)
new_ltEs21(xuu52001, xuu53001, ty_Float) → new_ltEs13(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Ordering) → new_ltEs16(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Int) → new_ltEs19(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, app(ty_Ratio, dbd)) → new_ltEs9(xuu52001, xuu53001, dbd)
new_ltEs21(xuu52001, xuu53001, app(ty_Maybe, dcb)) → new_ltEs12(xuu52001, xuu53001, dcb)
new_ltEs21(xuu52001, xuu53001, ty_Double) → new_ltEs15(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Bool) → new_ltEs17(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_ltEs10(xuu52001, xuu53001, dbe, dbf, dbg)
new_ltEs21(xuu52001, xuu53001, ty_Integer) → new_ltEs18(xuu52001, xuu53001)
new_asAs(False, xuu162) → False
new_asAs(True, xuu162) → xuu162
new_pePe(False, xuu194) → xuu194
new_pePe(True, xuu194) → True
new_ltEs10(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), cf, cg, da) → new_pePe(new_lt11(xuu52000, xuu53000, cf), new_asAs(new_esEs25(xuu52000, xuu53000, cf), new_pePe(new_lt12(xuu52001, xuu53001, cg), new_asAs(new_esEs24(xuu52001, xuu53001, cg), new_ltEs20(xuu52002, xuu53002, da)))))
new_lt11(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_lt9(xuu52000, xuu53000, fa, fb, fc)
new_lt11(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_lt15(xuu52000, xuu53000, bad, bae)
new_lt11(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_lt10(xuu52000, xuu53000, bdd, bde)
new_lt11(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, app(ty_[], bac)) → new_lt8(xuu52000, xuu53000, bac)
new_lt11(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_lt5(xuu52000, xuu53000, eh)
new_lt11(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_lt16(xuu52000, xuu53000, gg)
new_esEs25(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_esEs4(xuu52000, xuu53000, bdd, bde)
new_esEs25(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_esEs6(xuu52000, xuu53000, bad, bae)
new_esEs25(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(ty_[], bac)) → new_esEs15(xuu52000, xuu53000, bac)
new_esEs25(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_esEs10(xuu52000, xuu53000, eh)
new_esEs25(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_esEs7(xuu52000, xuu53000, gg)
new_esEs25(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_esEs5(xuu52000, xuu53000, fa, fb, fc)
new_lt12(xuu52001, xuu53001, app(ty_[], cfc)) → new_lt8(xuu52001, xuu53001, cfc)
new_lt12(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_lt5(xuu52001, xuu53001, ced)
new_lt12(xuu52001, xuu53001, ty_Ordering) → new_lt18(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_lt16(xuu52001, xuu53001, cfb)
new_lt12(xuu52001, xuu53001, ty_Char) → new_lt13(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_@0) → new_lt14(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_lt15(xuu52001, xuu53001, ceh, cfa)
new_lt12(xuu52001, xuu53001, ty_Double) → new_lt6(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_lt9(xuu52001, xuu53001, cee, cef, ceg)
new_lt12(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_lt10(xuu52001, xuu53001, ceb, cec)
new_lt12(xuu52001, xuu53001, ty_Int) → new_lt4(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Float) → new_lt17(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Bool) → new_lt19(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Integer) → new_lt7(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs5(xuu52001, xuu53001, cee, cef, ceg)
new_esEs24(xuu52001, xuu53001, ty_Char) → new_esEs17(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_esEs7(xuu52001, xuu53001, cfb)
new_esEs24(xuu52001, xuu53001, ty_@0) → new_esEs11(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_esEs6(xuu52001, xuu53001, ceh, cfa)
new_esEs24(xuu52001, xuu53001, ty_Double) → new_esEs16(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Ordering) → new_esEs8(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Int) → new_esEs14(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Integer) → new_esEs12(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_esEs4(xuu52001, xuu53001, ceb, cec)
new_esEs24(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_esEs10(xuu52001, xuu53001, ced)
new_esEs24(xuu52001, xuu53001, ty_Bool) → new_esEs9(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Float) → new_esEs13(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(ty_[], cfc)) → new_esEs15(xuu52001, xuu53001, cfc)
new_ltEs20(xuu52002, xuu53002, app(ty_Ratio, cff)) → new_ltEs9(xuu52002, xuu53002, cff)
new_ltEs20(xuu52002, xuu53002, ty_@0) → new_ltEs7(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Int) → new_ltEs19(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Double) → new_ltEs15(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, app(ty_Maybe, cgd)) → new_ltEs12(xuu52002, xuu53002, cgd)
new_ltEs20(xuu52002, xuu53002, app(ty_[], cge)) → new_ltEs14(xuu52002, xuu53002, cge)
new_ltEs20(xuu52002, xuu53002, ty_Integer) → new_ltEs18(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, app(app(ty_@2, cgb), cgc)) → new_ltEs11(xuu52002, xuu53002, cgb, cgc)
new_ltEs20(xuu52002, xuu53002, ty_Bool) → new_ltEs17(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Ordering) → new_ltEs16(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Float) → new_ltEs13(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Char) → new_ltEs6(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, app(app(ty_Either, cfd), cfe)) → new_ltEs8(xuu52002, xuu53002, cfd, cfe)
new_ltEs20(xuu52002, xuu53002, app(app(app(ty_@3, cfg), cfh), cga)) → new_ltEs10(xuu52002, xuu53002, cfg, cfh, cga)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Bool, cd) → new_ltEs17(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_[], dhd)) → new_ltEs14(xuu52000, xuu53000, dhd)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_@2, dha), dhb)) → new_ltEs11(xuu52000, xuu53000, dha, dhb)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(app(ty_@3, dfd), dfe), dff), cd) → new_ltEs10(xuu52000, xuu53000, dfd, dfe, dff)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_[], dgb), cd) → new_ltEs14(xuu52000, xuu53000, dgb)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Char, cd) → new_ltEs6(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(app(ty_@3, dgf), dgg), dgh)) → new_ltEs10(xuu52000, xuu53000, dgf, dgg, dgh)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Float, cd) → new_ltEs13(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_@2, dfg), dfh), cd) → new_ltEs11(xuu52000, xuu53000, dfg, dfh)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_@0, cd) → new_ltEs7(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Ratio, dfc), cd) → new_ltEs9(xuu52000, xuu53000, dfc)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Ordering, cd) → new_ltEs16(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Int, cd) → new_ltEs19(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Left(xuu53000), cc, cd) → False
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Double, cd) → new_ltEs15(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Integer, cd) → new_ltEs18(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Ratio, dge)) → new_ltEs9(xuu52000, xuu53000, dge)
new_ltEs8(Left(xuu52000), Right(xuu53000), cc, cd) → True
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_Either, dfa), dfb), cd) → new_ltEs8(xuu52000, xuu53000, dfa, dfb)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Maybe, dga), cd) → new_ltEs12(xuu52000, xuu53000, dga)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Maybe, dhc)) → new_ltEs12(xuu52000, xuu53000, dhc)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Maybe, deg)) → new_ltEs12(xuu52000, xuu53000, deg)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_Either, dgc), dgd)) → new_ltEs8(xuu52000, xuu53000, dgc, dgd)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_Either, ddg), ddh)) → new_ltEs8(xuu52000, xuu53000, ddg, ddh)
new_ltEs12(Nothing, Nothing, dd) → True
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Ratio, dea)) → new_ltEs9(xuu52000, xuu53000, dea)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_[], deh)) → new_ltEs14(xuu52000, xuu53000, deh)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_@2, dee), def)) → new_ltEs11(xuu52000, xuu53000, dee, def)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(app(ty_@3, deb), dec), ded)) → new_ltEs10(xuu52000, xuu53000, deb, dec, ded)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_ltEs12(Nothing, Just(xuu53000), dd) → True
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Nothing, dd) → False
new_ltEs13(xuu5200, xuu5300) → new_fsEs(new_compare32(xuu5200, xuu5300))
new_compare32(Float(xuu52000, xuu52001), Float(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_ltEs17(False, False) → True
new_ltEs17(True, False) → False
new_ltEs17(True, True) → True
new_ltEs17(False, True) → True
new_ltEs9(xuu5200, xuu5300, ce) → new_fsEs(new_compare7(xuu5200, xuu5300, ce))
new_ltEs15(xuu5200, xuu5300) → new_fsEs(new_compare13(xuu5200, xuu5300))
new_ltEs7(xuu5200, xuu5300) → new_fsEs(new_compare27(xuu5200, xuu5300))
new_compare27(@0, @0) → EQ
new_ltEs16(GT, GT) → True
new_ltEs16(LT, GT) → True
new_ltEs16(EQ, GT) → True
new_ltEs16(EQ, LT) → False
new_ltEs16(GT, EQ) → False
new_ltEs16(LT, EQ) → True
new_ltEs16(GT, LT) → False
new_ltEs16(EQ, EQ) → True
new_ltEs16(LT, LT) → True
new_esEs15(:(xuu50000, xuu50001), :(xuu4000, xuu4001), bdf) → new_asAs(new_esEs18(xuu50000, xuu4000, bdf), new_esEs15(xuu50001, xuu4001, bdf))
new_esEs15([], [], bdf) → True
new_esEs15(:(xuu50000, xuu50001), [], bdf) → False
new_esEs15([], :(xuu4000, xuu4001), bdf) → False
new_esEs18(xuu50000, xuu4000, app(app(ty_@2, beg), beh)) → new_esEs6(xuu50000, xuu4000, beg, beh)
new_esEs18(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs5(xuu50000, xuu4000, bdh, bea, beb)
new_esEs18(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(ty_Maybe, bef)) → new_esEs7(xuu50000, xuu4000, bef)
new_esEs18(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(app(ty_Either, bed), bee)) → new_esEs4(xuu50000, xuu4000, bed, bee)
new_esEs18(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(ty_[], bec)) → new_esEs15(xuu50000, xuu4000, bec)
new_esEs18(xuu50000, xuu4000, app(ty_Ratio, bdg)) → new_esEs10(xuu50000, xuu4000, bdg)
new_esEs10(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), dcd) → new_asAs(new_esEs28(xuu50000, xuu4000, dcd), new_esEs27(xuu50001, xuu4001, dcd))
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs14(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_primEqNat0(Succ(xuu500000), Zero) → False
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_esEs12(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, EQ) → True
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs8(GT, EQ) → False
new_esEs16(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_esEs13(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_[], bbc), baf) → new_esEs15(xuu50000, xuu4000, bbc)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_[], bcf)) → new_esEs15(xuu50000, xuu4000, bcf)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_@2, bbg), bbh), baf) → new_esEs6(xuu50000, xuu4000, bbg, bbh)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Ratio, bag), baf) → new_esEs10(xuu50000, xuu4000, bag)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_@0, baf) → new_esEs11(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Ordering, baf) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Ratio, bcb)) → new_esEs10(xuu50000, xuu4000, bcb)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs5(xuu50000, xuu4000, bah, bba, bbb)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Char, baf) → new_esEs17(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Bool, baf) → new_esEs9(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs5(xuu50000, xuu4000, bcc, bcd, bce)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Integer, baf) → new_esEs12(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Double, baf) → new_esEs16(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_@2, bdb), bdc)) → new_esEs6(xuu50000, xuu4000, bdb, bdc)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Int, baf) → new_esEs14(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Float, baf) → new_esEs13(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Right(xuu4000), bca, baf) → False
new_esEs4(Right(xuu50000), Left(xuu4000), bca, baf) → False
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_Either, hf), hg)) → new_esEs4(xuu50000, xuu4000, hf, hg)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Maybe, bda)) → new_esEs7(xuu50000, xuu4000, bda)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Maybe, hh)) → new_esEs7(xuu50000, xuu4000, hh)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_Either, bcg), bch)) → new_esEs4(xuu50000, xuu4000, bcg, bch)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_Either, bbd), bbe), baf) → new_esEs4(xuu50000, xuu4000, bbd, bbe)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Maybe, bbf), baf) → new_esEs7(xuu50000, xuu4000, bbf)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_[], he)) → new_esEs15(xuu50000, xuu4000, he)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_@2, baa), bab)) → new_esEs6(xuu50000, xuu4000, baa, bab)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Ratio, ha)) → new_esEs10(xuu50000, xuu4000, ha)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs7(Nothing, Nothing, gh) → True
new_esEs7(Just(xuu50000), Nothing, gh) → False
new_esEs7(Nothing, Just(xuu4000), gh) → False
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, hb), hc), hd)) → new_esEs5(xuu50000, xuu4000, hb, hc, hd)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs17(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_esEs11(@0, @0) → True
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), bhg, bhh, caa) → new_asAs(new_esEs23(xuu50000, xuu4000, bhg), new_asAs(new_esEs22(xuu50001, xuu4001, bhh), new_esEs21(xuu50002, xuu4002, caa)))
new_esEs23(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Maybe, cde)) → new_esEs7(xuu50000, xuu4000, cde)
new_esEs23(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_[], cdb)) → new_esEs15(xuu50000, xuu4000, cdb)
new_esEs23(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Ratio, ccf)) → new_esEs10(xuu50000, xuu4000, ccf)
new_esEs23(xuu50000, xuu4000, app(app(ty_@2, cdf), cdg)) → new_esEs6(xuu50000, xuu4000, cdf, cdg)
new_esEs23(xuu50000, xuu4000, app(app(ty_Either, cdc), cdd)) → new_esEs4(xuu50000, xuu4000, cdc, cdd)
new_esEs23(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(app(app(ty_@3, ccg), cch), cda)) → new_esEs5(xuu50000, xuu4000, ccg, cch, cda)
new_esEs22(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(app(ty_Either, cca), ccb)) → new_esEs4(xuu50001, xuu4001, cca, ccb)
new_esEs22(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs5(xuu50001, xuu4001, cbe, cbf, cbg)
new_esEs22(xuu50001, xuu4001, app(app(ty_@2, ccd), cce)) → new_esEs6(xuu50001, xuu4001, ccd, cce)
new_esEs22(xuu50001, xuu4001, app(ty_[], cbh)) → new_esEs15(xuu50001, xuu4001, cbh)
new_esEs22(xuu50001, xuu4001, app(ty_Ratio, cbd)) → new_esEs10(xuu50001, xuu4001, cbd)
new_esEs22(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(ty_Maybe, ccc)) → new_esEs7(xuu50001, xuu4001, ccc)
new_esEs21(xuu50002, xuu4002, app(app(ty_@2, cbb), cbc)) → new_esEs6(xuu50002, xuu4002, cbb, cbc)
new_esEs21(xuu50002, xuu4002, ty_Int) → new_esEs14(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, app(ty_[], caf)) → new_esEs15(xuu50002, xuu4002, caf)
new_esEs21(xuu50002, xuu4002, ty_Double) → new_esEs16(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, app(app(ty_Either, cag), cah)) → new_esEs4(xuu50002, xuu4002, cag, cah)
new_esEs21(xuu50002, xuu4002, app(app(app(ty_@3, cac), cad), cae)) → new_esEs5(xuu50002, xuu4002, cac, cad, cae)
new_esEs21(xuu50002, xuu4002, app(ty_Maybe, cba)) → new_esEs7(xuu50002, xuu4002, cba)
new_esEs21(xuu50002, xuu4002, app(ty_Ratio, cab)) → new_esEs10(xuu50002, xuu4002, cab)
new_esEs21(xuu50002, xuu4002, ty_Bool) → new_esEs9(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Char) → new_esEs17(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Float) → new_esEs13(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Ordering) → new_esEs8(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_@0) → new_esEs11(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Integer) → new_esEs12(xuu50002, xuu4002)
new_esEs9(True, True) → True
new_esEs9(False, True) → False
new_esEs9(True, False) → False
new_esEs9(False, False) → True
new_lt7(xuu52000, xuu53000) → new_esEs8(new_compare14(xuu52000, xuu53000), LT)
new_lt19(xuu52000, xuu53000) → new_esEs8(new_compare29(xuu52000, xuu53000), LT)
new_compare29(xuu52000, xuu53000) → new_compare210(xuu52000, xuu53000, new_esEs9(xuu52000, xuu53000))
new_compare210(xuu52000, xuu53000, True) → EQ
new_compare210(xuu52000, xuu53000, False) → new_compare16(xuu52000, xuu53000, new_ltEs17(xuu52000, xuu53000))
new_compare16(xuu52000, xuu53000, True) → LT
new_compare16(xuu52000, xuu53000, False) → GT
new_lt17(xuu52000, xuu53000) → new_esEs8(new_compare32(xuu52000, xuu53000), LT)
new_lt4(xuu520, xuu530) → new_esEs8(new_compare6(xuu520, xuu530), LT)
new_lt10(xuu52000, xuu53000, bdd, bde) → new_esEs8(new_compare19(xuu52000, xuu53000, bdd, bde), LT)
new_compare19(xuu52000, xuu53000, bdd, bde) → new_compare23(xuu52000, xuu53000, new_esEs4(xuu52000, xuu53000, bdd, bde), bdd, bde)
new_compare23(Left(xuu5200), Left(xuu5300), False, ca, cb) → new_compare10(xuu5200, xuu5300, new_ltEs4(xuu5200, xuu5300, ca), ca, cb)
new_compare23(Right(xuu5200), Left(xuu5300), False, ca, cb) → GT
new_compare23(Left(xuu5200), Right(xuu5300), False, ca, cb) → LT
new_ltEs4(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(app(app(ty_@3, cf), cg), da)) → new_ltEs10(xuu5200, xuu5300, cf, cg, da)
new_ltEs4(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(app(ty_@2, db), dc)) → new_ltEs11(xuu5200, xuu5300, db, dc)
new_ltEs4(xuu5200, xuu5300, app(ty_Maybe, dd)) → new_ltEs12(xuu5200, xuu5300, dd)
new_ltEs4(xuu5200, xuu5300, app(ty_[], de)) → new_ltEs14(xuu5200, xuu5300, de)
new_ltEs4(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(ty_Ratio, ce)) → new_ltEs9(xuu5200, xuu5300, ce)
new_ltEs4(xuu5200, xuu5300, app(app(ty_Either, cc), cd)) → new_ltEs8(xuu5200, xuu5300, cc, cd)
new_ltEs4(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_compare10(xuu167, xuu168, True, dhe, dhf) → LT
new_compare10(xuu167, xuu168, False, dhe, dhf) → GT
new_lt9(xuu52000, xuu53000, fa, fb, fc) → new_esEs8(new_compare8(xuu52000, xuu53000, fa, fb, fc), LT)
new_compare8(xuu52000, xuu53000, fa, fb, fc) → new_compare24(xuu52000, xuu53000, new_esEs5(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_compare24(xuu52000, xuu53000, False, fa, fb, fc) → new_compare12(xuu52000, xuu53000, new_ltEs10(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_compare24(xuu52000, xuu53000, True, fa, fb, fc) → EQ
new_compare12(xuu52000, xuu53000, True, fa, fb, fc) → LT
new_compare12(xuu52000, xuu53000, False, fa, fb, fc) → GT
new_lt6(xuu52000, xuu53000) → new_esEs8(new_compare13(xuu52000, xuu53000), LT)
new_lt15(xuu52000, xuu53000, bad, bae) → new_esEs8(new_compare17(xuu52000, xuu53000, bad, bae), LT)
new_lt14(xuu52000, xuu53000) → new_esEs8(new_compare27(xuu52000, xuu53000), LT)
new_lt13(xuu52000, xuu53000) → new_esEs8(new_compare15(xuu52000, xuu53000), LT)
new_lt16(xuu52000, xuu53000, gg) → new_esEs8(new_compare9(xuu52000, xuu53000, gg), LT)
new_compare9(xuu52000, xuu53000, gg) → new_compare25(xuu52000, xuu53000, new_esEs7(xuu52000, xuu53000, gg), gg)
new_compare25(xuu52000, xuu53000, True, gg) → EQ
new_compare25(xuu52000, xuu53000, False, gg) → new_compare18(xuu52000, xuu53000, new_ltEs12(xuu52000, xuu53000, gg), gg)
new_compare18(xuu52000, xuu53000, True, gg) → LT
new_compare18(xuu52000, xuu53000, False, gg) → GT
new_lt18(xuu52000, xuu53000) → new_esEs8(new_compare30(xuu52000, xuu53000), LT)
new_compare30(xuu52000, xuu53000) → new_compare28(xuu52000, xuu53000, new_esEs8(xuu52000, xuu53000))
new_compare28(xuu52000, xuu53000, True) → EQ
new_compare28(xuu52000, xuu53000, False) → new_compare110(xuu52000, xuu53000, new_ltEs16(xuu52000, xuu53000))
new_compare110(xuu52000, xuu53000, True) → LT
new_compare110(xuu52000, xuu53000, False) → GT
new_lt5(xuu52000, xuu53000, eh) → new_esEs8(new_compare7(xuu52000, xuu53000, eh), LT)
new_lt8(xuu52000, xuu53000, bac) → new_esEs8(new_compare1(xuu52000, xuu53000, bac), LT)
new_esEs20(xuu50000, xuu4000, app(ty_Maybe, bhd)) → new_esEs7(xuu50000, xuu4000, bhd)
new_esEs20(xuu50000, xuu4000, app(app(ty_Either, bhb), bhc)) → new_esEs4(xuu50000, xuu4000, bhb, bhc)
new_esEs20(xuu50000, xuu4000, app(app(ty_@2, bhe), bhf)) → new_esEs6(xuu50000, xuu4000, bhe, bhf)
new_esEs20(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, app(ty_Ratio, bge)) → new_esEs10(xuu50000, xuu4000, bge)
new_esEs20(xuu50000, xuu4000, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs5(xuu50000, xuu4000, bgf, bgg, bgh)
new_esEs20(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, app(ty_[], bha)) → new_esEs15(xuu50000, xuu4000, bha)
new_esEs20(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs5(xuu50001, xuu4001, bfd, bfe, bff)
new_esEs19(xuu50001, xuu4001, app(ty_Maybe, bgb)) → new_esEs7(xuu50001, xuu4001, bgb)
new_esEs19(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, app(app(ty_@2, bgc), bgd)) → new_esEs6(xuu50001, xuu4001, bgc, bgd)
new_esEs19(xuu50001, xuu4001, app(ty_[], bfg)) → new_esEs15(xuu50001, xuu4001, bfg)
new_esEs19(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, app(ty_Ratio, bfc)) → new_esEs10(xuu50001, xuu4001, bfc)
new_esEs19(xuu50001, xuu4001, app(app(ty_Either, bfh), bga)) → new_esEs4(xuu50001, xuu4001, bfh, bga)
new_esEs19(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs31(xuu5000, xuu400, ty_@0) → new_esEs11(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, ty_Ordering) → new_esEs8(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs5(xuu5000, xuu400, cgg, cgh, cha)
new_esEs31(xuu5000, xuu400, ty_Char) → new_esEs17(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, ty_Bool) → new_esEs9(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, ty_Integer) → new_esEs12(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, app(ty_[], chb)) → new_esEs15(xuu5000, xuu400, chb)
new_esEs31(xuu5000, xuu400, app(app(ty_Either, chc), chd)) → new_esEs4(xuu5000, xuu400, chc, chd)
new_esEs31(xuu5000, xuu400, ty_Int) → new_esEs14(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, app(ty_Ratio, cgf)) → new_esEs10(xuu5000, xuu400, cgf)
new_esEs31(xuu5000, xuu400, ty_Double) → new_esEs16(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, ty_Float) → new_esEs13(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, app(ty_Maybe, che)) → new_esEs7(xuu5000, xuu400, che)
new_esEs31(xuu5000, xuu400, app(app(ty_@2, chf), chg)) → new_esEs6(xuu5000, xuu400, chf, chg)

The set Q consists of the following terms:

new_primCompAux0(x0, EQ)
new_ltEs4(x0, x1, ty_Bool)
new_ltEs5(x0, x1, ty_Float)
new_compare29(x0, x1)
new_fsEs(x0)
new_primCompAux0(x0, GT)
new_esEs19(x0, x1, ty_Bool)
new_esEs18(x0, x1, ty_@0)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3)
new_compare16(x0, x1, False)
new_esEs32(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_compare9(x0, x1, x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, False)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Char)
new_compare8(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Double)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare23(x0, x1, True, x2, x3)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1)
new_compare17(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs31(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Float)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs11(@0, @0)
new_compare10(x0, x1, True, x2, x3)
new_compare111(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_ltEs4(x0, x1, ty_Int)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs8(GT, GT)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_primCmpNat1(x0, Zero)
new_ltEs21(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs4(x0, x1, ty_Integer)
new_esEs7(Nothing, Just(x0), x1)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_ltEs4(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(LT, LT)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, x2)
new_esEs21(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Ordering)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_@0)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Int)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, ty_Integer)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs7(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(False, False)
new_esEs7(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Integer)
new_ltEs4(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(ty_[], x2))
new_compare1(:(x0, x1), [], x2)
new_compare24(x0, x1, False, x2, x3, x4)
new_primEqNat0(Zero, Zero)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs9(True, True)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs29(x0, x1, ty_Double)
new_lt10(x0, x1, x2, x3)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(x0, Succ(x1))
new_primMulNat0(Zero, Zero)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs18(x0, x1)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Integer)
new_ltEs17(True, True)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(Left(x0), Left(x1), False, x2, x3)
new_esEs29(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_lt12(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare14(Integer(x0), Integer(x1))
new_primCmpNat0(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Zero)
new_compare23(Right(x0), Right(x1), False, x2, x3)
new_esEs24(x0, x1, ty_Bool)
new_primCompAux1(x0, x1, x2, x3)
new_esEs7(Nothing, Nothing, x0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1)
new_ltEs4(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(x0, x1, ty_Integer)
new_pePe(False, x0)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_compare1([], :(x0, x1), x2)
new_ltEs21(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_ltEs6(x0, x1)
new_ltEs12(Just(x0), Nothing, x1)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(Float(x0, x1), Float(x2, x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs30(x0, x1, ty_Float)
new_lt12(x0, x1, ty_Int)
new_esEs17(Char(x0), Char(x1))
new_esEs19(x0, x1, ty_Char)
new_primPlusNat0(Zero, Zero)
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs16(EQ, EQ)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Zero)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare25(x0, x1, True, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_esEs19(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_compare28(x0, x1, False)
new_esEs18(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Float)
new_compare16(x0, x1, True)
new_esEs23(x0, x1, ty_Float)
new_esEs18(x0, x1, ty_Int)
new_ltEs16(LT, GT)
new_ltEs16(GT, LT)
new_esEs25(x0, x1, ty_@0)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1)
new_primPlusNat1(Succ(x0), x1)
new_pePe(True, x0)
new_lt11(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt11(x0, x1, ty_Ordering)
new_primCompAux0(x0, LT)
new_esEs25(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_lt12(x0, x1, ty_Bool)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1)
new_compare10(x0, x1, False, x2, x3)
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1, x2)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Bool)
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt15(x0, x1, x2, x3)
new_primPlusNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare31(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_asAs(True, x0)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare26(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs32(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare31(x0, x1, ty_Char)
new_compare210(x0, x1, False)
new_ltEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Integer)
new_ltEs16(GT, GT)
new_esEs18(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_@0)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Double)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs13(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs5(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_primCmpNat2(Succ(x0), x1)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs14(x0, x1)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_compare18(x0, x1, True, x2)
new_esEs30(x0, x1, ty_Integer)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_compare13(Double(x0, x1), Double(x2, x3))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, x0)
new_compare31(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare15(Char(x0), Char(x1))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCmpNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare23(Left(x0), Right(x1), False, x2, x3)
new_compare23(Right(x0), Left(x1), False, x2, x3)
new_ltEs12(Nothing, Nothing, x0)
new_esEs18(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Char)
new_ltEs12(Nothing, Just(x0), x1)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Int)
new_esEs9(False, False)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs18(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_compare6(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Bool)
new_compare31(x0, x1, ty_Ordering)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs4(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_ltEs4(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Double)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_compare18(x0, x1, False, x2)
new_compare26(x0, x1, False, x2, x3)
new_esEs30(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_not(True)
new_ltEs19(x0, x1)
new_esEs20(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs21(x0, x1, ty_Float)
new_lt11(x0, x1, ty_Int)
new_lt9(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, x0)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_lt11(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_ltEs17(False, True)
new_ltEs17(True, False)
new_ltEs20(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_lt12(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, True)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt6(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Int)
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_compare28(x0, x1, True)
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs9(False, True)
new_esEs9(True, False)
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_ltEs20(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare31(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs15([], :(x0, x1), x2)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs15(:(x0, x1), [], x2)
new_esEs21(x0, x1, ty_Bool)
new_ltEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_compare27(@0, @0)
new_lt11(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs30(x0, x1, ty_@0)
new_lt11(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Integer)
new_ltEs9(x0, x1, x2)
new_compare25(x0, x1, False, x2)
new_esEs30(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt8(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs32(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs20(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_esEs29(x0, x1, ty_Int)
new_esEs15([], [], x0)
new_lt12(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_sr(x0, x1)
new_esEs31(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)

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_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_@0)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Double)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Int)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Char)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_@0)
new_esEs30(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Int)



↳ 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
                                          ↳ UsableRulesProof
                                            ↳ QDP
                                              ↳ QReductionProof
QDP
                                                  ↳ QDPSizeChangeProof
                                        ↳ QDP
                                  ↳ QDP

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

new_addToFM_C(xuu3, Branch(Left(xuu400), xuu41, xuu42, xuu43, xuu44), Right(xuu5000), xuu501, bc, bd, be) → new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Right(xuu5000), Left(xuu400), False, bc, bd), LT), bc, bd, be)
new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, False, bc, bd, be) → new_addToFM_C11(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Right(xuu5000), Left(xuu400), False, bc, bd), GT), bc, bd, be)
new_addToFM_C11(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu44, Right(xuu5000), xuu501, bc, bd, be)
new_addToFM_C(xuu3, Branch(Right(xuu400), xuu41, xuu42, xuu43, xuu44), Right(xuu5000), xuu501, bc, bd, be) → new_addToFM_C22(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Right(xuu5000), Right(xuu400), new_esEs31(xuu5000, xuu400, bd), bc, bd), LT), bc, bd, be)
new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu43, Right(xuu5000), xuu501, bc, bd, be)
new_addToFM_C22(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, True, bf, bg, bh) → new_addToFM_C(xuu35, xuu39, Right(xuu41), xuu42, bf, bg, bh)
new_addToFM_C22(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, False, bf, bg, bh) → new_addToFM_C12(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, new_esEs8(new_compare23(Right(xuu41), Right(xuu36), new_esEs32(xuu41, xuu36, bg), bf, bg), GT), bf, bg, bh)
new_addToFM_C12(xuu35, xuu36, xuu37, xuu38, xuu39, xuu40, xuu41, xuu42, True, bf, bg, bh) → new_addToFM_C(xuu35, xuu40, Right(xuu41), xuu42, bf, bg, bh)

The TRS R consists of the following rules:

new_esEs32(xuu41, xuu36, app(app(ty_@2, ge), gf)) → new_esEs6(xuu41, xuu36, ge, gf)
new_esEs32(xuu41, xuu36, app(ty_Maybe, gd)) → new_esEs7(xuu41, xuu36, gd)
new_esEs32(xuu41, xuu36, ty_Bool) → new_esEs9(xuu41, xuu36)
new_esEs32(xuu41, xuu36, ty_Int) → new_esEs14(xuu41, xuu36)
new_esEs32(xuu41, xuu36, app(app(app(ty_@3, ff), fg), fh)) → new_esEs5(xuu41, xuu36, ff, fg, fh)
new_esEs32(xuu41, xuu36, ty_@0) → new_esEs11(xuu41, xuu36)
new_esEs32(xuu41, xuu36, app(ty_Ratio, fd)) → new_esEs10(xuu41, xuu36, fd)
new_esEs32(xuu41, xuu36, ty_Char) → new_esEs17(xuu41, xuu36)
new_esEs32(xuu41, xuu36, ty_Ordering) → new_esEs8(xuu41, xuu36)
new_esEs32(xuu41, xuu36, app(ty_[], ga)) → new_esEs15(xuu41, xuu36, ga)
new_esEs32(xuu41, xuu36, ty_Float) → new_esEs13(xuu41, xuu36)
new_esEs32(xuu41, xuu36, app(app(ty_Either, gb), gc)) → new_esEs4(xuu41, xuu36, gb, gc)
new_esEs32(xuu41, xuu36, ty_Integer) → new_esEs12(xuu41, xuu36)
new_esEs32(xuu41, xuu36, ty_Double) → new_esEs16(xuu41, xuu36)
new_compare23(xuu520, xuu530, True, ca, cb) → EQ
new_compare23(Right(xuu5200), Right(xuu5300), False, ca, cb) → new_compare11(xuu5200, xuu5300, new_ltEs5(xuu5200, xuu5300, cb), ca, cb)
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_ltEs5(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, app(app(app(ty_@3, ea), eb), ec)) → new_ltEs10(xuu5200, xuu5300, ea, eb, ec)
new_ltEs5(xuu5200, xuu5300, app(app(ty_Either, df), dg)) → new_ltEs8(xuu5200, xuu5300, df, dg)
new_ltEs5(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, app(ty_Ratio, dh)) → new_ltEs9(xuu5200, xuu5300, dh)
new_ltEs5(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, app(app(ty_@2, ed), ee)) → new_ltEs11(xuu5200, xuu5300, ed, ee)
new_ltEs5(xuu5200, xuu5300, app(ty_Maybe, ef)) → new_ltEs12(xuu5200, xuu5300, ef)
new_ltEs5(xuu5200, xuu5300, app(ty_[], eg)) → new_ltEs14(xuu5200, xuu5300, eg)
new_ltEs5(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_compare11(xuu174, xuu175, True, cdh, cea) → LT
new_compare11(xuu174, xuu175, False, cdh, cea) → GT
new_ltEs19(xuu5200, xuu5300) → new_fsEs(new_compare6(xuu5200, xuu5300))
new_compare6(xuu52, xuu53) → new_primCmpInt(xuu52, xuu53)
new_fsEs(xuu177) → new_not(new_esEs8(xuu177, GT))
new_not(False) → True
new_not(True) → False
new_primCmpInt(Pos(Succ(xuu5200)), Pos(xuu530)) → new_primCmpNat1(xuu5200, xuu530)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(xuu5300))) → LT
new_primCmpInt(Pos(Succ(xuu5200)), Neg(xuu530)) → GT
new_primCmpInt(Pos(Zero), Neg(Succ(xuu5300))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(xuu5200)), Neg(xuu530)) → new_primCmpNat2(xuu530, xuu5200)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu5300))) → new_primCmpNat2(Zero, xuu5300)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu5300))) → new_primCmpNat1(xuu5300, Zero)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(xuu5200)), Pos(xuu530)) → LT
new_primCmpNat1(xuu5200, Zero) → GT
new_primCmpNat2(Zero, xuu5200) → LT
new_primCmpNat2(Succ(xuu5300), xuu5200) → new_primCmpNat0(xuu5300, xuu5200)
new_primCmpNat0(Zero, Succ(xuu53000)) → LT
new_primCmpNat0(Succ(xuu52000), Succ(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu52000), Zero) → GT
new_primCmpNat1(xuu5200, Succ(xuu5300)) → new_primCmpNat0(xuu5200, xuu5300)
new_ltEs18(xuu5200, xuu5300) → new_fsEs(new_compare14(xuu5200, xuu5300))
new_compare14(Integer(xuu52000), Integer(xuu53000)) → new_primCmpInt(xuu52000, xuu53000)
new_ltEs6(xuu5200, xuu5300) → new_fsEs(new_compare15(xuu5200, xuu5300))
new_compare15(Char(xuu52000), Char(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_ltEs14(xuu5200, xuu5300, de) → new_fsEs(new_compare1(xuu5200, xuu5300, de))
new_compare1(:(xuu52000, xuu52001), :(xuu53000, xuu53001), de) → new_primCompAux1(xuu52000, xuu53000, new_compare1(xuu52001, xuu53001, de), de)
new_compare1([], :(xuu53000, xuu53001), de) → LT
new_compare1(:(xuu52000, xuu52001), [], de) → GT
new_compare1([], [], de) → EQ
new_primCompAux1(xuu52000, xuu53000, xuu204, de) → new_primCompAux0(xuu204, new_compare31(xuu52000, xuu53000, de))
new_compare31(xuu52000, xuu53000, ty_Int) → new_compare6(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(ty_Maybe, dde)) → new_compare9(xuu52000, xuu53000, dde)
new_compare31(xuu52000, xuu53000, ty_@0) → new_compare27(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Float) → new_compare32(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Bool) → new_compare29(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Ordering) → new_compare30(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Integer) → new_compare14(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(app(app(ty_@3, dch), dda), ddb)) → new_compare8(xuu52000, xuu53000, dch, dda, ddb)
new_compare31(xuu52000, xuu53000, app(app(ty_Either, dce), dcf)) → new_compare19(xuu52000, xuu53000, dce, dcf)
new_compare31(xuu52000, xuu53000, app(app(ty_@2, ddc), ddd)) → new_compare17(xuu52000, xuu53000, ddc, ddd)
new_compare31(xuu52000, xuu53000, ty_Char) → new_compare15(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(ty_Ratio, dcg)) → new_compare7(xuu52000, xuu53000, dcg)
new_compare31(xuu52000, xuu53000, ty_Double) → new_compare13(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(ty_[], ddf)) → new_compare1(xuu52000, xuu53000, ddf)
new_primCompAux0(xuu218, GT) → GT
new_primCompAux0(xuu218, LT) → LT
new_primCompAux0(xuu218, EQ) → xuu218
new_compare13(Double(xuu52000, xuu52001), Double(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_sr(xuu50001, xuu4001) → new_primMulInt(xuu50001, xuu4001)
new_primMulInt(Pos(xuu500010), Pos(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Neg(xuu500010), Neg(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Pos(xuu500010), Neg(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Neg(xuu500010), Pos(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(xuu5000100), Succ(xuu400100)) → new_primPlusNat1(new_primMulNat0(xuu5000100, Succ(xuu400100)), xuu400100)
new_primMulNat0(Succ(xuu5000100), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu400100)) → Zero
new_primPlusNat1(Zero, xuu400100) → Succ(xuu400100)
new_primPlusNat1(Succ(xuu1400), xuu400100) → Succ(Succ(new_primPlusNat0(xuu1400, xuu400100)))
new_primPlusNat0(Succ(xuu55200), Zero) → Succ(xuu55200)
new_primPlusNat0(Zero, Succ(xuu13100)) → Succ(xuu13100)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(xuu55200), Succ(xuu13100)) → Succ(Succ(new_primPlusNat0(xuu55200, xuu13100)))
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Integer) → new_compare14(new_sr0(xuu52000, xuu53001), new_sr0(xuu53000, xuu52001))
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Int) → new_compare6(new_sr(xuu52000, xuu53001), new_sr(xuu53000, xuu52001))
new_sr0(Integer(xuu530000), Integer(xuu520010)) → Integer(new_primMulInt(xuu530000, xuu520010))
new_compare17(xuu52000, xuu53000, bad, bae) → new_compare26(xuu52000, xuu53000, new_esEs6(xuu52000, xuu53000, bad, bae), bad, bae)
new_esEs6(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), bfa, bfb) → new_asAs(new_esEs20(xuu50000, xuu4000, bfa), new_esEs19(xuu50001, xuu4001, bfb))
new_compare26(xuu52000, xuu53000, True, bad, bae) → EQ
new_compare26(xuu52000, xuu53000, False, bad, bae) → new_compare111(xuu52000, xuu53000, new_ltEs11(xuu52000, xuu53000, bad, bae), bad, bae)
new_ltEs11(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), db, dc) → new_pePe(new_lt20(xuu52000, xuu53000, db), new_asAs(new_esEs26(xuu52000, xuu53000, db), new_ltEs21(xuu52001, xuu53001, dc)))
new_compare111(xuu52000, xuu53000, False, bad, bae) → GT
new_compare111(xuu52000, xuu53000, True, bad, bae) → LT
new_lt20(xuu52000, xuu53000, app(ty_[], dba)) → new_lt8(xuu52000, xuu53000, dba)
new_lt20(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_lt16(xuu52000, xuu53000, dah)
new_lt20(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_lt5(xuu52000, xuu53000, dab)
new_lt20(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_lt9(xuu52000, xuu53000, dac, dad, dae)
new_lt20(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_lt10(xuu52000, xuu53000, chh, daa)
new_lt20(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_lt15(xuu52000, xuu53000, daf, dag)
new_esEs26(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_esEs10(xuu52000, xuu53000, dab)
new_esEs26(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_esEs7(xuu52000, xuu53000, dah)
new_esEs26(xuu52000, xuu53000, app(ty_[], dba)) → new_esEs15(xuu52000, xuu53000, dba)
new_esEs26(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_esEs4(xuu52000, xuu53000, chh, daa)
new_esEs26(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_esEs5(xuu52000, xuu53000, dac, dad, dae)
new_esEs26(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_esEs6(xuu52000, xuu53000, daf, dag)
new_esEs26(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_ltEs21(xuu52001, xuu53001, ty_@0) → new_ltEs7(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Char) → new_ltEs6(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, app(app(ty_Either, dbb), dbc)) → new_ltEs8(xuu52001, xuu53001, dbb, dbc)
new_ltEs21(xuu52001, xuu53001, app(app(ty_@2, dbh), dca)) → new_ltEs11(xuu52001, xuu53001, dbh, dca)
new_ltEs21(xuu52001, xuu53001, app(ty_[], dcc)) → new_ltEs14(xuu52001, xuu53001, dcc)
new_ltEs21(xuu52001, xuu53001, ty_Float) → new_ltEs13(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Ordering) → new_ltEs16(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Int) → new_ltEs19(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, app(ty_Ratio, dbd)) → new_ltEs9(xuu52001, xuu53001, dbd)
new_ltEs21(xuu52001, xuu53001, app(ty_Maybe, dcb)) → new_ltEs12(xuu52001, xuu53001, dcb)
new_ltEs21(xuu52001, xuu53001, ty_Double) → new_ltEs15(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Bool) → new_ltEs17(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_ltEs10(xuu52001, xuu53001, dbe, dbf, dbg)
new_ltEs21(xuu52001, xuu53001, ty_Integer) → new_ltEs18(xuu52001, xuu53001)
new_asAs(False, xuu162) → False
new_asAs(True, xuu162) → xuu162
new_pePe(False, xuu194) → xuu194
new_pePe(True, xuu194) → True
new_ltEs10(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), cf, cg, da) → new_pePe(new_lt11(xuu52000, xuu53000, cf), new_asAs(new_esEs25(xuu52000, xuu53000, cf), new_pePe(new_lt12(xuu52001, xuu53001, cg), new_asAs(new_esEs24(xuu52001, xuu53001, cg), new_ltEs20(xuu52002, xuu53002, da)))))
new_lt11(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_lt9(xuu52000, xuu53000, fa, fb, fc)
new_lt11(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_lt15(xuu52000, xuu53000, bad, bae)
new_lt11(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_lt10(xuu52000, xuu53000, bdd, bde)
new_lt11(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, app(ty_[], bac)) → new_lt8(xuu52000, xuu53000, bac)
new_lt11(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_lt5(xuu52000, xuu53000, eh)
new_lt11(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_lt16(xuu52000, xuu53000, gg)
new_esEs25(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_esEs4(xuu52000, xuu53000, bdd, bde)
new_esEs25(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_esEs6(xuu52000, xuu53000, bad, bae)
new_esEs25(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(ty_[], bac)) → new_esEs15(xuu52000, xuu53000, bac)
new_esEs25(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_esEs10(xuu52000, xuu53000, eh)
new_esEs25(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_esEs7(xuu52000, xuu53000, gg)
new_esEs25(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_esEs5(xuu52000, xuu53000, fa, fb, fc)
new_lt12(xuu52001, xuu53001, app(ty_[], cfc)) → new_lt8(xuu52001, xuu53001, cfc)
new_lt12(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_lt5(xuu52001, xuu53001, ced)
new_lt12(xuu52001, xuu53001, ty_Ordering) → new_lt18(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_lt16(xuu52001, xuu53001, cfb)
new_lt12(xuu52001, xuu53001, ty_Char) → new_lt13(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_@0) → new_lt14(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_lt15(xuu52001, xuu53001, ceh, cfa)
new_lt12(xuu52001, xuu53001, ty_Double) → new_lt6(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_lt9(xuu52001, xuu53001, cee, cef, ceg)
new_lt12(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_lt10(xuu52001, xuu53001, ceb, cec)
new_lt12(xuu52001, xuu53001, ty_Int) → new_lt4(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Float) → new_lt17(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Bool) → new_lt19(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Integer) → new_lt7(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs5(xuu52001, xuu53001, cee, cef, ceg)
new_esEs24(xuu52001, xuu53001, ty_Char) → new_esEs17(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_esEs7(xuu52001, xuu53001, cfb)
new_esEs24(xuu52001, xuu53001, ty_@0) → new_esEs11(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_esEs6(xuu52001, xuu53001, ceh, cfa)
new_esEs24(xuu52001, xuu53001, ty_Double) → new_esEs16(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Ordering) → new_esEs8(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Int) → new_esEs14(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Integer) → new_esEs12(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_esEs4(xuu52001, xuu53001, ceb, cec)
new_esEs24(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_esEs10(xuu52001, xuu53001, ced)
new_esEs24(xuu52001, xuu53001, ty_Bool) → new_esEs9(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Float) → new_esEs13(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(ty_[], cfc)) → new_esEs15(xuu52001, xuu53001, cfc)
new_ltEs20(xuu52002, xuu53002, app(ty_Ratio, cff)) → new_ltEs9(xuu52002, xuu53002, cff)
new_ltEs20(xuu52002, xuu53002, ty_@0) → new_ltEs7(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Int) → new_ltEs19(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Double) → new_ltEs15(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, app(ty_Maybe, cgd)) → new_ltEs12(xuu52002, xuu53002, cgd)
new_ltEs20(xuu52002, xuu53002, app(ty_[], cge)) → new_ltEs14(xuu52002, xuu53002, cge)
new_ltEs20(xuu52002, xuu53002, ty_Integer) → new_ltEs18(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, app(app(ty_@2, cgb), cgc)) → new_ltEs11(xuu52002, xuu53002, cgb, cgc)
new_ltEs20(xuu52002, xuu53002, ty_Bool) → new_ltEs17(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Ordering) → new_ltEs16(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Float) → new_ltEs13(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Char) → new_ltEs6(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, app(app(ty_Either, cfd), cfe)) → new_ltEs8(xuu52002, xuu53002, cfd, cfe)
new_ltEs20(xuu52002, xuu53002, app(app(app(ty_@3, cfg), cfh), cga)) → new_ltEs10(xuu52002, xuu53002, cfg, cfh, cga)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Bool, cd) → new_ltEs17(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_[], dhd)) → new_ltEs14(xuu52000, xuu53000, dhd)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_@2, dha), dhb)) → new_ltEs11(xuu52000, xuu53000, dha, dhb)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(app(ty_@3, dfd), dfe), dff), cd) → new_ltEs10(xuu52000, xuu53000, dfd, dfe, dff)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_[], dgb), cd) → new_ltEs14(xuu52000, xuu53000, dgb)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Char, cd) → new_ltEs6(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(app(ty_@3, dgf), dgg), dgh)) → new_ltEs10(xuu52000, xuu53000, dgf, dgg, dgh)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Float, cd) → new_ltEs13(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_@2, dfg), dfh), cd) → new_ltEs11(xuu52000, xuu53000, dfg, dfh)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_@0, cd) → new_ltEs7(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Ratio, dfc), cd) → new_ltEs9(xuu52000, xuu53000, dfc)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Ordering, cd) → new_ltEs16(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Int, cd) → new_ltEs19(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Left(xuu53000), cc, cd) → False
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Double, cd) → new_ltEs15(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Integer, cd) → new_ltEs18(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Ratio, dge)) → new_ltEs9(xuu52000, xuu53000, dge)
new_ltEs8(Left(xuu52000), Right(xuu53000), cc, cd) → True
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_Either, dfa), dfb), cd) → new_ltEs8(xuu52000, xuu53000, dfa, dfb)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Maybe, dga), cd) → new_ltEs12(xuu52000, xuu53000, dga)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Maybe, dhc)) → new_ltEs12(xuu52000, xuu53000, dhc)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Maybe, deg)) → new_ltEs12(xuu52000, xuu53000, deg)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_Either, dgc), dgd)) → new_ltEs8(xuu52000, xuu53000, dgc, dgd)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_Either, ddg), ddh)) → new_ltEs8(xuu52000, xuu53000, ddg, ddh)
new_ltEs12(Nothing, Nothing, dd) → True
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Ratio, dea)) → new_ltEs9(xuu52000, xuu53000, dea)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_[], deh)) → new_ltEs14(xuu52000, xuu53000, deh)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_@2, dee), def)) → new_ltEs11(xuu52000, xuu53000, dee, def)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(app(ty_@3, deb), dec), ded)) → new_ltEs10(xuu52000, xuu53000, deb, dec, ded)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_ltEs12(Nothing, Just(xuu53000), dd) → True
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Nothing, dd) → False
new_ltEs13(xuu5200, xuu5300) → new_fsEs(new_compare32(xuu5200, xuu5300))
new_compare32(Float(xuu52000, xuu52001), Float(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_ltEs17(False, False) → True
new_ltEs17(True, False) → False
new_ltEs17(True, True) → True
new_ltEs17(False, True) → True
new_ltEs9(xuu5200, xuu5300, ce) → new_fsEs(new_compare7(xuu5200, xuu5300, ce))
new_ltEs15(xuu5200, xuu5300) → new_fsEs(new_compare13(xuu5200, xuu5300))
new_ltEs7(xuu5200, xuu5300) → new_fsEs(new_compare27(xuu5200, xuu5300))
new_compare27(@0, @0) → EQ
new_ltEs16(GT, GT) → True
new_ltEs16(LT, GT) → True
new_ltEs16(EQ, GT) → True
new_ltEs16(EQ, LT) → False
new_ltEs16(GT, EQ) → False
new_ltEs16(LT, EQ) → True
new_ltEs16(GT, LT) → False
new_ltEs16(EQ, EQ) → True
new_ltEs16(LT, LT) → True
new_esEs15(:(xuu50000, xuu50001), :(xuu4000, xuu4001), bdf) → new_asAs(new_esEs18(xuu50000, xuu4000, bdf), new_esEs15(xuu50001, xuu4001, bdf))
new_esEs15([], [], bdf) → True
new_esEs15(:(xuu50000, xuu50001), [], bdf) → False
new_esEs15([], :(xuu4000, xuu4001), bdf) → False
new_esEs18(xuu50000, xuu4000, app(app(ty_@2, beg), beh)) → new_esEs6(xuu50000, xuu4000, beg, beh)
new_esEs18(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs5(xuu50000, xuu4000, bdh, bea, beb)
new_esEs18(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(ty_Maybe, bef)) → new_esEs7(xuu50000, xuu4000, bef)
new_esEs18(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(app(ty_Either, bed), bee)) → new_esEs4(xuu50000, xuu4000, bed, bee)
new_esEs18(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(ty_[], bec)) → new_esEs15(xuu50000, xuu4000, bec)
new_esEs18(xuu50000, xuu4000, app(ty_Ratio, bdg)) → new_esEs10(xuu50000, xuu4000, bdg)
new_esEs10(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), dcd) → new_asAs(new_esEs28(xuu50000, xuu4000, dcd), new_esEs27(xuu50001, xuu4001, dcd))
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs14(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_primEqNat0(Succ(xuu500000), Zero) → False
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_esEs12(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, EQ) → True
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs8(GT, EQ) → False
new_esEs16(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_esEs13(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_[], bbc), baf) → new_esEs15(xuu50000, xuu4000, bbc)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_[], bcf)) → new_esEs15(xuu50000, xuu4000, bcf)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_@2, bbg), bbh), baf) → new_esEs6(xuu50000, xuu4000, bbg, bbh)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Ratio, bag), baf) → new_esEs10(xuu50000, xuu4000, bag)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_@0, baf) → new_esEs11(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Ordering, baf) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Ratio, bcb)) → new_esEs10(xuu50000, xuu4000, bcb)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs5(xuu50000, xuu4000, bah, bba, bbb)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Char, baf) → new_esEs17(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Bool, baf) → new_esEs9(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs5(xuu50000, xuu4000, bcc, bcd, bce)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Integer, baf) → new_esEs12(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Double, baf) → new_esEs16(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_@2, bdb), bdc)) → new_esEs6(xuu50000, xuu4000, bdb, bdc)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Int, baf) → new_esEs14(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Float, baf) → new_esEs13(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Right(xuu4000), bca, baf) → False
new_esEs4(Right(xuu50000), Left(xuu4000), bca, baf) → False
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_Either, hf), hg)) → new_esEs4(xuu50000, xuu4000, hf, hg)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Maybe, bda)) → new_esEs7(xuu50000, xuu4000, bda)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Maybe, hh)) → new_esEs7(xuu50000, xuu4000, hh)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_Either, bcg), bch)) → new_esEs4(xuu50000, xuu4000, bcg, bch)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_Either, bbd), bbe), baf) → new_esEs4(xuu50000, xuu4000, bbd, bbe)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Maybe, bbf), baf) → new_esEs7(xuu50000, xuu4000, bbf)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_[], he)) → new_esEs15(xuu50000, xuu4000, he)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_@2, baa), bab)) → new_esEs6(xuu50000, xuu4000, baa, bab)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Ratio, ha)) → new_esEs10(xuu50000, xuu4000, ha)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs7(Nothing, Nothing, gh) → True
new_esEs7(Just(xuu50000), Nothing, gh) → False
new_esEs7(Nothing, Just(xuu4000), gh) → False
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, hb), hc), hd)) → new_esEs5(xuu50000, xuu4000, hb, hc, hd)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs17(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_esEs11(@0, @0) → True
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), bhg, bhh, caa) → new_asAs(new_esEs23(xuu50000, xuu4000, bhg), new_asAs(new_esEs22(xuu50001, xuu4001, bhh), new_esEs21(xuu50002, xuu4002, caa)))
new_esEs23(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Maybe, cde)) → new_esEs7(xuu50000, xuu4000, cde)
new_esEs23(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_[], cdb)) → new_esEs15(xuu50000, xuu4000, cdb)
new_esEs23(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Ratio, ccf)) → new_esEs10(xuu50000, xuu4000, ccf)
new_esEs23(xuu50000, xuu4000, app(app(ty_@2, cdf), cdg)) → new_esEs6(xuu50000, xuu4000, cdf, cdg)
new_esEs23(xuu50000, xuu4000, app(app(ty_Either, cdc), cdd)) → new_esEs4(xuu50000, xuu4000, cdc, cdd)
new_esEs23(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(app(app(ty_@3, ccg), cch), cda)) → new_esEs5(xuu50000, xuu4000, ccg, cch, cda)
new_esEs22(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(app(ty_Either, cca), ccb)) → new_esEs4(xuu50001, xuu4001, cca, ccb)
new_esEs22(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs5(xuu50001, xuu4001, cbe, cbf, cbg)
new_esEs22(xuu50001, xuu4001, app(app(ty_@2, ccd), cce)) → new_esEs6(xuu50001, xuu4001, ccd, cce)
new_esEs22(xuu50001, xuu4001, app(ty_[], cbh)) → new_esEs15(xuu50001, xuu4001, cbh)
new_esEs22(xuu50001, xuu4001, app(ty_Ratio, cbd)) → new_esEs10(xuu50001, xuu4001, cbd)
new_esEs22(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(ty_Maybe, ccc)) → new_esEs7(xuu50001, xuu4001, ccc)
new_esEs21(xuu50002, xuu4002, app(app(ty_@2, cbb), cbc)) → new_esEs6(xuu50002, xuu4002, cbb, cbc)
new_esEs21(xuu50002, xuu4002, ty_Int) → new_esEs14(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, app(ty_[], caf)) → new_esEs15(xuu50002, xuu4002, caf)
new_esEs21(xuu50002, xuu4002, ty_Double) → new_esEs16(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, app(app(ty_Either, cag), cah)) → new_esEs4(xuu50002, xuu4002, cag, cah)
new_esEs21(xuu50002, xuu4002, app(app(app(ty_@3, cac), cad), cae)) → new_esEs5(xuu50002, xuu4002, cac, cad, cae)
new_esEs21(xuu50002, xuu4002, app(ty_Maybe, cba)) → new_esEs7(xuu50002, xuu4002, cba)
new_esEs21(xuu50002, xuu4002, app(ty_Ratio, cab)) → new_esEs10(xuu50002, xuu4002, cab)
new_esEs21(xuu50002, xuu4002, ty_Bool) → new_esEs9(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Char) → new_esEs17(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Float) → new_esEs13(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Ordering) → new_esEs8(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_@0) → new_esEs11(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Integer) → new_esEs12(xuu50002, xuu4002)
new_esEs9(True, True) → True
new_esEs9(False, True) → False
new_esEs9(True, False) → False
new_esEs9(False, False) → True
new_lt7(xuu52000, xuu53000) → new_esEs8(new_compare14(xuu52000, xuu53000), LT)
new_lt19(xuu52000, xuu53000) → new_esEs8(new_compare29(xuu52000, xuu53000), LT)
new_compare29(xuu52000, xuu53000) → new_compare210(xuu52000, xuu53000, new_esEs9(xuu52000, xuu53000))
new_compare210(xuu52000, xuu53000, True) → EQ
new_compare210(xuu52000, xuu53000, False) → new_compare16(xuu52000, xuu53000, new_ltEs17(xuu52000, xuu53000))
new_compare16(xuu52000, xuu53000, True) → LT
new_compare16(xuu52000, xuu53000, False) → GT
new_lt17(xuu52000, xuu53000) → new_esEs8(new_compare32(xuu52000, xuu53000), LT)
new_lt4(xuu520, xuu530) → new_esEs8(new_compare6(xuu520, xuu530), LT)
new_lt10(xuu52000, xuu53000, bdd, bde) → new_esEs8(new_compare19(xuu52000, xuu53000, bdd, bde), LT)
new_compare19(xuu52000, xuu53000, bdd, bde) → new_compare23(xuu52000, xuu53000, new_esEs4(xuu52000, xuu53000, bdd, bde), bdd, bde)
new_compare23(Left(xuu5200), Left(xuu5300), False, ca, cb) → new_compare10(xuu5200, xuu5300, new_ltEs4(xuu5200, xuu5300, ca), ca, cb)
new_compare23(Right(xuu5200), Left(xuu5300), False, ca, cb) → GT
new_compare23(Left(xuu5200), Right(xuu5300), False, ca, cb) → LT
new_ltEs4(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(app(app(ty_@3, cf), cg), da)) → new_ltEs10(xuu5200, xuu5300, cf, cg, da)
new_ltEs4(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(app(ty_@2, db), dc)) → new_ltEs11(xuu5200, xuu5300, db, dc)
new_ltEs4(xuu5200, xuu5300, app(ty_Maybe, dd)) → new_ltEs12(xuu5200, xuu5300, dd)
new_ltEs4(xuu5200, xuu5300, app(ty_[], de)) → new_ltEs14(xuu5200, xuu5300, de)
new_ltEs4(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(ty_Ratio, ce)) → new_ltEs9(xuu5200, xuu5300, ce)
new_ltEs4(xuu5200, xuu5300, app(app(ty_Either, cc), cd)) → new_ltEs8(xuu5200, xuu5300, cc, cd)
new_ltEs4(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_compare10(xuu167, xuu168, True, dhe, dhf) → LT
new_compare10(xuu167, xuu168, False, dhe, dhf) → GT
new_lt9(xuu52000, xuu53000, fa, fb, fc) → new_esEs8(new_compare8(xuu52000, xuu53000, fa, fb, fc), LT)
new_compare8(xuu52000, xuu53000, fa, fb, fc) → new_compare24(xuu52000, xuu53000, new_esEs5(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_compare24(xuu52000, xuu53000, False, fa, fb, fc) → new_compare12(xuu52000, xuu53000, new_ltEs10(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_compare24(xuu52000, xuu53000, True, fa, fb, fc) → EQ
new_compare12(xuu52000, xuu53000, True, fa, fb, fc) → LT
new_compare12(xuu52000, xuu53000, False, fa, fb, fc) → GT
new_lt6(xuu52000, xuu53000) → new_esEs8(new_compare13(xuu52000, xuu53000), LT)
new_lt15(xuu52000, xuu53000, bad, bae) → new_esEs8(new_compare17(xuu52000, xuu53000, bad, bae), LT)
new_lt14(xuu52000, xuu53000) → new_esEs8(new_compare27(xuu52000, xuu53000), LT)
new_lt13(xuu52000, xuu53000) → new_esEs8(new_compare15(xuu52000, xuu53000), LT)
new_lt16(xuu52000, xuu53000, gg) → new_esEs8(new_compare9(xuu52000, xuu53000, gg), LT)
new_compare9(xuu52000, xuu53000, gg) → new_compare25(xuu52000, xuu53000, new_esEs7(xuu52000, xuu53000, gg), gg)
new_compare25(xuu52000, xuu53000, True, gg) → EQ
new_compare25(xuu52000, xuu53000, False, gg) → new_compare18(xuu52000, xuu53000, new_ltEs12(xuu52000, xuu53000, gg), gg)
new_compare18(xuu52000, xuu53000, True, gg) → LT
new_compare18(xuu52000, xuu53000, False, gg) → GT
new_lt18(xuu52000, xuu53000) → new_esEs8(new_compare30(xuu52000, xuu53000), LT)
new_compare30(xuu52000, xuu53000) → new_compare28(xuu52000, xuu53000, new_esEs8(xuu52000, xuu53000))
new_compare28(xuu52000, xuu53000, True) → EQ
new_compare28(xuu52000, xuu53000, False) → new_compare110(xuu52000, xuu53000, new_ltEs16(xuu52000, xuu53000))
new_compare110(xuu52000, xuu53000, True) → LT
new_compare110(xuu52000, xuu53000, False) → GT
new_lt5(xuu52000, xuu53000, eh) → new_esEs8(new_compare7(xuu52000, xuu53000, eh), LT)
new_lt8(xuu52000, xuu53000, bac) → new_esEs8(new_compare1(xuu52000, xuu53000, bac), LT)
new_esEs20(xuu50000, xuu4000, app(ty_Maybe, bhd)) → new_esEs7(xuu50000, xuu4000, bhd)
new_esEs20(xuu50000, xuu4000, app(app(ty_Either, bhb), bhc)) → new_esEs4(xuu50000, xuu4000, bhb, bhc)
new_esEs20(xuu50000, xuu4000, app(app(ty_@2, bhe), bhf)) → new_esEs6(xuu50000, xuu4000, bhe, bhf)
new_esEs20(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, app(ty_Ratio, bge)) → new_esEs10(xuu50000, xuu4000, bge)
new_esEs20(xuu50000, xuu4000, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs5(xuu50000, xuu4000, bgf, bgg, bgh)
new_esEs20(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, app(ty_[], bha)) → new_esEs15(xuu50000, xuu4000, bha)
new_esEs20(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs5(xuu50001, xuu4001, bfd, bfe, bff)
new_esEs19(xuu50001, xuu4001, app(ty_Maybe, bgb)) → new_esEs7(xuu50001, xuu4001, bgb)
new_esEs19(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, app(app(ty_@2, bgc), bgd)) → new_esEs6(xuu50001, xuu4001, bgc, bgd)
new_esEs19(xuu50001, xuu4001, app(ty_[], bfg)) → new_esEs15(xuu50001, xuu4001, bfg)
new_esEs19(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, app(ty_Ratio, bfc)) → new_esEs10(xuu50001, xuu4001, bfc)
new_esEs19(xuu50001, xuu4001, app(app(ty_Either, bfh), bga)) → new_esEs4(xuu50001, xuu4001, bfh, bga)
new_esEs19(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs31(xuu5000, xuu400, ty_@0) → new_esEs11(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, ty_Ordering) → new_esEs8(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs5(xuu5000, xuu400, cgg, cgh, cha)
new_esEs31(xuu5000, xuu400, ty_Char) → new_esEs17(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, ty_Bool) → new_esEs9(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, ty_Integer) → new_esEs12(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, app(ty_[], chb)) → new_esEs15(xuu5000, xuu400, chb)
new_esEs31(xuu5000, xuu400, app(app(ty_Either, chc), chd)) → new_esEs4(xuu5000, xuu400, chc, chd)
new_esEs31(xuu5000, xuu400, ty_Int) → new_esEs14(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, app(ty_Ratio, cgf)) → new_esEs10(xuu5000, xuu400, cgf)
new_esEs31(xuu5000, xuu400, ty_Double) → new_esEs16(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, ty_Float) → new_esEs13(xuu5000, xuu400)
new_esEs31(xuu5000, xuu400, app(ty_Maybe, che)) → new_esEs7(xuu5000, xuu400, che)
new_esEs31(xuu5000, xuu400, app(app(ty_@2, chf), chg)) → new_esEs6(xuu5000, xuu400, chf, chg)

The set Q consists of the following terms:

new_primCompAux0(x0, EQ)
new_ltEs4(x0, x1, ty_Bool)
new_ltEs5(x0, x1, ty_Float)
new_compare29(x0, x1)
new_fsEs(x0)
new_primCompAux0(x0, GT)
new_esEs19(x0, x1, ty_Bool)
new_esEs18(x0, x1, ty_@0)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3)
new_compare16(x0, x1, False)
new_esEs32(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_compare9(x0, x1, x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, False)
new_esEs22(x0, x1, ty_Char)
new_compare8(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Double)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare23(x0, x1, True, x2, x3)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1)
new_compare17(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs31(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Float)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs11(@0, @0)
new_compare10(x0, x1, True, x2, x3)
new_compare111(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_ltEs4(x0, x1, ty_Int)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs8(GT, GT)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_primCmpNat1(x0, Zero)
new_ltEs21(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs4(x0, x1, ty_Integer)
new_esEs7(Nothing, Just(x0), x1)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_ltEs4(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(LT, LT)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, x2)
new_esEs21(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Ordering)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Int)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, ty_Integer)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs7(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(False, False)
new_esEs7(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Integer)
new_ltEs4(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(ty_[], x2))
new_compare1(:(x0, x1), [], x2)
new_compare24(x0, x1, False, x2, x3, x4)
new_primEqNat0(Zero, Zero)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs9(True, True)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt10(x0, x1, x2, x3)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(x0, Succ(x1))
new_primMulNat0(Zero, Zero)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs18(x0, x1)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Integer)
new_ltEs17(True, True)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(Left(x0), Left(x1), False, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_lt12(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare14(Integer(x0), Integer(x1))
new_primCmpNat0(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Zero)
new_compare23(Right(x0), Right(x1), False, x2, x3)
new_esEs24(x0, x1, ty_Bool)
new_primCompAux1(x0, x1, x2, x3)
new_esEs7(Nothing, Nothing, x0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1)
new_ltEs4(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(x0, x1, ty_Integer)
new_pePe(False, x0)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_compare1([], :(x0, x1), x2)
new_ltEs21(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_ltEs6(x0, x1)
new_ltEs12(Just(x0), Nothing, x1)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(Float(x0, x1), Float(x2, x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_lt12(x0, x1, ty_Int)
new_esEs17(Char(x0), Char(x1))
new_esEs19(x0, x1, ty_Char)
new_primPlusNat0(Zero, Zero)
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs16(EQ, EQ)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Zero)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare25(x0, x1, True, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_esEs19(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_compare28(x0, x1, False)
new_esEs18(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Float)
new_compare16(x0, x1, True)
new_esEs23(x0, x1, ty_Float)
new_esEs18(x0, x1, ty_Int)
new_ltEs16(LT, GT)
new_ltEs16(GT, LT)
new_esEs25(x0, x1, ty_@0)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1)
new_primPlusNat1(Succ(x0), x1)
new_pePe(True, x0)
new_lt11(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt11(x0, x1, ty_Ordering)
new_primCompAux0(x0, LT)
new_esEs25(x0, x1, ty_Ordering)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_lt12(x0, x1, ty_Bool)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1)
new_compare10(x0, x1, False, x2, x3)
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1, x2)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Bool)
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt15(x0, x1, x2, x3)
new_primPlusNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare31(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_asAs(True, x0)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare26(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs32(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare31(x0, x1, ty_Char)
new_compare210(x0, x1, False)
new_ltEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Integer)
new_ltEs16(GT, GT)
new_esEs18(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_@0)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Double)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs13(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs5(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_primCmpNat2(Succ(x0), x1)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs14(x0, x1)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_compare18(x0, x1, True, x2)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_compare13(Double(x0, x1), Double(x2, x3))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, x0)
new_compare31(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare15(Char(x0), Char(x1))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCmpNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare23(Left(x0), Right(x1), False, x2, x3)
new_compare23(Right(x0), Left(x1), False, x2, x3)
new_ltEs12(Nothing, Nothing, x0)
new_esEs18(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Char)
new_ltEs12(Nothing, Just(x0), x1)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Int)
new_esEs9(False, False)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs18(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_compare6(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqNat0(Zero, Succ(x0))
new_compare31(x0, x1, ty_Ordering)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs4(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_ltEs4(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Double)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_compare18(x0, x1, False, x2)
new_compare26(x0, x1, False, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_not(True)
new_ltEs19(x0, x1)
new_esEs20(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs21(x0, x1, ty_Float)
new_lt11(x0, x1, ty_Int)
new_lt9(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare12(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_primCmpNat2(Zero, x0)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_lt11(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_ltEs17(False, True)
new_ltEs17(True, False)
new_ltEs20(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_lt12(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, True)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt6(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Int)
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_compare28(x0, x1, True)
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs9(False, True)
new_esEs9(True, False)
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_ltEs20(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare31(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs15([], :(x0, x1), x2)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs15(:(x0, x1), [], x2)
new_esEs21(x0, x1, ty_Bool)
new_ltEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_compare27(@0, @0)
new_lt11(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_lt11(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Integer)
new_ltEs9(x0, x1, x2)
new_compare25(x0, x1, False, x2)
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt8(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs32(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs20(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_esEs15([], [], x0)
new_lt12(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_sr(x0, x1)
new_esEs31(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)

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_C2(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, h, ba, bb) → new_addToFM_C(xuu16, xuu20, Left(xuu22), xuu23, h, ba, bb)
new_addToFM_C20(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu43, Left(xuu5000), xuu501, bc, bd, be)
new_addToFM_C1(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, h, ba, bb) → new_addToFM_C(xuu16, xuu21, Left(xuu22), xuu23, h, ba, bb)
new_addToFM_C20(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, False, bc, bd, be) → new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Left(xuu5000), Right(xuu400), False, bc, bd), GT), bc, bd, be)
new_addToFM_C(xuu3, Branch(Right(xuu400), xuu41, xuu42, xuu43, xuu44), Left(xuu5000), xuu501, bc, bd, be) → new_addToFM_C20(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Left(xuu5000), Right(xuu400), False, bc, bd), LT), bc, bd, be)
new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu44, Left(xuu5000), xuu501, bc, bd, be)
new_addToFM_C(xuu3, Branch(Left(xuu400), xuu41, xuu42, xuu43, xuu44), Left(xuu5000), xuu501, bc, bd, be) → new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Left(xuu5000), Left(xuu400), new_esEs30(xuu5000, xuu400, bc), bc, bd), LT), bc, bd, be)
new_addToFM_C2(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, False, h, ba, bb) → new_addToFM_C1(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, new_esEs8(new_compare23(Left(xuu22), Left(xuu17), new_esEs29(xuu22, xuu17, h), h, ba), GT), h, ba, bb)

The TRS R consists of the following rules:

new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Maybe, hh)) → new_esEs7(xuu50000, xuu4000, hh)
new_esEs20(xuu50000, xuu4000, app(ty_Maybe, bhd)) → new_esEs7(xuu50000, xuu4000, bhd)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_[], he)) → new_esEs15(xuu50000, xuu4000, he)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs21(xuu50002, xuu4002, app(app(ty_@2, cbb), cbc)) → new_esEs6(xuu50002, xuu4002, cbb, cbc)
new_ltEs16(GT, GT) → True
new_primCmpNat2(Zero, xuu5200) → LT
new_compare31(xuu52000, xuu53000, ty_Int) → new_compare6(xuu52000, xuu53000)
new_ltEs17(False, False) → True
new_esEs31(xuu5000, xuu400, ty_@0) → new_esEs11(xuu5000, xuu400)
new_esEs25(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_compare9(xuu52000, xuu53000, gg) → new_compare25(xuu52000, xuu53000, new_esEs7(xuu52000, xuu53000, gg), gg)
new_compare23(Left(xuu5200), Left(xuu5300), False, ca, cb) → new_compare10(xuu5200, xuu5300, new_ltEs4(xuu5200, xuu5300, ca), ca, cb)
new_esEs18(xuu50000, xuu4000, app(app(ty_@2, beg), beh)) → new_esEs6(xuu50000, xuu4000, beg, beh)
new_compare1(:(xuu52000, xuu52001), :(xuu53000, xuu53001), de) → new_primCompAux1(xuu52000, xuu53000, new_compare1(xuu52001, xuu53001, de), de)
new_esEs24(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs5(xuu52001, xuu53001, cee, cef, ceg)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Bool, cd) → new_ltEs17(xuu52000, xuu53000)
new_esEs18(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_ltEs20(xuu52002, xuu53002, app(ty_Ratio, cff)) → new_ltEs9(xuu52002, xuu53002, cff)
new_esEs17(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_esEs31(xuu5000, xuu400, ty_Ordering) → new_esEs8(xuu5000, xuu400)
new_esEs24(xuu52001, xuu53001, ty_Char) → new_esEs17(xuu52001, xuu53001)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_compare10(xuu167, xuu168, True, dhe, dhf) → LT
new_compare31(xuu52000, xuu53000, app(ty_Maybe, dde)) → new_compare9(xuu52000, xuu53000, dde)
new_lt12(xuu52001, xuu53001, app(ty_[], cfc)) → new_lt8(xuu52001, xuu53001, cfc)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_ltEs16(LT, GT) → True
new_ltEs5(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs31(xuu5000, xuu400, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs5(xuu5000, xuu400, cgg, cgh, cha)
new_ltEs4(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_esEs21(xuu50002, xuu4002, ty_Int) → new_esEs14(xuu50002, xuu4002)
new_ltEs12(Nothing, Nothing, dd) → True
new_esEs26(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_compare19(xuu52000, xuu53000, bdd, bde) → new_compare23(xuu52000, xuu53000, new_esEs4(xuu52000, xuu53000, bdd, bde), bdd, bde)
new_primMulNat0(Zero, Zero) → Zero
new_lt20(xuu52000, xuu53000, app(ty_[], dba)) → new_lt8(xuu52000, xuu53000, dba)
new_esEs26(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_esEs10(xuu52000, xuu53000, dab)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_esEs15(:(xuu50000, xuu50001), :(xuu4000, xuu4001), bdf) → new_asAs(new_esEs18(xuu50000, xuu4000, bdf), new_esEs15(xuu50001, xuu4001, bdf))
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_[], bbc), baf) → new_esEs15(xuu50000, xuu4000, bbc)
new_compare25(xuu52000, xuu53000, True, gg) → EQ
new_ltEs5(xuu5200, xuu5300, app(app(app(ty_@3, ea), eb), ec)) → new_ltEs10(xuu5200, xuu5300, ea, eb, ec)
new_esEs22(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_compare24(xuu52000, xuu53000, False, fa, fb, fc) → new_compare12(xuu52000, xuu53000, new_ltEs10(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_lt9(xuu52000, xuu53000, fa, fb, fc) → new_esEs8(new_compare8(xuu52000, xuu53000, fa, fb, fc), LT)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, app(ty_[], caf)) → new_esEs15(xuu50002, xuu4002, caf)
new_ltEs4(xuu5200, xuu5300, app(app(app(ty_@3, cf), cg), da)) → new_ltEs10(xuu5200, xuu5300, cf, cg, da)
new_lt12(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_lt5(xuu52001, xuu53001, ced)
new_lt14(xuu52000, xuu53000) → new_esEs8(new_compare27(xuu52000, xuu53000), LT)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_[], bcf)) → new_esEs15(xuu50000, xuu4000, bcf)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs29(xuu22, xuu17, app(app(ty_Either, ead), eae)) → new_esEs4(xuu22, xuu17, ead, eae)
new_ltEs18(xuu5200, xuu5300) → new_fsEs(new_compare14(xuu5200, xuu5300))
new_compare1([], :(xuu53000, xuu53001), de) → LT
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_esEs29(xuu22, xuu17, app(ty_Maybe, eaf)) → new_esEs7(xuu22, xuu17, eaf)
new_esEs20(xuu50000, xuu4000, app(app(ty_Either, bhb), bhc)) → new_esEs4(xuu50000, xuu4000, bhb, bhc)
new_lt11(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_esEs23(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_compare30(xuu52000, xuu53000) → new_compare28(xuu52000, xuu53000, new_esEs8(xuu52000, xuu53000))
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_@2, bbg), bbh), baf) → new_esEs6(xuu50000, xuu4000, bbg, bbh)
new_esEs31(xuu5000, xuu400, ty_Char) → new_esEs17(xuu5000, xuu400)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_@2, baa), bab)) → new_esEs6(xuu50000, xuu4000, baa, bab)
new_esEs30(xuu5000, xuu400, ty_Bool) → new_esEs9(xuu5000, xuu400)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Ratio, bag), baf) → new_esEs10(xuu50000, xuu4000, bag)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs29(xuu22, xuu17, ty_Bool) → new_esEs9(xuu22, xuu17)
new_esEs12(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs5(xuu50001, xuu4001, bfd, bfe, bff)
new_esEs20(xuu50000, xuu4000, app(app(ty_@2, bhe), bhf)) → new_esEs6(xuu50000, xuu4000, bhe, bhf)
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_compare31(xuu52000, xuu53000, ty_@0) → new_compare27(xuu52000, xuu53000)
new_primCmpNat1(xuu5200, Succ(xuu5300)) → new_primCmpNat0(xuu5200, xuu5300)
new_lt20(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_@0, baf) → new_esEs11(xuu50000, xuu4000)
new_ltEs11(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), db, dc) → new_pePe(new_lt20(xuu52000, xuu53000, db), new_asAs(new_esEs26(xuu52000, xuu53000, db), new_ltEs21(xuu52001, xuu53001, dc)))
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Ordering, baf) → new_esEs8(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_esEs32(xuu41, xuu36, app(app(ty_@2, ge), gf)) → new_esEs6(xuu41, xuu36, ge, gf)
new_compare25(xuu52000, xuu53000, False, gg) → new_compare18(xuu52000, xuu53000, new_ltEs12(xuu52000, xuu53000, gg), gg)
new_pePe(False, xuu194) → xuu194
new_esEs29(xuu22, xuu17, ty_Double) → new_esEs16(xuu22, xuu17)
new_esEs25(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_esEs4(xuu52000, xuu53000, bdd, bde)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_esEs31(xuu5000, xuu400, ty_Bool) → new_esEs9(xuu5000, xuu400)
new_compare31(xuu52000, xuu53000, ty_Float) → new_compare32(xuu52000, xuu53000)
new_esEs22(xuu50001, xuu4001, app(app(ty_Either, cca), ccb)) → new_esEs4(xuu50001, xuu4001, cca, ccb)
new_esEs20(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_primCmpNat1(xuu5200, Zero) → GT
new_compare31(xuu52000, xuu53000, ty_Bool) → new_compare29(xuu52000, xuu53000)
new_compare15(Char(xuu52000), Char(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_ltEs21(xuu52001, xuu53001, ty_@0) → new_ltEs7(xuu52001, xuu53001)
new_lt11(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_lt9(xuu52000, xuu53000, fa, fb, fc)
new_esEs32(xuu41, xuu36, app(ty_Maybe, gd)) → new_esEs7(xuu41, xuu36, gd)
new_esEs24(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_esEs7(xuu52001, xuu53001, cfb)
new_esEs24(xuu52001, xuu53001, ty_@0) → new_esEs11(xuu52001, xuu53001)
new_ltEs16(EQ, GT) → True
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_[], dhd)) → new_ltEs14(xuu52000, xuu53000, dhd)
new_esEs22(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs23(xuu50000, xuu4000, app(ty_Maybe, cde)) → new_esEs7(xuu50000, xuu4000, cde)
new_esEs22(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_ltEs4(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_esEs22(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_lt20(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_lt16(xuu52000, xuu53000, dah)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Ratio, bcb)) → new_esEs10(xuu50000, xuu4000, bcb)
new_primCmpNat0(Zero, Succ(xuu53000)) → LT
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_@2, dha), dhb)) → new_ltEs11(xuu52000, xuu53000, dha, dhb)
new_esEs25(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_esEs6(xuu52000, xuu53000, bad, bae)
new_lt11(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_lt15(xuu52000, xuu53000, bad, bae)
new_esEs8(LT, LT) → True
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Ratio, dea)) → new_ltEs9(xuu52000, xuu53000, dea)
new_esEs20(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs19(xuu50001, xuu4001, app(ty_Maybe, bgb)) → new_esEs7(xuu50001, xuu4001, bgb)
new_esEs23(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs16(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_ltEs21(xuu52001, xuu53001, ty_Char) → new_ltEs6(xuu52001, xuu53001)
new_pePe(True, xuu194) → True
new_esEs24(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_esEs6(xuu52001, xuu53001, ceh, cfa)
new_primEqNat0(Zero, Zero) → True
new_esEs23(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs26(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), bhg, bhh, caa) → new_asAs(new_esEs23(xuu50000, xuu4000, bhg), new_asAs(new_esEs22(xuu50001, xuu4001, bhh), new_esEs21(xuu50002, xuu4002, caa)))
new_primMulNat0(Succ(xuu5000100), Succ(xuu400100)) → new_primPlusNat1(new_primMulNat0(xuu5000100, Succ(xuu400100)), xuu400100)
new_compare111(xuu52000, xuu53000, False, bad, bae) → GT
new_ltEs20(xuu52002, xuu53002, ty_@0) → new_ltEs7(xuu52002, xuu53002)
new_esEs22(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs31(xuu5000, xuu400, ty_Integer) → new_esEs12(xuu5000, xuu400)
new_esEs29(xuu22, xuu17, ty_Int) → new_esEs14(xuu22, xuu17)
new_lt20(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_ltEs4(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_ltEs21(xuu52001, xuu53001, app(app(ty_Either, dbb), dbc)) → new_ltEs8(xuu52001, xuu53001, dbb, dbc)
new_ltEs16(EQ, LT) → False
new_lt12(xuu52001, xuu53001, ty_Ordering) → new_lt18(xuu52001, xuu53001)
new_esEs19(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_ltEs16(GT, EQ) → False
new_sr(xuu50001, xuu4001) → new_primMulInt(xuu50001, xuu4001)
new_compare12(xuu52000, xuu53000, True, fa, fb, fc) → LT
new_esEs32(xuu41, xuu36, ty_Bool) → new_esEs9(xuu41, xuu36)
new_esEs18(xuu50000, xuu4000, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs5(xuu50000, xuu4000, bdh, bea, beb)
new_esEs25(xuu52000, xuu53000, app(ty_[], bac)) → new_esEs15(xuu52000, xuu53000, bac)
new_esEs24(xuu52001, xuu53001, ty_Double) → new_esEs16(xuu52001, xuu53001)
new_esEs23(xuu50000, xuu4000, app(ty_[], cdb)) → new_esEs15(xuu50000, xuu4000, cdb)
new_lt15(xuu52000, xuu53000, bad, bae) → new_esEs8(new_compare17(xuu52000, xuu53000, bad, bae), LT)
new_ltEs21(xuu52001, xuu53001, app(app(ty_@2, dbh), dca)) → new_ltEs11(xuu52001, xuu53001, dbh, dca)
new_ltEs20(xuu52002, xuu53002, ty_Int) → new_ltEs19(xuu52002, xuu53002)
new_esEs26(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs8(GT, GT) → True
new_esEs21(xuu50002, xuu4002, ty_Double) → new_esEs16(xuu50002, xuu4002)
new_esEs31(xuu5000, xuu400, app(ty_[], chb)) → new_esEs15(xuu5000, xuu400, chb)
new_lt12(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_lt16(xuu52001, xuu53001, cfb)
new_primCmpInt(Pos(Succ(xuu5200)), Pos(xuu530)) → new_primCmpNat1(xuu5200, xuu530)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_lt19(xuu52000, xuu53000) → new_esEs8(new_compare29(xuu52000, xuu53000), LT)
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Integer) → new_compare14(new_sr0(xuu52000, xuu53001), new_sr0(xuu53000, xuu52001))
new_esEs26(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_esEs32(xuu41, xuu36, ty_Int) → new_esEs14(xuu41, xuu36)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_Either, bcg), bch)) → new_esEs4(xuu50000, xuu4000, bcg, bch)
new_compare24(xuu52000, xuu53000, True, fa, fb, fc) → EQ
new_ltEs5(xuu5200, xuu5300, app(app(ty_Either, df), dg)) → new_ltEs8(xuu5200, xuu5300, df, dg)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs4(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_esEs20(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_ltEs16(LT, EQ) → True
new_esEs31(xuu5000, xuu400, app(app(ty_Either, chc), chd)) → new_esEs4(xuu5000, xuu400, chc, chd)
new_lt12(xuu52001, xuu53001, ty_Char) → new_lt13(xuu52001, xuu53001)
new_esEs23(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_Either, bbd), bbe), baf) → new_esEs4(xuu50000, xuu4000, bbd, bbe)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs5(xuu50000, xuu4000, bah, bba, bbb)
new_esEs25(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_esEs10(xuu52000, xuu53000, eh)
new_ltEs5(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Ratio, ha)) → new_esEs10(xuu50000, xuu4000, ha)
new_lt20(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_ltEs17(True, False) → False
new_compare16(xuu52000, xuu53000, True) → LT
new_ltEs5(xuu5200, xuu5300, app(ty_Ratio, dh)) → new_ltEs9(xuu5200, xuu5300, dh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt10(xuu52000, xuu53000, bdd, bde) → new_esEs8(new_compare19(xuu52000, xuu53000, bdd, bde), LT)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(app(ty_@3, dfd), dfe), dff), cd) → new_ltEs10(xuu52000, xuu53000, dfd, dfe, dff)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs32(xuu41, xuu36, app(app(app(ty_@3, ff), fg), fh)) → new_esEs5(xuu41, xuu36, ff, fg, fh)
new_primCmpNat2(Succ(xuu5300), xuu5200) → new_primCmpNat0(xuu5300, xuu5200)
new_esEs32(xuu41, xuu36, ty_@0) → new_esEs11(xuu41, xuu36)
new_esEs19(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primCompAux0(xuu218, GT) → GT
new_compare31(xuu52000, xuu53000, ty_Ordering) → new_compare30(xuu52000, xuu53000)
new_ltEs21(xuu52001, xuu53001, app(ty_[], dcc)) → new_ltEs14(xuu52001, xuu53001, dcc)
new_lt11(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_lt10(xuu52000, xuu53000, bdd, bde)
new_esEs8(EQ, EQ) → True
new_compare26(xuu52000, xuu53000, True, bad, bae) → EQ
new_primPlusNat1(Zero, xuu400100) → Succ(xuu400100)
new_esEs32(xuu41, xuu36, app(ty_Ratio, fd)) → new_esEs10(xuu41, xuu36, fd)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_[], dgb), cd) → new_ltEs14(xuu52000, xuu53000, dgb)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Char, cd) → new_ltEs6(xuu52000, xuu53000)
new_esEs22(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs21(xuu50002, xuu4002, app(app(ty_Either, cag), cah)) → new_esEs4(xuu50002, xuu4002, cag, cah)
new_compare29(xuu52000, xuu53000) → new_compare210(xuu52000, xuu53000, new_esEs9(xuu52000, xuu53000))
new_esEs32(xuu41, xuu36, ty_Char) → new_esEs17(xuu41, xuu36)
new_esEs22(xuu50001, xuu4001, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs5(xuu50001, xuu4001, cbe, cbf, cbg)
new_esEs18(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_compare8(xuu52000, xuu53000, fa, fb, fc) → new_compare24(xuu52000, xuu53000, new_esEs5(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Char, baf) → new_esEs17(xuu50000, xuu4000)
new_esEs26(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, ty_Float) → new_esEs13(xuu5000, xuu400)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(xuu5200, xuu5300) → new_fsEs(new_compare6(xuu5200, xuu5300))
new_ltEs20(xuu52002, xuu53002, ty_Double) → new_ltEs15(xuu52002, xuu53002)
new_ltEs16(GT, LT) → False
new_compare6(xuu52, xuu53) → new_primCmpInt(xuu52, xuu53)
new_esEs19(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_ltEs4(xuu5200, xuu5300, app(app(ty_@2, db), dc)) → new_ltEs11(xuu5200, xuu5300, db, dc)
new_esEs29(xuu22, xuu17, ty_Float) → new_esEs13(xuu22, xuu17)
new_compare13(Double(xuu52000, xuu52001), Double(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_primCmpNat0(Succ(xuu52000), Succ(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_ltEs9(xuu5200, xuu5300, ce) → new_fsEs(new_compare7(xuu5200, xuu5300, ce))
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs5(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_compare10(xuu167, xuu168, False, dhe, dhf) → GT
new_lt11(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_lt5(xuu52000, xuu53000, eh) → new_esEs8(new_compare7(xuu52000, xuu53000, eh), LT)
new_ltEs21(xuu52001, xuu53001, ty_Float) → new_ltEs13(xuu52001, xuu53001)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(app(ty_@3, dgf), dgg), dgh)) → new_ltEs10(xuu52000, xuu53000, dgf, dgg, dgh)
new_compare14(Integer(xuu52000), Integer(xuu53000)) → new_primCmpInt(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Float, cd) → new_ltEs13(xuu52000, xuu53000)
new_esEs19(xuu50001, xuu4001, app(app(ty_@2, bgc), bgd)) → new_esEs6(xuu50001, xuu4001, bgc, bgd)
new_ltEs5(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(ty_Maybe, dd)) → new_ltEs12(xuu5200, xuu5300, dd)
new_lt7(xuu52000, xuu53000) → new_esEs8(new_compare14(xuu52000, xuu53000), LT)
new_esEs30(xuu5000, xuu400, ty_Int) → new_esEs14(xuu5000, xuu400)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Bool, baf) → new_esEs9(xuu50000, xuu4000)
new_esEs24(xuu52001, xuu53001, ty_Ordering) → new_esEs8(xuu52001, xuu53001)
new_esEs18(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_@2, dfg), dfh), cd) → new_ltEs11(xuu52000, xuu53000, dfg, dfh)
new_lt6(xuu52000, xuu53000) → new_esEs8(new_compare13(xuu52000, xuu53000), LT)
new_ltEs4(xuu5200, xuu5300, app(ty_[], de)) → new_ltEs14(xuu5200, xuu5300, de)
new_lt12(xuu52001, xuu53001, ty_@0) → new_lt14(xuu52001, xuu53001)
new_esEs7(Nothing, Nothing, gh) → True
new_esEs15([], [], bdf) → True
new_lt20(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_lt5(xuu52000, xuu53000, dab)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_esEs18(xuu50000, xuu4000, app(ty_Maybe, bef)) → new_esEs7(xuu50000, xuu4000, bef)
new_lt4(xuu520, xuu530) → new_esEs8(new_compare6(xuu520, xuu530), LT)
new_ltEs20(xuu52002, xuu53002, app(ty_Maybe, cgd)) → new_ltEs12(xuu52002, xuu53002, cgd)
new_primPlusNat0(Succ(xuu55200), Zero) → Succ(xuu55200)
new_primPlusNat0(Zero, Succ(xuu13100)) → Succ(xuu13100)
new_compare31(xuu52000, xuu53000, ty_Integer) → new_compare14(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(app(app(ty_@3, dch), dda), ddb)) → new_compare8(xuu52000, xuu53000, dch, dda, ddb)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_esEs19(xuu50001, xuu4001, app(ty_[], bfg)) → new_esEs15(xuu50001, xuu4001, bfg)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu52000), Zero) → GT
new_lt11(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs5(xuu50000, xuu4000, bcc, bcd, bce)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Maybe, dga), cd) → new_ltEs12(xuu52000, xuu53000, dga)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_[], deh)) → new_ltEs14(xuu52000, xuu53000, deh)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu5300))) → LT
new_compare11(xuu174, xuu175, True, cdh, cea) → LT
new_ltEs21(xuu52001, xuu53001, ty_Ordering) → new_ltEs16(xuu52001, xuu53001)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_esEs23(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_lt20(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_sr0(Integer(xuu530000), Integer(xuu520010)) → Integer(new_primMulInt(xuu530000, xuu520010))
new_esEs31(xuu5000, xuu400, ty_Int) → new_esEs14(xuu5000, xuu400)
new_ltEs5(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_esEs31(xuu5000, xuu400, app(ty_Ratio, cgf)) → new_esEs10(xuu5000, xuu400, cgf)
new_ltEs20(xuu52002, xuu53002, app(ty_[], cge)) → new_ltEs14(xuu52002, xuu53002, cge)
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_esEs7(Just(xuu50000), Nothing, gh) → False
new_esEs7(Nothing, Just(xuu4000), gh) → False
new_esEs13(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Maybe, deg)) → new_ltEs12(xuu52000, xuu53000, deg)
new_esEs24(xuu52001, xuu53001, ty_Int) → new_esEs14(xuu52001, xuu53001)
new_ltEs4(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_esEs30(xuu5000, xuu400, ty_Integer) → new_esEs12(xuu5000, xuu400)
new_esEs22(xuu50001, xuu4001, app(app(ty_@2, ccd), cce)) → new_esEs6(xuu50001, xuu4001, ccd, cce)
new_ltEs20(xuu52002, xuu53002, ty_Integer) → new_ltEs18(xuu52002, xuu53002)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_Either, ddg), ddh)) → new_ltEs8(xuu52000, xuu53000, ddg, ddh)
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_esEs18(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_ltEs20(xuu52002, xuu53002, app(app(ty_@2, cgb), cgc)) → new_ltEs11(xuu52002, xuu53002, cgb, cgc)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Maybe, dhc)) → new_ltEs12(xuu52000, xuu53000, dhc)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_@0, cd) → new_ltEs7(xuu52000, xuu53000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Ratio, ccf)) → new_esEs10(xuu50000, xuu4000, ccf)
new_esEs6(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), bfa, bfb) → new_asAs(new_esEs20(xuu50000, xuu4000, bfa), new_esEs19(xuu50001, xuu4001, bfb))
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Integer, baf) → new_esEs12(xuu50000, xuu4000)
new_lt20(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_lt9(xuu52000, xuu53000, dac, dad, dae)
new_ltEs16(EQ, EQ) → True
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Double, baf) → new_esEs16(xuu50000, xuu4000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Ratio, dfc), cd) → new_ltEs9(xuu52000, xuu53000, dfc)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_compare31(xuu52000, xuu53000, app(app(ty_Either, dce), dcf)) → new_compare19(xuu52000, xuu53000, dce, dcf)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_lt12(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_lt15(xuu52001, xuu53001, ceh, cfa)
new_primCompAux0(xuu218, LT) → LT
new_lt20(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, app(ty_Ratio, dcd)) → new_esEs10(xuu5000, xuu400, dcd)
new_not(False) → True
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_Either, dgc), dgd)) → new_ltEs8(xuu52000, xuu53000, dgc, dgd)
new_esEs20(xuu50000, xuu4000, app(ty_Ratio, bge)) → new_esEs10(xuu50000, xuu4000, bge)
new_esEs29(xuu22, xuu17, ty_Integer) → new_esEs12(xuu22, xuu17)
new_compare12(xuu52000, xuu53000, False, fa, fb, fc) → GT
new_esEs23(xuu50000, xuu4000, app(app(ty_@2, cdf), cdg)) → new_esEs6(xuu50000, xuu4000, cdf, cdg)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(app(ty_@2, ddc), ddd)) → new_compare17(xuu52000, xuu53000, ddc, ddd)
new_lt11(xuu52000, xuu53000, app(ty_[], bac)) → new_lt8(xuu52000, xuu53000, bac)
new_esEs30(xuu5000, xuu400, app(app(ty_Either, bca), baf)) → new_esEs4(xuu5000, xuu400, bca, baf)
new_esEs19(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_esEs32(xuu41, xuu36, ty_Ordering) → new_esEs8(xuu41, xuu36)
new_ltEs21(xuu52001, xuu53001, ty_Int) → new_ltEs19(xuu52001, xuu53001)
new_ltEs10(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), cf, cg, da) → new_pePe(new_lt11(xuu52000, xuu53000, cf), new_asAs(new_esEs25(xuu52000, xuu53000, cf), new_pePe(new_lt12(xuu52001, xuu53001, cg), new_asAs(new_esEs24(xuu52001, xuu53001, cg), new_ltEs20(xuu52002, xuu53002, da)))))
new_ltEs5(xuu5200, xuu5300, app(app(ty_@2, ed), ee)) → new_ltEs11(xuu5200, xuu5300, ed, ee)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_@2, dee), def)) → new_ltEs11(xuu52000, xuu53000, dee, def)
new_esEs24(xuu52001, xuu53001, ty_Integer) → new_esEs12(xuu52001, xuu53001)
new_esEs32(xuu41, xuu36, app(ty_[], ga)) → new_esEs15(xuu41, xuu36, ga)
new_lt20(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_compare28(xuu52000, xuu53000, True) → EQ
new_lt20(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_lt12(xuu52001, xuu53001, ty_Double) → new_lt6(xuu52001, xuu53001)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_@2, bdb), bdc)) → new_esEs6(xuu50000, xuu4000, bdb, bdc)
new_lt11(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_lt5(xuu52000, xuu53000, eh)
new_esEs18(xuu50000, xuu4000, app(app(ty_Either, bed), bee)) → new_esEs4(xuu50000, xuu4000, bed, bee)
new_esEs9(True, True) → True
new_compare11(xuu174, xuu175, False, cdh, cea) → GT
new_lt11(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_esEs20(xuu50000, xuu4000, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs5(xuu50000, xuu4000, bgf, bgg, bgh)
new_primCmpInt(Pos(Succ(xuu5200)), Neg(xuu530)) → GT
new_lt8(xuu52000, xuu53000, bac) → new_esEs8(new_compare1(xuu52000, xuu53000, bac), LT)
new_esEs30(xuu5000, xuu400, ty_@0) → new_esEs11(xuu5000, xuu400)
new_esEs21(xuu50002, xuu4002, app(app(app(ty_@3, cac), cad), cae)) → new_esEs5(xuu50002, xuu4002, cac, cad, cae)
new_esEs21(xuu50002, xuu4002, app(ty_Maybe, cba)) → new_esEs7(xuu50002, xuu4002, cba)
new_ltEs4(xuu5200, xuu5300, app(ty_Ratio, ce)) → new_ltEs9(xuu5200, xuu5300, ce)
new_primMulInt(Pos(xuu500010), Pos(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_lt12(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_lt9(xuu52001, xuu53001, cee, cef, ceg)
new_esEs18(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(app(ty_Either, cdc), cdd)) → new_esEs4(xuu50000, xuu4000, cdc, cdd)
new_ltEs20(xuu52002, xuu53002, ty_Bool) → new_ltEs17(xuu52002, xuu53002)
new_lt20(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_lt10(xuu52000, xuu53000, chh, daa)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Maybe, bbf), baf) → new_esEs7(xuu50000, xuu4000, bbf)
new_compare23(Right(xuu5200), Left(xuu5300), False, ca, cb) → GT
new_primMulInt(Neg(xuu500010), Neg(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_ltEs5(xuu5200, xuu5300, app(ty_Maybe, ef)) → new_ltEs12(xuu5200, xuu5300, ef)
new_compare110(xuu52000, xuu53000, True) → LT
new_esEs29(xuu22, xuu17, app(app(ty_@2, eag), eah)) → new_esEs6(xuu22, xuu17, eag, eah)
new_esEs21(xuu50002, xuu4002, app(ty_Ratio, cab)) → new_esEs10(xuu50002, xuu4002, cab)
new_lt20(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, app(ty_Maybe, gh)) → new_esEs7(xuu5000, xuu400, gh)
new_primEqNat0(Succ(xuu500000), Zero) → False
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_Either, dfa), dfb), cd) → new_ltEs8(xuu52000, xuu53000, dfa, dfb)
new_primPlusNat0(Zero, Zero) → Zero
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(app(ty_@3, deb), dec), ded)) → new_ltEs10(xuu52000, xuu53000, deb, dec, ded)
new_compare110(xuu52000, xuu53000, False) → GT
new_ltEs6(xuu5200, xuu5300) → new_fsEs(new_compare15(xuu5200, xuu5300))
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_esEs4(xuu52001, xuu53001, ceb, cec)
new_compare17(xuu52000, xuu53000, bad, bae) → new_compare26(xuu52000, xuu53000, new_esEs6(xuu52000, xuu53000, bad, bae), bad, bae)
new_ltEs21(xuu52001, xuu53001, app(ty_Ratio, dbd)) → new_ltEs9(xuu52001, xuu53001, dbd)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Ordering, cd) → new_ltEs16(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, ty_Bool) → new_esEs9(xuu50002, xuu4002)
new_esEs11(@0, @0) → True
new_compare210(xuu52000, xuu53000, True) → EQ
new_esEs25(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs10(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), dcd) → new_asAs(new_esEs28(xuu50000, xuu4000, dcd), new_esEs27(xuu50001, xuu4001, dcd))
new_ltEs20(xuu52002, xuu53002, ty_Ordering) → new_ltEs16(xuu52002, xuu53002)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Int, baf) → new_esEs14(xuu50000, xuu4000)
new_compare31(xuu52000, xuu53000, ty_Char) → new_compare15(xuu52000, xuu53000)
new_primPlusNat1(Succ(xuu1400), xuu400100) → Succ(Succ(new_primPlusNat0(xuu1400, xuu400100)))
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_esEs29(xuu22, xuu17, app(app(app(ty_@3, dhh), eaa), eab)) → new_esEs5(xuu22, xuu17, dhh, eaa, eab)
new_esEs22(xuu50001, xuu4001, app(ty_[], cbh)) → new_esEs15(xuu50001, xuu4001, cbh)
new_esEs21(xuu50002, xuu4002, ty_Char) → new_esEs17(xuu50002, xuu4002)
new_ltEs4(xuu5200, xuu5300, app(app(ty_Either, cc), cd)) → new_ltEs8(xuu5200, xuu5300, cc, cd)
new_esEs18(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_compare23(xuu520, xuu530, True, ca, cb) → EQ
new_lt20(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_lt15(xuu52000, xuu53000, daf, dag)
new_esEs20(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu5300))) → GT
new_esEs32(xuu41, xuu36, ty_Float) → new_esEs13(xuu41, xuu36)
new_ltEs20(xuu52002, xuu53002, ty_Float) → new_ltEs13(xuu52002, xuu53002)
new_compare31(xuu52000, xuu53000, app(ty_Ratio, dcg)) → new_compare7(xuu52000, xuu53000, dcg)
new_esEs15(:(xuu50000, xuu50001), [], bdf) → False
new_esEs15([], :(xuu4000, xuu4001), bdf) → False
new_ltEs21(xuu52001, xuu53001, app(ty_Maybe, dcb)) → new_ltEs12(xuu52001, xuu53001, dcb)
new_esEs18(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs25(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_esEs7(xuu52000, xuu53000, gg)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, hb), hc), hd)) → new_esEs5(xuu50000, xuu4000, hb, hc, hd)
new_esEs9(False, True) → False
new_esEs9(True, False) → False
new_lt12(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_lt10(xuu52001, xuu53001, ceb, cec)
new_compare32(Float(xuu52000, xuu52001), Float(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_ltEs7(xuu5200, xuu5300) → new_fsEs(new_compare27(xuu5200, xuu5300))
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_compare31(xuu52000, xuu53000, ty_Double) → new_compare13(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, ty_Float) → new_esEs13(xuu50002, xuu4002)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCompAux1(xuu52000, xuu53000, xuu204, de) → new_primCompAux0(xuu204, new_compare31(xuu52000, xuu53000, de))
new_esEs7(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs26(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_asAs(False, xuu162) → False
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_ltEs13(xuu5200, xuu5300) → new_fsEs(new_compare32(xuu5200, xuu5300))
new_primMulInt(Pos(xuu500010), Neg(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Neg(xuu500010), Pos(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_compare23(Left(xuu5200), Right(xuu5300), False, ca, cb) → LT
new_primCmpInt(Neg(Succ(xuu5200)), Neg(xuu530)) → new_primCmpNat2(xuu530, xuu5200)
new_primMulNat0(Succ(xuu5000100), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu400100)) → Zero
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Int, cd) → new_ltEs19(xuu52000, xuu53000)
new_esEs21(xuu50002, xuu4002, ty_Ordering) → new_esEs8(xuu50002, xuu4002)
new_compare26(xuu52000, xuu53000, False, bad, bae) → new_compare111(xuu52000, xuu53000, new_ltEs11(xuu52000, xuu53000, bad, bae), bad, bae)
new_esEs31(xuu5000, xuu400, ty_Double) → new_esEs16(xuu5000, xuu400)
new_esEs26(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_esEs7(xuu52000, xuu53000, dah)
new_esEs29(xuu22, xuu17, ty_Char) → new_esEs17(xuu22, xuu17)
new_lt18(xuu52000, xuu53000) → new_esEs8(new_compare30(xuu52000, xuu53000), LT)
new_ltEs21(xuu52001, xuu53001, ty_Double) → new_ltEs15(xuu52001, xuu53001)
new_ltEs8(Right(xuu52000), Left(xuu53000), cc, cd) → False
new_esEs18(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, app(ty_[], bha)) → new_esEs15(xuu50000, xuu4000, bha)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Maybe, bda)) → new_esEs7(xuu50000, xuu4000, bda)
new_ltEs17(True, True) → True
new_ltEs14(xuu5200, xuu5300, de) → new_fsEs(new_compare1(xuu5200, xuu5300, de))
new_lt11(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_compare18(xuu52000, xuu53000, True, gg) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(xuu5300))) → new_primCmpNat2(Zero, xuu5300)
new_esEs29(xuu22, xuu17, app(ty_Ratio, dhg)) → new_esEs10(xuu22, xuu17, dhg)
new_lt13(xuu52000, xuu53000) → new_esEs8(new_compare15(xuu52000, xuu53000), LT)
new_esEs24(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_esEs10(xuu52001, xuu53001, ced)
new_ltEs12(Nothing, Just(xuu53000), dd) → True
new_esEs23(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Double, cd) → new_ltEs15(xuu52000, xuu53000)
new_ltEs5(xuu5200, xuu5300, app(ty_[], eg)) → new_ltEs14(xuu5200, xuu5300, eg)
new_ltEs4(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_compare210(xuu52000, xuu53000, False) → new_compare16(xuu52000, xuu53000, new_ltEs17(xuu52000, xuu53000))
new_esEs20(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_compare18(xuu52000, xuu53000, False, gg) → GT
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_Either, hf), hg)) → new_esEs4(xuu50000, xuu4000, hf, hg)
new_esEs9(False, False) → True
new_esEs22(xuu50001, xuu4001, app(ty_Ratio, cbd)) → new_esEs10(xuu50001, xuu4001, cbd)
new_esEs26(xuu52000, xuu53000, app(ty_[], dba)) → new_esEs15(xuu52000, xuu53000, dba)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Float, baf) → new_esEs13(xuu50000, xuu4000)
new_ltEs5(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_esEs14(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs17(xuu50000, xuu4000)
new_lt12(xuu52001, xuu53001, ty_Int) → new_lt4(xuu52001, xuu53001)
new_lt11(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Integer, cd) → new_ltEs18(xuu52000, xuu53000)
new_esEs32(xuu41, xuu36, app(app(ty_Either, gb), gc)) → new_esEs4(xuu41, xuu36, gb, gc)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, app(ty_Ratio, bfc)) → new_esEs10(xuu50001, xuu4001, bfc)
new_esEs30(xuu5000, xuu400, app(app(ty_@2, bfa), bfb)) → new_esEs6(xuu5000, xuu400, bfa, bfb)
new_esEs31(xuu5000, xuu400, ty_Float) → new_esEs13(xuu5000, xuu400)
new_esEs20(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_ltEs17(False, True) → True
new_esEs25(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_esEs5(xuu52000, xuu53000, fa, fb, fc)
new_ltEs21(xuu52001, xuu53001, ty_Bool) → new_ltEs17(xuu52001, xuu53001)
new_ltEs4(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_esEs29(xuu22, xuu17, ty_@0) → new_esEs11(xuu22, xuu17)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs13(xuu50000, xuu4000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, ty_Char) → new_esEs17(xuu5000, xuu400)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu5300))) → new_primCmpNat1(xuu5300, Zero)
new_ltEs21(xuu52001, xuu53001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_ltEs10(xuu52001, xuu53001, dbe, dbf, dbg)
new_esEs30(xuu5000, xuu400, ty_Ordering) → new_esEs8(xuu5000, xuu400)
new_esEs22(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs14(xuu50000, xuu4000)
new_compare31(xuu52000, xuu53000, app(ty_[], ddf)) → new_compare1(xuu52000, xuu53000, ddf)
new_esEs22(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs24(xuu52001, xuu53001, ty_Bool) → new_esEs9(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Float) → new_lt17(xuu52001, xuu53001)
new_ltEs20(xuu52002, xuu53002, ty_Char) → new_ltEs6(xuu52002, xuu53002)
new_esEs20(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_primPlusNat0(Succ(xuu55200), Succ(xuu13100)) → Succ(Succ(new_primPlusNat0(xuu55200, xuu13100)))
new_ltEs4(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_ltEs21(xuu52001, xuu53001, ty_Integer) → new_ltEs18(xuu52001, xuu53001)
new_compare23(Right(xuu5200), Right(xuu5300), False, ca, cb) → new_compare11(xuu5200, xuu5300, new_ltEs5(xuu5200, xuu5300, cb), ca, cb)
new_esEs21(xuu50002, xuu4002, ty_@0) → new_esEs11(xuu50002, xuu4002)
new_compare111(xuu52000, xuu53000, True, bad, bae) → LT
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Ratio, dge)) → new_ltEs9(xuu52000, xuu53000, dge)
new_esEs26(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_esEs4(xuu52000, xuu53000, chh, daa)
new_asAs(True, xuu162) → xuu162
new_esEs19(xuu50001, xuu4001, app(app(ty_Either, bfh), bga)) → new_esEs4(xuu50001, xuu4001, bfh, bga)
new_esEs32(xuu41, xuu36, ty_Integer) → new_esEs12(xuu41, xuu36)
new_compare27(@0, @0) → EQ
new_lt12(xuu52001, xuu53001, ty_Bool) → new_lt19(xuu52001, xuu53001)
new_esEs19(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs26(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_esEs5(xuu52000, xuu53000, dac, dad, dae)
new_esEs4(Left(xuu50000), Right(xuu4000), bca, baf) → False
new_esEs4(Right(xuu50000), Left(xuu4000), bca, baf) → False
new_esEs31(xuu5000, xuu400, app(ty_Maybe, che)) → new_esEs7(xuu5000, xuu400, che)
new_ltEs5(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_ltEs20(xuu52002, xuu53002, app(app(ty_Either, cfd), cfe)) → new_ltEs8(xuu52002, xuu53002, cfd, cfe)
new_esEs32(xuu41, xuu36, ty_Double) → new_esEs16(xuu41, xuu36)
new_ltEs16(LT, LT) → True
new_ltEs12(Just(xuu52000), Nothing, dd) → False
new_compare1(:(xuu52000, xuu52001), [], de) → GT
new_lt16(xuu52000, xuu53000, gg) → new_esEs8(new_compare9(xuu52000, xuu53000, gg), LT)
new_fsEs(xuu177) → new_not(new_esEs8(xuu177, GT))
new_esEs24(xuu52001, xuu53001, ty_Float) → new_esEs13(xuu52001, xuu53001)
new_esEs26(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_esEs6(xuu52000, xuu53000, daf, dag)
new_esEs23(xuu50000, xuu4000, app(app(app(ty_@3, ccg), cch), cda)) → new_esEs5(xuu50000, xuu4000, ccg, cch, cda)
new_esEs19(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs26(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_esEs29(xuu22, xuu17, app(ty_[], eac)) → new_esEs15(xuu22, xuu17, eac)
new_ltEs20(xuu52002, xuu53002, app(app(app(ty_@3, cfg), cfh), cga)) → new_ltEs10(xuu52002, xuu53002, cfg, cfh, cga)
new_esEs30(xuu5000, xuu400, ty_Double) → new_esEs16(xuu5000, xuu400)
new_ltEs8(Left(xuu52000), Right(xuu53000), cc, cd) → True
new_esEs21(xuu50002, xuu4002, ty_Integer) → new_esEs12(xuu50002, xuu4002)
new_lt17(xuu52000, xuu53000) → new_esEs8(new_compare32(xuu52000, xuu53000), LT)
new_esEs30(xuu5000, xuu400, app(app(app(ty_@3, bhg), bhh), caa)) → new_esEs5(xuu5000, xuu400, bhg, bhh, caa)
new_lt11(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_esEs30(xuu5000, xuu400, app(ty_[], bdf)) → new_esEs15(xuu5000, xuu400, bdf)
new_lt11(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_lt16(xuu52000, xuu53000, gg)
new_ltEs5(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_lt12(xuu52001, xuu53001, ty_Integer) → new_lt7(xuu52001, xuu53001)
new_esEs31(xuu5000, xuu400, app(app(ty_@2, chf), chg)) → new_esEs6(xuu5000, xuu400, chf, chg)
new_ltEs15(xuu5200, xuu5300) → new_fsEs(new_compare13(xuu5200, xuu5300))
new_esEs18(xuu50000, xuu4000, app(ty_[], bec)) → new_esEs15(xuu50000, xuu4000, bec)
new_compare28(xuu52000, xuu53000, False) → new_compare110(xuu52000, xuu53000, new_ltEs16(xuu52000, xuu53000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(xuu218, EQ) → xuu218
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Int) → new_compare6(new_sr(xuu52000, xuu53001), new_sr(xuu53000, xuu52001))
new_esEs29(xuu22, xuu17, ty_Ordering) → new_esEs8(xuu22, xuu17)
new_esEs24(xuu52001, xuu53001, app(ty_[], cfc)) → new_esEs15(xuu52001, xuu53001, cfc)
new_esEs18(xuu50000, xuu4000, app(ty_Ratio, bdg)) → new_esEs10(xuu50000, xuu4000, bdg)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs16(xuu50000, xuu4000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(xuu50001, xuu4001, app(ty_Maybe, ccc)) → new_esEs7(xuu50001, xuu4001, ccc)
new_primCmpInt(Neg(Succ(xuu5200)), Pos(xuu530)) → LT
new_not(True) → False
new_compare16(xuu52000, xuu53000, False) → GT
new_compare1([], [], de) → EQ

The set Q consists of the following terms:

new_primCompAux0(x0, EQ)
new_ltEs4(x0, x1, ty_Bool)
new_ltEs5(x0, x1, ty_Float)
new_compare29(x0, x1)
new_fsEs(x0)
new_primCompAux0(x0, GT)
new_esEs19(x0, x1, ty_Bool)
new_esEs18(x0, x1, ty_@0)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3)
new_compare16(x0, x1, False)
new_esEs32(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_compare9(x0, x1, x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, False)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Char)
new_compare8(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Double)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare23(x0, x1, True, x2, x3)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1)
new_compare17(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs31(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Float)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs11(@0, @0)
new_compare10(x0, x1, True, x2, x3)
new_compare111(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_ltEs4(x0, x1, ty_Int)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs8(GT, GT)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_primCmpNat1(x0, Zero)
new_ltEs21(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs4(x0, x1, ty_Integer)
new_esEs7(Nothing, Just(x0), x1)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_ltEs4(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(LT, LT)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, x2)
new_esEs21(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Ordering)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_@0)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Int)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, ty_Integer)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs7(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(False, False)
new_esEs7(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Integer)
new_ltEs4(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(ty_[], x2))
new_compare1(:(x0, x1), [], x2)
new_compare24(x0, x1, False, x2, x3, x4)
new_primEqNat0(Zero, Zero)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs9(True, True)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs29(x0, x1, ty_Double)
new_lt10(x0, x1, x2, x3)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(x0, Succ(x1))
new_primMulNat0(Zero, Zero)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs18(x0, x1)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Integer)
new_ltEs17(True, True)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(Left(x0), Left(x1), False, x2, x3)
new_esEs29(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_lt12(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare14(Integer(x0), Integer(x1))
new_primCmpNat0(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Zero)
new_compare23(Right(x0), Right(x1), False, x2, x3)
new_esEs24(x0, x1, ty_Bool)
new_primCompAux1(x0, x1, x2, x3)
new_esEs7(Nothing, Nothing, x0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1)
new_ltEs4(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(x0, x1, ty_Integer)
new_pePe(False, x0)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_compare1([], :(x0, x1), x2)
new_ltEs21(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_ltEs6(x0, x1)
new_ltEs12(Just(x0), Nothing, x1)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(Float(x0, x1), Float(x2, x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs30(x0, x1, ty_Float)
new_lt12(x0, x1, ty_Int)
new_esEs17(Char(x0), Char(x1))
new_esEs19(x0, x1, ty_Char)
new_primPlusNat0(Zero, Zero)
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs16(EQ, EQ)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Zero)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare25(x0, x1, True, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_esEs19(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_compare28(x0, x1, False)
new_esEs18(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Float)
new_compare16(x0, x1, True)
new_esEs23(x0, x1, ty_Float)
new_esEs18(x0, x1, ty_Int)
new_ltEs16(LT, GT)
new_ltEs16(GT, LT)
new_esEs25(x0, x1, ty_@0)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1)
new_primPlusNat1(Succ(x0), x1)
new_pePe(True, x0)
new_lt11(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt11(x0, x1, ty_Ordering)
new_primCompAux0(x0, LT)
new_esEs25(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_lt12(x0, x1, ty_Bool)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1)
new_compare10(x0, x1, False, x2, x3)
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1, x2)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Bool)
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt15(x0, x1, x2, x3)
new_primPlusNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare31(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_asAs(True, x0)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare26(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs32(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare31(x0, x1, ty_Char)
new_compare210(x0, x1, False)
new_ltEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Integer)
new_ltEs16(GT, GT)
new_esEs18(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_@0)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Double)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs13(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs5(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_primCmpNat2(Succ(x0), x1)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs14(x0, x1)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_compare18(x0, x1, True, x2)
new_esEs30(x0, x1, ty_Integer)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_compare13(Double(x0, x1), Double(x2, x3))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, x0)
new_compare31(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare15(Char(x0), Char(x1))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCmpNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare23(Left(x0), Right(x1), False, x2, x3)
new_compare23(Right(x0), Left(x1), False, x2, x3)
new_ltEs12(Nothing, Nothing, x0)
new_esEs18(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Char)
new_ltEs12(Nothing, Just(x0), x1)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Int)
new_esEs9(False, False)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs18(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_compare6(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Bool)
new_compare31(x0, x1, ty_Ordering)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs4(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_ltEs4(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Double)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_compare18(x0, x1, False, x2)
new_compare26(x0, x1, False, x2, x3)
new_esEs30(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_not(True)
new_ltEs19(x0, x1)
new_esEs20(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs21(x0, x1, ty_Float)
new_lt11(x0, x1, ty_Int)
new_lt9(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, x0)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_lt11(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_ltEs17(False, True)
new_ltEs17(True, False)
new_ltEs20(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_lt12(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, True)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt6(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Int)
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_compare28(x0, x1, True)
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs9(False, True)
new_esEs9(True, False)
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_ltEs20(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare31(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs15([], :(x0, x1), x2)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs15(:(x0, x1), [], x2)
new_esEs21(x0, x1, ty_Bool)
new_ltEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_compare27(@0, @0)
new_lt11(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs30(x0, x1, ty_@0)
new_lt11(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Integer)
new_ltEs9(x0, x1, x2)
new_compare25(x0, x1, False, x2)
new_esEs30(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt8(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs32(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs20(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_esEs29(x0, x1, ty_Int)
new_esEs15([], [], x0)
new_lt12(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_sr(x0, x1)
new_esEs31(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)

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_C2(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, h, ba, bb) → new_addToFM_C(xuu16, xuu20, Left(xuu22), xuu23, h, ba, bb)
new_addToFM_C20(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu43, Left(xuu5000), xuu501, bc, bd, be)
new_addToFM_C1(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, h, ba, bb) → new_addToFM_C(xuu16, xuu21, Left(xuu22), xuu23, h, ba, bb)
new_addToFM_C20(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, False, bc, bd, be) → new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Left(xuu5000), Right(xuu400), False, bc, bd), GT), bc, bd, be)
new_addToFM_C(xuu3, Branch(Right(xuu400), xuu41, xuu42, xuu43, xuu44), Left(xuu5000), xuu501, bc, bd, be) → new_addToFM_C20(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Left(xuu5000), Right(xuu400), False, bc, bd), LT), bc, bd, be)
new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu44, Left(xuu5000), xuu501, bc, bd, be)
new_addToFM_C(xuu3, Branch(Left(xuu400), xuu41, xuu42, xuu43, xuu44), Left(xuu5000), xuu501, bc, bd, be) → new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Left(xuu5000), Left(xuu400), new_esEs30(xuu5000, xuu400, bc), bc, bd), LT), bc, bd, be)
new_addToFM_C2(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, False, h, ba, bb) → new_addToFM_C1(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, new_esEs8(new_compare23(Left(xuu22), Left(xuu17), new_esEs29(xuu22, xuu17, h), h, ba), GT), h, ba, bb)

The TRS R consists of the following rules:

new_esEs30(xuu5000, xuu400, ty_Bool) → new_esEs9(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, ty_Float) → new_esEs13(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, ty_Int) → new_esEs14(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, ty_Integer) → new_esEs12(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, app(ty_Ratio, dcd)) → new_esEs10(xuu5000, xuu400, dcd)
new_esEs30(xuu5000, xuu400, app(app(ty_Either, bca), baf)) → new_esEs4(xuu5000, xuu400, bca, baf)
new_esEs30(xuu5000, xuu400, ty_@0) → new_esEs11(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, app(ty_Maybe, gh)) → new_esEs7(xuu5000, xuu400, gh)
new_esEs30(xuu5000, xuu400, app(app(ty_@2, bfa), bfb)) → new_esEs6(xuu5000, xuu400, bfa, bfb)
new_esEs30(xuu5000, xuu400, ty_Char) → new_esEs17(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, ty_Ordering) → new_esEs8(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, ty_Double) → new_esEs16(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, app(app(app(ty_@3, bhg), bhh), caa)) → new_esEs5(xuu5000, xuu400, bhg, bhh, caa)
new_esEs30(xuu5000, xuu400, app(ty_[], bdf)) → new_esEs15(xuu5000, xuu400, bdf)
new_compare23(Left(xuu5200), Left(xuu5300), False, ca, cb) → new_compare10(xuu5200, xuu5300, new_ltEs4(xuu5200, xuu5300, ca), ca, cb)
new_compare23(xuu520, xuu530, True, ca, cb) → EQ
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_ltEs4(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(app(app(ty_@3, cf), cg), da)) → new_ltEs10(xuu5200, xuu5300, cf, cg, da)
new_ltEs4(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(app(ty_@2, db), dc)) → new_ltEs11(xuu5200, xuu5300, db, dc)
new_ltEs4(xuu5200, xuu5300, app(ty_Maybe, dd)) → new_ltEs12(xuu5200, xuu5300, dd)
new_ltEs4(xuu5200, xuu5300, app(ty_[], de)) → new_ltEs14(xuu5200, xuu5300, de)
new_ltEs4(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(ty_Ratio, ce)) → new_ltEs9(xuu5200, xuu5300, ce)
new_ltEs4(xuu5200, xuu5300, app(app(ty_Either, cc), cd)) → new_ltEs8(xuu5200, xuu5300, cc, cd)
new_ltEs4(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_compare10(xuu167, xuu168, True, dhe, dhf) → LT
new_compare10(xuu167, xuu168, False, dhe, dhf) → GT
new_ltEs6(xuu5200, xuu5300) → new_fsEs(new_compare15(xuu5200, xuu5300))
new_compare15(Char(xuu52000), Char(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_fsEs(xuu177) → new_not(new_esEs8(xuu177, GT))
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_not(False) → True
new_not(True) → False
new_primCmpNat0(Zero, Succ(xuu53000)) → LT
new_primCmpNat0(Succ(xuu52000), Succ(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu52000), Zero) → GT
new_ltEs15(xuu5200, xuu5300) → new_fsEs(new_compare13(xuu5200, xuu5300))
new_compare13(Double(xuu52000, xuu52001), Double(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_sr(xuu50001, xuu4001) → new_primMulInt(xuu50001, xuu4001)
new_compare6(xuu52, xuu53) → new_primCmpInt(xuu52, xuu53)
new_primCmpInt(Pos(Succ(xuu5200)), Pos(xuu530)) → new_primCmpNat1(xuu5200, xuu530)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(xuu5300))) → LT
new_primCmpInt(Pos(Succ(xuu5200)), Neg(xuu530)) → GT
new_primCmpInt(Pos(Zero), Neg(Succ(xuu5300))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(xuu5200)), Neg(xuu530)) → new_primCmpNat2(xuu530, xuu5200)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu5300))) → new_primCmpNat2(Zero, xuu5300)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu5300))) → new_primCmpNat1(xuu5300, Zero)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(xuu5200)), Pos(xuu530)) → LT
new_primCmpNat1(xuu5200, Zero) → GT
new_primCmpNat2(Zero, xuu5200) → LT
new_primCmpNat2(Succ(xuu5300), xuu5200) → new_primCmpNat0(xuu5300, xuu5200)
new_primCmpNat1(xuu5200, Succ(xuu5300)) → new_primCmpNat0(xuu5200, xuu5300)
new_primMulInt(Pos(xuu500010), Pos(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Neg(xuu500010), Neg(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Pos(xuu500010), Neg(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Neg(xuu500010), Pos(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(xuu5000100), Succ(xuu400100)) → new_primPlusNat1(new_primMulNat0(xuu5000100, Succ(xuu400100)), xuu400100)
new_primMulNat0(Succ(xuu5000100), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu400100)) → Zero
new_primPlusNat1(Zero, xuu400100) → Succ(xuu400100)
new_primPlusNat1(Succ(xuu1400), xuu400100) → Succ(Succ(new_primPlusNat0(xuu1400, xuu400100)))
new_primPlusNat0(Succ(xuu55200), Zero) → Succ(xuu55200)
new_primPlusNat0(Zero, Succ(xuu13100)) → Succ(xuu13100)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(xuu55200), Succ(xuu13100)) → Succ(Succ(new_primPlusNat0(xuu55200, xuu13100)))
new_ltEs19(xuu5200, xuu5300) → new_fsEs(new_compare6(xuu5200, xuu5300))
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Bool, cd) → new_ltEs17(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_[], dhd)) → new_ltEs14(xuu52000, xuu53000, dhd)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_@2, dha), dhb)) → new_ltEs11(xuu52000, xuu53000, dha, dhb)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(app(ty_@3, dfd), dfe), dff), cd) → new_ltEs10(xuu52000, xuu53000, dfd, dfe, dff)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_[], dgb), cd) → new_ltEs14(xuu52000, xuu53000, dgb)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Char, cd) → new_ltEs6(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(app(ty_@3, dgf), dgg), dgh)) → new_ltEs10(xuu52000, xuu53000, dgf, dgg, dgh)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Float, cd) → new_ltEs13(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_@2, dfg), dfh), cd) → new_ltEs11(xuu52000, xuu53000, dfg, dfh)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_@0, cd) → new_ltEs7(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Ratio, dfc), cd) → new_ltEs9(xuu52000, xuu53000, dfc)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Ordering, cd) → new_ltEs16(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Int, cd) → new_ltEs19(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Left(xuu53000), cc, cd) → False
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Double, cd) → new_ltEs15(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Integer, cd) → new_ltEs18(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Ratio, dge)) → new_ltEs9(xuu52000, xuu53000, dge)
new_ltEs8(Left(xuu52000), Right(xuu53000), cc, cd) → True
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_Either, dfa), dfb), cd) → new_ltEs8(xuu52000, xuu53000, dfa, dfb)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Maybe, dga), cd) → new_ltEs12(xuu52000, xuu53000, dga)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Maybe, dhc)) → new_ltEs12(xuu52000, xuu53000, dhc)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Maybe, deg)) → new_ltEs12(xuu52000, xuu53000, deg)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_Either, dgc), dgd)) → new_ltEs8(xuu52000, xuu53000, dgc, dgd)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_Either, ddg), ddh)) → new_ltEs8(xuu52000, xuu53000, ddg, ddh)
new_ltEs12(Nothing, Nothing, dd) → True
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Ratio, dea)) → new_ltEs9(xuu52000, xuu53000, dea)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_[], deh)) → new_ltEs14(xuu52000, xuu53000, deh)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_@2, dee), def)) → new_ltEs11(xuu52000, xuu53000, dee, def)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(app(ty_@3, deb), dec), ded)) → new_ltEs10(xuu52000, xuu53000, deb, dec, ded)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_ltEs12(Nothing, Just(xuu53000), dd) → True
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Nothing, dd) → False
new_ltEs13(xuu5200, xuu5300) → new_fsEs(new_compare32(xuu5200, xuu5300))
new_compare32(Float(xuu52000, xuu52001), Float(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_ltEs18(xuu5200, xuu5300) → new_fsEs(new_compare14(xuu5200, xuu5300))
new_compare14(Integer(xuu52000), Integer(xuu53000)) → new_primCmpInt(xuu52000, xuu53000)
new_ltEs17(False, False) → True
new_ltEs17(True, False) → False
new_ltEs17(True, True) → True
new_ltEs17(False, True) → True
new_ltEs10(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), cf, cg, da) → new_pePe(new_lt11(xuu52000, xuu53000, cf), new_asAs(new_esEs25(xuu52000, xuu53000, cf), new_pePe(new_lt12(xuu52001, xuu53001, cg), new_asAs(new_esEs24(xuu52001, xuu53001, cg), new_ltEs20(xuu52002, xuu53002, da)))))
new_lt11(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_lt9(xuu52000, xuu53000, fa, fb, fc)
new_lt11(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_lt15(xuu52000, xuu53000, bad, bae)
new_lt11(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_lt10(xuu52000, xuu53000, bdd, bde)
new_lt11(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, app(ty_[], bac)) → new_lt8(xuu52000, xuu53000, bac)
new_lt11(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_lt5(xuu52000, xuu53000, eh)
new_lt11(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_lt16(xuu52000, xuu53000, gg)
new_esEs25(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_esEs4(xuu52000, xuu53000, bdd, bde)
new_esEs25(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_esEs6(xuu52000, xuu53000, bad, bae)
new_esEs25(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(ty_[], bac)) → new_esEs15(xuu52000, xuu53000, bac)
new_esEs25(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_esEs10(xuu52000, xuu53000, eh)
new_esEs25(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_esEs7(xuu52000, xuu53000, gg)
new_esEs25(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_esEs5(xuu52000, xuu53000, fa, fb, fc)
new_lt12(xuu52001, xuu53001, app(ty_[], cfc)) → new_lt8(xuu52001, xuu53001, cfc)
new_lt12(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_lt5(xuu52001, xuu53001, ced)
new_lt12(xuu52001, xuu53001, ty_Ordering) → new_lt18(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_lt16(xuu52001, xuu53001, cfb)
new_lt12(xuu52001, xuu53001, ty_Char) → new_lt13(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_@0) → new_lt14(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_lt15(xuu52001, xuu53001, ceh, cfa)
new_lt12(xuu52001, xuu53001, ty_Double) → new_lt6(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_lt9(xuu52001, xuu53001, cee, cef, ceg)
new_lt12(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_lt10(xuu52001, xuu53001, ceb, cec)
new_lt12(xuu52001, xuu53001, ty_Int) → new_lt4(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Float) → new_lt17(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Bool) → new_lt19(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Integer) → new_lt7(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs5(xuu52001, xuu53001, cee, cef, ceg)
new_esEs24(xuu52001, xuu53001, ty_Char) → new_esEs17(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_esEs7(xuu52001, xuu53001, cfb)
new_esEs24(xuu52001, xuu53001, ty_@0) → new_esEs11(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_esEs6(xuu52001, xuu53001, ceh, cfa)
new_esEs24(xuu52001, xuu53001, ty_Double) → new_esEs16(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Ordering) → new_esEs8(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Int) → new_esEs14(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Integer) → new_esEs12(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_esEs4(xuu52001, xuu53001, ceb, cec)
new_esEs24(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_esEs10(xuu52001, xuu53001, ced)
new_esEs24(xuu52001, xuu53001, ty_Bool) → new_esEs9(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Float) → new_esEs13(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(ty_[], cfc)) → new_esEs15(xuu52001, xuu53001, cfc)
new_ltEs20(xuu52002, xuu53002, app(ty_Ratio, cff)) → new_ltEs9(xuu52002, xuu53002, cff)
new_ltEs20(xuu52002, xuu53002, ty_@0) → new_ltEs7(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Int) → new_ltEs19(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Double) → new_ltEs15(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, app(ty_Maybe, cgd)) → new_ltEs12(xuu52002, xuu53002, cgd)
new_ltEs20(xuu52002, xuu53002, app(ty_[], cge)) → new_ltEs14(xuu52002, xuu53002, cge)
new_ltEs20(xuu52002, xuu53002, ty_Integer) → new_ltEs18(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, app(app(ty_@2, cgb), cgc)) → new_ltEs11(xuu52002, xuu53002, cgb, cgc)
new_ltEs20(xuu52002, xuu53002, ty_Bool) → new_ltEs17(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Ordering) → new_ltEs16(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Float) → new_ltEs13(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Char) → new_ltEs6(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, app(app(ty_Either, cfd), cfe)) → new_ltEs8(xuu52002, xuu53002, cfd, cfe)
new_ltEs20(xuu52002, xuu53002, app(app(app(ty_@3, cfg), cfh), cga)) → new_ltEs10(xuu52002, xuu53002, cfg, cfh, cga)
new_asAs(False, xuu162) → False
new_asAs(True, xuu162) → xuu162
new_pePe(False, xuu194) → xuu194
new_pePe(True, xuu194) → True
new_ltEs16(GT, GT) → True
new_ltEs16(LT, GT) → True
new_ltEs16(EQ, GT) → True
new_ltEs16(EQ, LT) → False
new_ltEs16(GT, EQ) → False
new_ltEs16(LT, EQ) → True
new_ltEs16(GT, LT) → False
new_ltEs16(EQ, EQ) → True
new_ltEs16(LT, LT) → True
new_ltEs11(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), db, dc) → new_pePe(new_lt20(xuu52000, xuu53000, db), new_asAs(new_esEs26(xuu52000, xuu53000, db), new_ltEs21(xuu52001, xuu53001, dc)))
new_lt20(xuu52000, xuu53000, app(ty_[], dba)) → new_lt8(xuu52000, xuu53000, dba)
new_lt20(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_lt16(xuu52000, xuu53000, dah)
new_lt20(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_lt5(xuu52000, xuu53000, dab)
new_lt20(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_lt9(xuu52000, xuu53000, dac, dad, dae)
new_lt20(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_lt10(xuu52000, xuu53000, chh, daa)
new_lt20(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_lt15(xuu52000, xuu53000, daf, dag)
new_esEs26(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_esEs10(xuu52000, xuu53000, dab)
new_esEs26(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_esEs7(xuu52000, xuu53000, dah)
new_esEs26(xuu52000, xuu53000, app(ty_[], dba)) → new_esEs15(xuu52000, xuu53000, dba)
new_esEs26(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_esEs4(xuu52000, xuu53000, chh, daa)
new_esEs26(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_esEs5(xuu52000, xuu53000, dac, dad, dae)
new_esEs26(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_esEs6(xuu52000, xuu53000, daf, dag)
new_esEs26(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_ltEs21(xuu52001, xuu53001, ty_@0) → new_ltEs7(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Char) → new_ltEs6(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, app(app(ty_Either, dbb), dbc)) → new_ltEs8(xuu52001, xuu53001, dbb, dbc)
new_ltEs21(xuu52001, xuu53001, app(app(ty_@2, dbh), dca)) → new_ltEs11(xuu52001, xuu53001, dbh, dca)
new_ltEs21(xuu52001, xuu53001, app(ty_[], dcc)) → new_ltEs14(xuu52001, xuu53001, dcc)
new_ltEs21(xuu52001, xuu53001, ty_Float) → new_ltEs13(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Ordering) → new_ltEs16(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Int) → new_ltEs19(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, app(ty_Ratio, dbd)) → new_ltEs9(xuu52001, xuu53001, dbd)
new_ltEs21(xuu52001, xuu53001, app(ty_Maybe, dcb)) → new_ltEs12(xuu52001, xuu53001, dcb)
new_ltEs21(xuu52001, xuu53001, ty_Double) → new_ltEs15(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Bool) → new_ltEs17(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_ltEs10(xuu52001, xuu53001, dbe, dbf, dbg)
new_ltEs21(xuu52001, xuu53001, ty_Integer) → new_ltEs18(xuu52001, xuu53001)
new_ltEs9(xuu5200, xuu5300, ce) → new_fsEs(new_compare7(xuu5200, xuu5300, ce))
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Integer) → new_compare14(new_sr0(xuu52000, xuu53001), new_sr0(xuu53000, xuu52001))
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Int) → new_compare6(new_sr(xuu52000, xuu53001), new_sr(xuu53000, xuu52001))
new_sr0(Integer(xuu530000), Integer(xuu520010)) → Integer(new_primMulInt(xuu530000, xuu520010))
new_ltEs14(xuu5200, xuu5300, de) → new_fsEs(new_compare1(xuu5200, xuu5300, de))
new_compare1(:(xuu52000, xuu52001), :(xuu53000, xuu53001), de) → new_primCompAux1(xuu52000, xuu53000, new_compare1(xuu52001, xuu53001, de), de)
new_compare1([], :(xuu53000, xuu53001), de) → LT
new_compare1(:(xuu52000, xuu52001), [], de) → GT
new_compare1([], [], de) → EQ
new_primCompAux1(xuu52000, xuu53000, xuu204, de) → new_primCompAux0(xuu204, new_compare31(xuu52000, xuu53000, de))
new_compare31(xuu52000, xuu53000, ty_Int) → new_compare6(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(ty_Maybe, dde)) → new_compare9(xuu52000, xuu53000, dde)
new_compare31(xuu52000, xuu53000, ty_@0) → new_compare27(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Float) → new_compare32(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Bool) → new_compare29(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Ordering) → new_compare30(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Integer) → new_compare14(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(app(app(ty_@3, dch), dda), ddb)) → new_compare8(xuu52000, xuu53000, dch, dda, ddb)
new_compare31(xuu52000, xuu53000, app(app(ty_Either, dce), dcf)) → new_compare19(xuu52000, xuu53000, dce, dcf)
new_compare31(xuu52000, xuu53000, app(app(ty_@2, ddc), ddd)) → new_compare17(xuu52000, xuu53000, ddc, ddd)
new_compare31(xuu52000, xuu53000, ty_Char) → new_compare15(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(ty_Ratio, dcg)) → new_compare7(xuu52000, xuu53000, dcg)
new_compare31(xuu52000, xuu53000, ty_Double) → new_compare13(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(ty_[], ddf)) → new_compare1(xuu52000, xuu53000, ddf)
new_primCompAux0(xuu218, GT) → GT
new_primCompAux0(xuu218, LT) → LT
new_primCompAux0(xuu218, EQ) → xuu218
new_compare17(xuu52000, xuu53000, bad, bae) → new_compare26(xuu52000, xuu53000, new_esEs6(xuu52000, xuu53000, bad, bae), bad, bae)
new_esEs6(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), bfa, bfb) → new_asAs(new_esEs20(xuu50000, xuu4000, bfa), new_esEs19(xuu50001, xuu4001, bfb))
new_compare26(xuu52000, xuu53000, True, bad, bae) → EQ
new_compare26(xuu52000, xuu53000, False, bad, bae) → new_compare111(xuu52000, xuu53000, new_ltEs11(xuu52000, xuu53000, bad, bae), bad, bae)
new_compare111(xuu52000, xuu53000, False, bad, bae) → GT
new_compare111(xuu52000, xuu53000, True, bad, bae) → LT
new_esEs20(xuu50000, xuu4000, app(ty_Maybe, bhd)) → new_esEs7(xuu50000, xuu4000, bhd)
new_esEs20(xuu50000, xuu4000, app(app(ty_Either, bhb), bhc)) → new_esEs4(xuu50000, xuu4000, bhb, bhc)
new_esEs20(xuu50000, xuu4000, app(app(ty_@2, bhe), bhf)) → new_esEs6(xuu50000, xuu4000, bhe, bhf)
new_esEs20(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, app(ty_Ratio, bge)) → new_esEs10(xuu50000, xuu4000, bge)
new_esEs20(xuu50000, xuu4000, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs5(xuu50000, xuu4000, bgf, bgg, bgh)
new_esEs20(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, app(ty_[], bha)) → new_esEs15(xuu50000, xuu4000, bha)
new_esEs20(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs5(xuu50001, xuu4001, bfd, bfe, bff)
new_esEs19(xuu50001, xuu4001, app(ty_Maybe, bgb)) → new_esEs7(xuu50001, xuu4001, bgb)
new_esEs19(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, app(app(ty_@2, bgc), bgd)) → new_esEs6(xuu50001, xuu4001, bgc, bgd)
new_esEs19(xuu50001, xuu4001, app(ty_[], bfg)) → new_esEs15(xuu50001, xuu4001, bfg)
new_esEs19(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, app(ty_Ratio, bfc)) → new_esEs10(xuu50001, xuu4001, bfc)
new_esEs19(xuu50001, xuu4001, app(app(ty_Either, bfh), bga)) → new_esEs4(xuu50001, xuu4001, bfh, bga)
new_esEs19(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs8(EQ, EQ) → True
new_esEs8(LT, EQ) → False
new_esEs8(GT, EQ) → False
new_esEs11(@0, @0) → True
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_[], bbc), baf) → new_esEs15(xuu50000, xuu4000, bbc)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_[], bcf)) → new_esEs15(xuu50000, xuu4000, bcf)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_@2, bbg), bbh), baf) → new_esEs6(xuu50000, xuu4000, bbg, bbh)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Ratio, bag), baf) → new_esEs10(xuu50000, xuu4000, bag)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_@0, baf) → new_esEs11(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Ordering, baf) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Ratio, bcb)) → new_esEs10(xuu50000, xuu4000, bcb)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs5(xuu50000, xuu4000, bah, bba, bbb)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Char, baf) → new_esEs17(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Bool, baf) → new_esEs9(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs5(xuu50000, xuu4000, bcc, bcd, bce)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Integer, baf) → new_esEs12(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Double, baf) → new_esEs16(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_@2, bdb), bdc)) → new_esEs6(xuu50000, xuu4000, bdb, bdc)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Int, baf) → new_esEs14(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Float, baf) → new_esEs13(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Right(xuu4000), bca, baf) → False
new_esEs4(Right(xuu50000), Left(xuu4000), bca, baf) → False
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_Either, hf), hg)) → new_esEs4(xuu50000, xuu4000, hf, hg)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Maybe, bda)) → new_esEs7(xuu50000, xuu4000, bda)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Maybe, hh)) → new_esEs7(xuu50000, xuu4000, hh)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_Either, bcg), bch)) → new_esEs4(xuu50000, xuu4000, bcg, bch)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_Either, bbd), bbe), baf) → new_esEs4(xuu50000, xuu4000, bbd, bbe)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Maybe, bbf), baf) → new_esEs7(xuu50000, xuu4000, bbf)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_[], he)) → new_esEs15(xuu50000, xuu4000, he)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_@2, baa), bab)) → new_esEs6(xuu50000, xuu4000, baa, bab)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Ratio, ha)) → new_esEs10(xuu50000, xuu4000, ha)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs7(Nothing, Nothing, gh) → True
new_esEs7(Just(xuu50000), Nothing, gh) → False
new_esEs7(Nothing, Just(xuu4000), gh) → False
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, hb), hc), hd)) → new_esEs5(xuu50000, xuu4000, hb, hc, hd)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs16(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_esEs14(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_primEqNat0(Succ(xuu500000), Zero) → False
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_esEs13(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_esEs17(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), bhg, bhh, caa) → new_asAs(new_esEs23(xuu50000, xuu4000, bhg), new_asAs(new_esEs22(xuu50001, xuu4001, bhh), new_esEs21(xuu50002, xuu4002, caa)))
new_esEs23(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Maybe, cde)) → new_esEs7(xuu50000, xuu4000, cde)
new_esEs23(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_[], cdb)) → new_esEs15(xuu50000, xuu4000, cdb)
new_esEs23(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Ratio, ccf)) → new_esEs10(xuu50000, xuu4000, ccf)
new_esEs23(xuu50000, xuu4000, app(app(ty_@2, cdf), cdg)) → new_esEs6(xuu50000, xuu4000, cdf, cdg)
new_esEs23(xuu50000, xuu4000, app(app(ty_Either, cdc), cdd)) → new_esEs4(xuu50000, xuu4000, cdc, cdd)
new_esEs23(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(app(app(ty_@3, ccg), cch), cda)) → new_esEs5(xuu50000, xuu4000, ccg, cch, cda)
new_esEs22(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(app(ty_Either, cca), ccb)) → new_esEs4(xuu50001, xuu4001, cca, ccb)
new_esEs22(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs5(xuu50001, xuu4001, cbe, cbf, cbg)
new_esEs22(xuu50001, xuu4001, app(app(ty_@2, ccd), cce)) → new_esEs6(xuu50001, xuu4001, ccd, cce)
new_esEs22(xuu50001, xuu4001, app(ty_[], cbh)) → new_esEs15(xuu50001, xuu4001, cbh)
new_esEs22(xuu50001, xuu4001, app(ty_Ratio, cbd)) → new_esEs10(xuu50001, xuu4001, cbd)
new_esEs22(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(ty_Maybe, ccc)) → new_esEs7(xuu50001, xuu4001, ccc)
new_esEs21(xuu50002, xuu4002, app(app(ty_@2, cbb), cbc)) → new_esEs6(xuu50002, xuu4002, cbb, cbc)
new_esEs21(xuu50002, xuu4002, ty_Int) → new_esEs14(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, app(ty_[], caf)) → new_esEs15(xuu50002, xuu4002, caf)
new_esEs21(xuu50002, xuu4002, ty_Double) → new_esEs16(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, app(app(ty_Either, cag), cah)) → new_esEs4(xuu50002, xuu4002, cag, cah)
new_esEs21(xuu50002, xuu4002, app(app(app(ty_@3, cac), cad), cae)) → new_esEs5(xuu50002, xuu4002, cac, cad, cae)
new_esEs21(xuu50002, xuu4002, app(ty_Maybe, cba)) → new_esEs7(xuu50002, xuu4002, cba)
new_esEs21(xuu50002, xuu4002, app(ty_Ratio, cab)) → new_esEs10(xuu50002, xuu4002, cab)
new_esEs21(xuu50002, xuu4002, ty_Bool) → new_esEs9(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Char) → new_esEs17(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Float) → new_esEs13(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Ordering) → new_esEs8(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_@0) → new_esEs11(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Integer) → new_esEs12(xuu50002, xuu4002)
new_esEs12(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_esEs9(True, True) → True
new_esEs9(False, True) → False
new_esEs9(True, False) → False
new_esEs9(False, False) → True
new_esEs10(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), dcd) → new_asAs(new_esEs28(xuu50000, xuu4000, dcd), new_esEs27(xuu50001, xuu4001, dcd))
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs15(:(xuu50000, xuu50001), :(xuu4000, xuu4001), bdf) → new_asAs(new_esEs18(xuu50000, xuu4000, bdf), new_esEs15(xuu50001, xuu4001, bdf))
new_esEs15([], [], bdf) → True
new_esEs15(:(xuu50000, xuu50001), [], bdf) → False
new_esEs15([], :(xuu4000, xuu4001), bdf) → False
new_esEs18(xuu50000, xuu4000, app(app(ty_@2, beg), beh)) → new_esEs6(xuu50000, xuu4000, beg, beh)
new_esEs18(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs5(xuu50000, xuu4000, bdh, bea, beb)
new_esEs18(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(ty_Maybe, bef)) → new_esEs7(xuu50000, xuu4000, bef)
new_esEs18(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(app(ty_Either, bed), bee)) → new_esEs4(xuu50000, xuu4000, bed, bee)
new_esEs18(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(ty_[], bec)) → new_esEs15(xuu50000, xuu4000, bec)
new_esEs18(xuu50000, xuu4000, app(ty_Ratio, bdg)) → new_esEs10(xuu50000, xuu4000, bdg)
new_compare19(xuu52000, xuu53000, bdd, bde) → new_compare23(xuu52000, xuu53000, new_esEs4(xuu52000, xuu53000, bdd, bde), bdd, bde)
new_compare23(Right(xuu5200), Left(xuu5300), False, ca, cb) → GT
new_compare23(Left(xuu5200), Right(xuu5300), False, ca, cb) → LT
new_compare23(Right(xuu5200), Right(xuu5300), False, ca, cb) → new_compare11(xuu5200, xuu5300, new_ltEs5(xuu5200, xuu5300, cb), ca, cb)
new_ltEs5(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, app(app(app(ty_@3, ea), eb), ec)) → new_ltEs10(xuu5200, xuu5300, ea, eb, ec)
new_ltEs5(xuu5200, xuu5300, app(app(ty_Either, df), dg)) → new_ltEs8(xuu5200, xuu5300, df, dg)
new_ltEs5(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, app(ty_Ratio, dh)) → new_ltEs9(xuu5200, xuu5300, dh)
new_ltEs5(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, app(app(ty_@2, ed), ee)) → new_ltEs11(xuu5200, xuu5300, ed, ee)
new_ltEs5(xuu5200, xuu5300, app(ty_Maybe, ef)) → new_ltEs12(xuu5200, xuu5300, ef)
new_ltEs5(xuu5200, xuu5300, app(ty_[], eg)) → new_ltEs14(xuu5200, xuu5300, eg)
new_ltEs5(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_compare11(xuu174, xuu175, True, cdh, cea) → LT
new_compare11(xuu174, xuu175, False, cdh, cea) → GT
new_ltEs7(xuu5200, xuu5300) → new_fsEs(new_compare27(xuu5200, xuu5300))
new_compare27(@0, @0) → EQ
new_compare8(xuu52000, xuu53000, fa, fb, fc) → new_compare24(xuu52000, xuu53000, new_esEs5(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_compare24(xuu52000, xuu53000, False, fa, fb, fc) → new_compare12(xuu52000, xuu53000, new_ltEs10(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_compare24(xuu52000, xuu53000, True, fa, fb, fc) → EQ
new_compare12(xuu52000, xuu53000, True, fa, fb, fc) → LT
new_compare12(xuu52000, xuu53000, False, fa, fb, fc) → GT
new_compare30(xuu52000, xuu53000) → new_compare28(xuu52000, xuu53000, new_esEs8(xuu52000, xuu53000))
new_compare28(xuu52000, xuu53000, True) → EQ
new_compare28(xuu52000, xuu53000, False) → new_compare110(xuu52000, xuu53000, new_ltEs16(xuu52000, xuu53000))
new_compare110(xuu52000, xuu53000, True) → LT
new_compare110(xuu52000, xuu53000, False) → GT
new_compare29(xuu52000, xuu53000) → new_compare210(xuu52000, xuu53000, new_esEs9(xuu52000, xuu53000))
new_compare210(xuu52000, xuu53000, True) → EQ
new_compare210(xuu52000, xuu53000, False) → new_compare16(xuu52000, xuu53000, new_ltEs17(xuu52000, xuu53000))
new_compare16(xuu52000, xuu53000, True) → LT
new_compare16(xuu52000, xuu53000, False) → GT
new_compare9(xuu52000, xuu53000, gg) → new_compare25(xuu52000, xuu53000, new_esEs7(xuu52000, xuu53000, gg), gg)
new_compare25(xuu52000, xuu53000, True, gg) → EQ
new_compare25(xuu52000, xuu53000, False, gg) → new_compare18(xuu52000, xuu53000, new_ltEs12(xuu52000, xuu53000, gg), gg)
new_compare18(xuu52000, xuu53000, True, gg) → LT
new_compare18(xuu52000, xuu53000, False, gg) → GT
new_lt15(xuu52000, xuu53000, bad, bae) → new_esEs8(new_compare17(xuu52000, xuu53000, bad, bae), LT)
new_lt14(xuu52000, xuu53000) → new_esEs8(new_compare27(xuu52000, xuu53000), LT)
new_lt10(xuu52000, xuu53000, bdd, bde) → new_esEs8(new_compare19(xuu52000, xuu53000, bdd, bde), LT)
new_lt6(xuu52000, xuu53000) → new_esEs8(new_compare13(xuu52000, xuu53000), LT)
new_lt18(xuu52000, xuu53000) → new_esEs8(new_compare30(xuu52000, xuu53000), LT)
new_lt19(xuu52000, xuu53000) → new_esEs8(new_compare29(xuu52000, xuu53000), LT)
new_lt9(xuu52000, xuu53000, fa, fb, fc) → new_esEs8(new_compare8(xuu52000, xuu53000, fa, fb, fc), LT)
new_lt13(xuu52000, xuu53000) → new_esEs8(new_compare15(xuu52000, xuu53000), LT)
new_lt5(xuu52000, xuu53000, eh) → new_esEs8(new_compare7(xuu52000, xuu53000, eh), LT)
new_lt4(xuu520, xuu530) → new_esEs8(new_compare6(xuu520, xuu530), LT)
new_lt7(xuu52000, xuu53000) → new_esEs8(new_compare14(xuu52000, xuu53000), LT)
new_lt16(xuu52000, xuu53000, gg) → new_esEs8(new_compare9(xuu52000, xuu53000, gg), LT)
new_lt17(xuu52000, xuu53000) → new_esEs8(new_compare32(xuu52000, xuu53000), LT)
new_lt8(xuu52000, xuu53000, bac) → new_esEs8(new_compare1(xuu52000, xuu53000, bac), LT)
new_esEs29(xuu22, xuu17, app(app(ty_Either, ead), eae)) → new_esEs4(xuu22, xuu17, ead, eae)
new_esEs29(xuu22, xuu17, app(ty_Maybe, eaf)) → new_esEs7(xuu22, xuu17, eaf)
new_esEs29(xuu22, xuu17, ty_Bool) → new_esEs9(xuu22, xuu17)
new_esEs29(xuu22, xuu17, ty_Double) → new_esEs16(xuu22, xuu17)
new_esEs29(xuu22, xuu17, ty_Int) → new_esEs14(xuu22, xuu17)
new_esEs29(xuu22, xuu17, ty_Float) → new_esEs13(xuu22, xuu17)
new_esEs29(xuu22, xuu17, ty_Integer) → new_esEs12(xuu22, xuu17)
new_esEs29(xuu22, xuu17, app(app(ty_@2, eag), eah)) → new_esEs6(xuu22, xuu17, eag, eah)
new_esEs29(xuu22, xuu17, app(app(app(ty_@3, dhh), eaa), eab)) → new_esEs5(xuu22, xuu17, dhh, eaa, eab)
new_esEs29(xuu22, xuu17, ty_Char) → new_esEs17(xuu22, xuu17)
new_esEs29(xuu22, xuu17, app(ty_Ratio, dhg)) → new_esEs10(xuu22, xuu17, dhg)
new_esEs29(xuu22, xuu17, ty_@0) → new_esEs11(xuu22, xuu17)
new_esEs29(xuu22, xuu17, app(ty_[], eac)) → new_esEs15(xuu22, xuu17, eac)
new_esEs29(xuu22, xuu17, ty_Ordering) → new_esEs8(xuu22, xuu17)

The set Q consists of the following terms:

new_primCompAux0(x0, EQ)
new_ltEs4(x0, x1, ty_Bool)
new_ltEs5(x0, x1, ty_Float)
new_compare29(x0, x1)
new_fsEs(x0)
new_primCompAux0(x0, GT)
new_esEs19(x0, x1, ty_Bool)
new_esEs18(x0, x1, ty_@0)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3)
new_compare16(x0, x1, False)
new_esEs32(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_compare9(x0, x1, x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, False)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Char)
new_compare8(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Double)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare23(x0, x1, True, x2, x3)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1)
new_compare17(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs31(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Float)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs11(@0, @0)
new_compare10(x0, x1, True, x2, x3)
new_compare111(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_ltEs4(x0, x1, ty_Int)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs8(GT, GT)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_primCmpNat1(x0, Zero)
new_ltEs21(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs4(x0, x1, ty_Integer)
new_esEs7(Nothing, Just(x0), x1)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_ltEs4(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(LT, LT)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, x2)
new_esEs21(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Ordering)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_@0)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Int)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, ty_Integer)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs7(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(False, False)
new_esEs7(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Integer)
new_ltEs4(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(ty_[], x2))
new_compare1(:(x0, x1), [], x2)
new_compare24(x0, x1, False, x2, x3, x4)
new_primEqNat0(Zero, Zero)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs9(True, True)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs29(x0, x1, ty_Double)
new_lt10(x0, x1, x2, x3)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(x0, Succ(x1))
new_primMulNat0(Zero, Zero)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs18(x0, x1)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Integer)
new_ltEs17(True, True)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(Left(x0), Left(x1), False, x2, x3)
new_esEs29(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_lt12(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare14(Integer(x0), Integer(x1))
new_primCmpNat0(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Zero)
new_compare23(Right(x0), Right(x1), False, x2, x3)
new_esEs24(x0, x1, ty_Bool)
new_primCompAux1(x0, x1, x2, x3)
new_esEs7(Nothing, Nothing, x0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1)
new_ltEs4(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(x0, x1, ty_Integer)
new_pePe(False, x0)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_compare1([], :(x0, x1), x2)
new_ltEs21(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_ltEs6(x0, x1)
new_ltEs12(Just(x0), Nothing, x1)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(Float(x0, x1), Float(x2, x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs30(x0, x1, ty_Float)
new_lt12(x0, x1, ty_Int)
new_esEs17(Char(x0), Char(x1))
new_esEs19(x0, x1, ty_Char)
new_primPlusNat0(Zero, Zero)
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs16(EQ, EQ)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Zero)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare25(x0, x1, True, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_esEs19(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_compare28(x0, x1, False)
new_esEs18(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Float)
new_compare16(x0, x1, True)
new_esEs23(x0, x1, ty_Float)
new_esEs18(x0, x1, ty_Int)
new_ltEs16(LT, GT)
new_ltEs16(GT, LT)
new_esEs25(x0, x1, ty_@0)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1)
new_primPlusNat1(Succ(x0), x1)
new_pePe(True, x0)
new_lt11(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt11(x0, x1, ty_Ordering)
new_primCompAux0(x0, LT)
new_esEs25(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_lt12(x0, x1, ty_Bool)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1)
new_compare10(x0, x1, False, x2, x3)
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1, x2)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Bool)
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt15(x0, x1, x2, x3)
new_primPlusNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare31(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_asAs(True, x0)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare26(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs32(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare31(x0, x1, ty_Char)
new_compare210(x0, x1, False)
new_ltEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Integer)
new_ltEs16(GT, GT)
new_esEs18(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_@0)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Double)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs13(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs5(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_primCmpNat2(Succ(x0), x1)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs14(x0, x1)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_compare18(x0, x1, True, x2)
new_esEs30(x0, x1, ty_Integer)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_compare13(Double(x0, x1), Double(x2, x3))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, x0)
new_compare31(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare15(Char(x0), Char(x1))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCmpNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare23(Left(x0), Right(x1), False, x2, x3)
new_compare23(Right(x0), Left(x1), False, x2, x3)
new_ltEs12(Nothing, Nothing, x0)
new_esEs18(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Char)
new_ltEs12(Nothing, Just(x0), x1)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Int)
new_esEs9(False, False)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs18(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_compare6(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Bool)
new_compare31(x0, x1, ty_Ordering)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs4(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_ltEs4(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Double)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_compare18(x0, x1, False, x2)
new_compare26(x0, x1, False, x2, x3)
new_esEs30(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_not(True)
new_ltEs19(x0, x1)
new_esEs20(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs21(x0, x1, ty_Float)
new_lt11(x0, x1, ty_Int)
new_lt9(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, x0)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_lt11(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_ltEs17(False, True)
new_ltEs17(True, False)
new_ltEs20(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_lt12(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, True)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt6(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Int)
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_compare28(x0, x1, True)
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs9(False, True)
new_esEs9(True, False)
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_ltEs20(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare31(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs15([], :(x0, x1), x2)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs15(:(x0, x1), [], x2)
new_esEs21(x0, x1, ty_Bool)
new_ltEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_compare27(@0, @0)
new_lt11(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs30(x0, x1, ty_@0)
new_lt11(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Integer)
new_ltEs9(x0, x1, x2)
new_compare25(x0, x1, False, x2)
new_esEs30(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt8(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs32(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs20(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_esEs29(x0, x1, ty_Int)
new_esEs15([], [], x0)
new_lt12(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_sr(x0, x1)
new_esEs31(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)

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_esEs32(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Float)
new_esEs31(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Ordering)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Float)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Double)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Integer)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)



↳ 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_C2(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, h, ba, bb) → new_addToFM_C(xuu16, xuu20, Left(xuu22), xuu23, h, ba, bb)
new_addToFM_C20(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu43, Left(xuu5000), xuu501, bc, bd, be)
new_addToFM_C1(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, h, ba, bb) → new_addToFM_C(xuu16, xuu21, Left(xuu22), xuu23, h, ba, bb)
new_addToFM_C20(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, False, bc, bd, be) → new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Left(xuu5000), Right(xuu400), False, bc, bd), GT), bc, bd, be)
new_addToFM_C(xuu3, Branch(Right(xuu400), xuu41, xuu42, xuu43, xuu44), Left(xuu5000), xuu501, bc, bd, be) → new_addToFM_C20(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Left(xuu5000), Right(xuu400), False, bc, bd), LT), bc, bd, be)
new_addToFM_C(xuu3, Branch(Left(xuu400), xuu41, xuu42, xuu43, xuu44), Left(xuu5000), xuu501, bc, bd, be) → new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs8(new_compare23(Left(xuu5000), Left(xuu400), new_esEs30(xuu5000, xuu400, bc), bc, bd), LT), bc, bd, be)
new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, bc, bd, be) → new_addToFM_C(xuu3, xuu44, Left(xuu5000), xuu501, bc, bd, be)
new_addToFM_C2(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, False, h, ba, bb) → new_addToFM_C1(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, new_esEs8(new_compare23(Left(xuu22), Left(xuu17), new_esEs29(xuu22, xuu17, h), h, ba), GT), h, ba, bb)

The TRS R consists of the following rules:

new_esEs30(xuu5000, xuu400, ty_Bool) → new_esEs9(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, ty_Float) → new_esEs13(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, ty_Int) → new_esEs14(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, ty_Integer) → new_esEs12(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, app(ty_Ratio, dcd)) → new_esEs10(xuu5000, xuu400, dcd)
new_esEs30(xuu5000, xuu400, app(app(ty_Either, bca), baf)) → new_esEs4(xuu5000, xuu400, bca, baf)
new_esEs30(xuu5000, xuu400, ty_@0) → new_esEs11(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, app(ty_Maybe, gh)) → new_esEs7(xuu5000, xuu400, gh)
new_esEs30(xuu5000, xuu400, app(app(ty_@2, bfa), bfb)) → new_esEs6(xuu5000, xuu400, bfa, bfb)
new_esEs30(xuu5000, xuu400, ty_Char) → new_esEs17(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, ty_Ordering) → new_esEs8(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, ty_Double) → new_esEs16(xuu5000, xuu400)
new_esEs30(xuu5000, xuu400, app(app(app(ty_@3, bhg), bhh), caa)) → new_esEs5(xuu5000, xuu400, bhg, bhh, caa)
new_esEs30(xuu5000, xuu400, app(ty_[], bdf)) → new_esEs15(xuu5000, xuu400, bdf)
new_compare23(Left(xuu5200), Left(xuu5300), False, ca, cb) → new_compare10(xuu5200, xuu5300, new_ltEs4(xuu5200, xuu5300, ca), ca, cb)
new_compare23(xuu520, xuu530, True, ca, cb) → EQ
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_ltEs4(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(app(app(ty_@3, cf), cg), da)) → new_ltEs10(xuu5200, xuu5300, cf, cg, da)
new_ltEs4(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(app(ty_@2, db), dc)) → new_ltEs11(xuu5200, xuu5300, db, dc)
new_ltEs4(xuu5200, xuu5300, app(ty_Maybe, dd)) → new_ltEs12(xuu5200, xuu5300, dd)
new_ltEs4(xuu5200, xuu5300, app(ty_[], de)) → new_ltEs14(xuu5200, xuu5300, de)
new_ltEs4(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, app(ty_Ratio, ce)) → new_ltEs9(xuu5200, xuu5300, ce)
new_ltEs4(xuu5200, xuu5300, app(app(ty_Either, cc), cd)) → new_ltEs8(xuu5200, xuu5300, cc, cd)
new_ltEs4(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_ltEs4(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_compare10(xuu167, xuu168, True, dhe, dhf) → LT
new_compare10(xuu167, xuu168, False, dhe, dhf) → GT
new_ltEs6(xuu5200, xuu5300) → new_fsEs(new_compare15(xuu5200, xuu5300))
new_compare15(Char(xuu52000), Char(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_fsEs(xuu177) → new_not(new_esEs8(xuu177, GT))
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_not(False) → True
new_not(True) → False
new_primCmpNat0(Zero, Succ(xuu53000)) → LT
new_primCmpNat0(Succ(xuu52000), Succ(xuu53000)) → new_primCmpNat0(xuu52000, xuu53000)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu52000), Zero) → GT
new_ltEs15(xuu5200, xuu5300) → new_fsEs(new_compare13(xuu5200, xuu5300))
new_compare13(Double(xuu52000, xuu52001), Double(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_sr(xuu50001, xuu4001) → new_primMulInt(xuu50001, xuu4001)
new_compare6(xuu52, xuu53) → new_primCmpInt(xuu52, xuu53)
new_primCmpInt(Pos(Succ(xuu5200)), Pos(xuu530)) → new_primCmpNat1(xuu5200, xuu530)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(xuu5300))) → LT
new_primCmpInt(Pos(Succ(xuu5200)), Neg(xuu530)) → GT
new_primCmpInt(Pos(Zero), Neg(Succ(xuu5300))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(xuu5200)), Neg(xuu530)) → new_primCmpNat2(xuu530, xuu5200)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu5300))) → new_primCmpNat2(Zero, xuu5300)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu5300))) → new_primCmpNat1(xuu5300, Zero)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(xuu5200)), Pos(xuu530)) → LT
new_primCmpNat1(xuu5200, Zero) → GT
new_primCmpNat2(Zero, xuu5200) → LT
new_primCmpNat2(Succ(xuu5300), xuu5200) → new_primCmpNat0(xuu5300, xuu5200)
new_primCmpNat1(xuu5200, Succ(xuu5300)) → new_primCmpNat0(xuu5200, xuu5300)
new_primMulInt(Pos(xuu500010), Pos(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Neg(xuu500010), Neg(xuu40010)) → Pos(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Pos(xuu500010), Neg(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_primMulInt(Neg(xuu500010), Pos(xuu40010)) → Neg(new_primMulNat0(xuu500010, xuu40010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(xuu5000100), Succ(xuu400100)) → new_primPlusNat1(new_primMulNat0(xuu5000100, Succ(xuu400100)), xuu400100)
new_primMulNat0(Succ(xuu5000100), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu400100)) → Zero
new_primPlusNat1(Zero, xuu400100) → Succ(xuu400100)
new_primPlusNat1(Succ(xuu1400), xuu400100) → Succ(Succ(new_primPlusNat0(xuu1400, xuu400100)))
new_primPlusNat0(Succ(xuu55200), Zero) → Succ(xuu55200)
new_primPlusNat0(Zero, Succ(xuu13100)) → Succ(xuu13100)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(xuu55200), Succ(xuu13100)) → Succ(Succ(new_primPlusNat0(xuu55200, xuu13100)))
new_ltEs19(xuu5200, xuu5300) → new_fsEs(new_compare6(xuu5200, xuu5300))
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Bool, cd) → new_ltEs17(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_[], dhd)) → new_ltEs14(xuu52000, xuu53000, dhd)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_@2, dha), dhb)) → new_ltEs11(xuu52000, xuu53000, dha, dhb)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(app(ty_@3, dfd), dfe), dff), cd) → new_ltEs10(xuu52000, xuu53000, dfd, dfe, dff)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_[], dgb), cd) → new_ltEs14(xuu52000, xuu53000, dgb)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Char, cd) → new_ltEs6(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(app(ty_@3, dgf), dgg), dgh)) → new_ltEs10(xuu52000, xuu53000, dgf, dgg, dgh)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Float, cd) → new_ltEs13(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_@2, dfg), dfh), cd) → new_ltEs11(xuu52000, xuu53000, dfg, dfh)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_@0, cd) → new_ltEs7(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Ratio, dfc), cd) → new_ltEs9(xuu52000, xuu53000, dfc)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Ordering, cd) → new_ltEs16(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Int, cd) → new_ltEs19(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Left(xuu53000), cc, cd) → False
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Double, cd) → new_ltEs15(xuu52000, xuu53000)
new_ltEs8(Left(xuu52000), Left(xuu53000), ty_Integer, cd) → new_ltEs18(xuu52000, xuu53000)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Ratio, dge)) → new_ltEs9(xuu52000, xuu53000, dge)
new_ltEs8(Left(xuu52000), Right(xuu53000), cc, cd) → True
new_ltEs8(Left(xuu52000), Left(xuu53000), app(app(ty_Either, dfa), dfb), cd) → new_ltEs8(xuu52000, xuu53000, dfa, dfb)
new_ltEs8(Left(xuu52000), Left(xuu53000), app(ty_Maybe, dga), cd) → new_ltEs12(xuu52000, xuu53000, dga)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(ty_Maybe, dhc)) → new_ltEs12(xuu52000, xuu53000, dhc)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Maybe, deg)) → new_ltEs12(xuu52000, xuu53000, deg)
new_ltEs8(Right(xuu52000), Right(xuu53000), cc, app(app(ty_Either, dgc), dgd)) → new_ltEs8(xuu52000, xuu53000, dgc, dgd)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_Either, ddg), ddh)) → new_ltEs8(xuu52000, xuu53000, ddg, ddh)
new_ltEs12(Nothing, Nothing, dd) → True
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Ordering) → new_ltEs16(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_@0) → new_ltEs7(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Double) → new_ltEs15(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_Ratio, dea)) → new_ltEs9(xuu52000, xuu53000, dea)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(ty_[], deh)) → new_ltEs14(xuu52000, xuu53000, deh)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Int) → new_ltEs19(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(ty_@2, dee), def)) → new_ltEs11(xuu52000, xuu53000, dee, def)
new_ltEs12(Just(xuu52000), Just(xuu53000), app(app(app(ty_@3, deb), dec), ded)) → new_ltEs10(xuu52000, xuu53000, deb, dec, ded)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Bool) → new_ltEs17(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Char) → new_ltEs6(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Integer) → new_ltEs18(xuu52000, xuu53000)
new_ltEs12(Nothing, Just(xuu53000), dd) → True
new_ltEs12(Just(xuu52000), Just(xuu53000), ty_Float) → new_ltEs13(xuu52000, xuu53000)
new_ltEs12(Just(xuu52000), Nothing, dd) → False
new_ltEs13(xuu5200, xuu5300) → new_fsEs(new_compare32(xuu5200, xuu5300))
new_compare32(Float(xuu52000, xuu52001), Float(xuu53000, xuu53001)) → new_compare6(new_sr(xuu52000, xuu53000), new_sr(xuu52001, xuu53001))
new_ltEs18(xuu5200, xuu5300) → new_fsEs(new_compare14(xuu5200, xuu5300))
new_compare14(Integer(xuu52000), Integer(xuu53000)) → new_primCmpInt(xuu52000, xuu53000)
new_ltEs17(False, False) → True
new_ltEs17(True, False) → False
new_ltEs17(True, True) → True
new_ltEs17(False, True) → True
new_ltEs10(@3(xuu52000, xuu52001, xuu52002), @3(xuu53000, xuu53001, xuu53002), cf, cg, da) → new_pePe(new_lt11(xuu52000, xuu53000, cf), new_asAs(new_esEs25(xuu52000, xuu53000, cf), new_pePe(new_lt12(xuu52001, xuu53001, cg), new_asAs(new_esEs24(xuu52001, xuu53001, cg), new_ltEs20(xuu52002, xuu53002, da)))))
new_lt11(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_lt9(xuu52000, xuu53000, fa, fb, fc)
new_lt11(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_lt15(xuu52000, xuu53000, bad, bae)
new_lt11(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_lt10(xuu52000, xuu53000, bdd, bde)
new_lt11(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, app(ty_[], bac)) → new_lt8(xuu52000, xuu53000, bac)
new_lt11(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_lt5(xuu52000, xuu53000, eh)
new_lt11(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_lt11(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_lt16(xuu52000, xuu53000, gg)
new_esEs25(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(app(ty_Either, bdd), bde)) → new_esEs4(xuu52000, xuu53000, bdd, bde)
new_esEs25(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(app(ty_@2, bad), bae)) → new_esEs6(xuu52000, xuu53000, bad, bae)
new_esEs25(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(ty_[], bac)) → new_esEs15(xuu52000, xuu53000, bac)
new_esEs25(xuu52000, xuu53000, app(ty_Ratio, eh)) → new_esEs10(xuu52000, xuu53000, eh)
new_esEs25(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_esEs25(xuu52000, xuu53000, app(ty_Maybe, gg)) → new_esEs7(xuu52000, xuu53000, gg)
new_esEs25(xuu52000, xuu53000, app(app(app(ty_@3, fa), fb), fc)) → new_esEs5(xuu52000, xuu53000, fa, fb, fc)
new_lt12(xuu52001, xuu53001, app(ty_[], cfc)) → new_lt8(xuu52001, xuu53001, cfc)
new_lt12(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_lt5(xuu52001, xuu53001, ced)
new_lt12(xuu52001, xuu53001, ty_Ordering) → new_lt18(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_lt16(xuu52001, xuu53001, cfb)
new_lt12(xuu52001, xuu53001, ty_Char) → new_lt13(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_@0) → new_lt14(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_lt15(xuu52001, xuu53001, ceh, cfa)
new_lt12(xuu52001, xuu53001, ty_Double) → new_lt6(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_lt9(xuu52001, xuu53001, cee, cef, ceg)
new_lt12(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_lt10(xuu52001, xuu53001, ceb, cec)
new_lt12(xuu52001, xuu53001, ty_Int) → new_lt4(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Float) → new_lt17(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Bool) → new_lt19(xuu52001, xuu53001)
new_lt12(xuu52001, xuu53001, ty_Integer) → new_lt7(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs5(xuu52001, xuu53001, cee, cef, ceg)
new_esEs24(xuu52001, xuu53001, ty_Char) → new_esEs17(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(ty_Maybe, cfb)) → new_esEs7(xuu52001, xuu53001, cfb)
new_esEs24(xuu52001, xuu53001, ty_@0) → new_esEs11(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(app(ty_@2, ceh), cfa)) → new_esEs6(xuu52001, xuu53001, ceh, cfa)
new_esEs24(xuu52001, xuu53001, ty_Double) → new_esEs16(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Ordering) → new_esEs8(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Int) → new_esEs14(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Integer) → new_esEs12(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(app(ty_Either, ceb), cec)) → new_esEs4(xuu52001, xuu53001, ceb, cec)
new_esEs24(xuu52001, xuu53001, app(ty_Ratio, ced)) → new_esEs10(xuu52001, xuu53001, ced)
new_esEs24(xuu52001, xuu53001, ty_Bool) → new_esEs9(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, ty_Float) → new_esEs13(xuu52001, xuu53001)
new_esEs24(xuu52001, xuu53001, app(ty_[], cfc)) → new_esEs15(xuu52001, xuu53001, cfc)
new_ltEs20(xuu52002, xuu53002, app(ty_Ratio, cff)) → new_ltEs9(xuu52002, xuu53002, cff)
new_ltEs20(xuu52002, xuu53002, ty_@0) → new_ltEs7(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Int) → new_ltEs19(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Double) → new_ltEs15(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, app(ty_Maybe, cgd)) → new_ltEs12(xuu52002, xuu53002, cgd)
new_ltEs20(xuu52002, xuu53002, app(ty_[], cge)) → new_ltEs14(xuu52002, xuu53002, cge)
new_ltEs20(xuu52002, xuu53002, ty_Integer) → new_ltEs18(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, app(app(ty_@2, cgb), cgc)) → new_ltEs11(xuu52002, xuu53002, cgb, cgc)
new_ltEs20(xuu52002, xuu53002, ty_Bool) → new_ltEs17(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Ordering) → new_ltEs16(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Float) → new_ltEs13(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, ty_Char) → new_ltEs6(xuu52002, xuu53002)
new_ltEs20(xuu52002, xuu53002, app(app(ty_Either, cfd), cfe)) → new_ltEs8(xuu52002, xuu53002, cfd, cfe)
new_ltEs20(xuu52002, xuu53002, app(app(app(ty_@3, cfg), cfh), cga)) → new_ltEs10(xuu52002, xuu53002, cfg, cfh, cga)
new_asAs(False, xuu162) → False
new_asAs(True, xuu162) → xuu162
new_pePe(False, xuu194) → xuu194
new_pePe(True, xuu194) → True
new_ltEs16(GT, GT) → True
new_ltEs16(LT, GT) → True
new_ltEs16(EQ, GT) → True
new_ltEs16(EQ, LT) → False
new_ltEs16(GT, EQ) → False
new_ltEs16(LT, EQ) → True
new_ltEs16(GT, LT) → False
new_ltEs16(EQ, EQ) → True
new_ltEs16(LT, LT) → True
new_ltEs11(@2(xuu52000, xuu52001), @2(xuu53000, xuu53001), db, dc) → new_pePe(new_lt20(xuu52000, xuu53000, db), new_asAs(new_esEs26(xuu52000, xuu53000, db), new_ltEs21(xuu52001, xuu53001, dc)))
new_lt20(xuu52000, xuu53000, app(ty_[], dba)) → new_lt8(xuu52000, xuu53000, dba)
new_lt20(xuu52000, xuu53000, ty_Float) → new_lt17(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_lt16(xuu52000, xuu53000, dah)
new_lt20(xuu52000, xuu53000, ty_Integer) → new_lt7(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, ty_Int) → new_lt4(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_lt5(xuu52000, xuu53000, dab)
new_lt20(xuu52000, xuu53000, ty_Char) → new_lt13(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_lt9(xuu52000, xuu53000, dac, dad, dae)
new_lt20(xuu52000, xuu53000, ty_Bool) → new_lt19(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, ty_Ordering) → new_lt18(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, ty_Double) → new_lt6(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_lt10(xuu52000, xuu53000, chh, daa)
new_lt20(xuu52000, xuu53000, ty_@0) → new_lt14(xuu52000, xuu53000)
new_lt20(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_lt15(xuu52000, xuu53000, daf, dag)
new_esEs26(xuu52000, xuu53000, ty_Float) → new_esEs13(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, app(ty_Ratio, dab)) → new_esEs10(xuu52000, xuu53000, dab)
new_esEs26(xuu52000, xuu53000, ty_Char) → new_esEs17(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Ordering) → new_esEs8(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Bool) → new_esEs9(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Integer) → new_esEs12(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_@0) → new_esEs11(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, ty_Int) → new_esEs14(xuu52000, xuu53000)
new_esEs26(xuu52000, xuu53000, app(ty_Maybe, dah)) → new_esEs7(xuu52000, xuu53000, dah)
new_esEs26(xuu52000, xuu53000, app(ty_[], dba)) → new_esEs15(xuu52000, xuu53000, dba)
new_esEs26(xuu52000, xuu53000, app(app(ty_Either, chh), daa)) → new_esEs4(xuu52000, xuu53000, chh, daa)
new_esEs26(xuu52000, xuu53000, app(app(app(ty_@3, dac), dad), dae)) → new_esEs5(xuu52000, xuu53000, dac, dad, dae)
new_esEs26(xuu52000, xuu53000, app(app(ty_@2, daf), dag)) → new_esEs6(xuu52000, xuu53000, daf, dag)
new_esEs26(xuu52000, xuu53000, ty_Double) → new_esEs16(xuu52000, xuu53000)
new_ltEs21(xuu52001, xuu53001, ty_@0) → new_ltEs7(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Char) → new_ltEs6(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, app(app(ty_Either, dbb), dbc)) → new_ltEs8(xuu52001, xuu53001, dbb, dbc)
new_ltEs21(xuu52001, xuu53001, app(app(ty_@2, dbh), dca)) → new_ltEs11(xuu52001, xuu53001, dbh, dca)
new_ltEs21(xuu52001, xuu53001, app(ty_[], dcc)) → new_ltEs14(xuu52001, xuu53001, dcc)
new_ltEs21(xuu52001, xuu53001, ty_Float) → new_ltEs13(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Ordering) → new_ltEs16(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Int) → new_ltEs19(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, app(ty_Ratio, dbd)) → new_ltEs9(xuu52001, xuu53001, dbd)
new_ltEs21(xuu52001, xuu53001, app(ty_Maybe, dcb)) → new_ltEs12(xuu52001, xuu53001, dcb)
new_ltEs21(xuu52001, xuu53001, ty_Double) → new_ltEs15(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, ty_Bool) → new_ltEs17(xuu52001, xuu53001)
new_ltEs21(xuu52001, xuu53001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_ltEs10(xuu52001, xuu53001, dbe, dbf, dbg)
new_ltEs21(xuu52001, xuu53001, ty_Integer) → new_ltEs18(xuu52001, xuu53001)
new_ltEs9(xuu5200, xuu5300, ce) → new_fsEs(new_compare7(xuu5200, xuu5300, ce))
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Integer) → new_compare14(new_sr0(xuu52000, xuu53001), new_sr0(xuu53000, xuu52001))
new_compare7(:%(xuu52000, xuu52001), :%(xuu53000, xuu53001), ty_Int) → new_compare6(new_sr(xuu52000, xuu53001), new_sr(xuu53000, xuu52001))
new_sr0(Integer(xuu530000), Integer(xuu520010)) → Integer(new_primMulInt(xuu530000, xuu520010))
new_ltEs14(xuu5200, xuu5300, de) → new_fsEs(new_compare1(xuu5200, xuu5300, de))
new_compare1(:(xuu52000, xuu52001), :(xuu53000, xuu53001), de) → new_primCompAux1(xuu52000, xuu53000, new_compare1(xuu52001, xuu53001, de), de)
new_compare1([], :(xuu53000, xuu53001), de) → LT
new_compare1(:(xuu52000, xuu52001), [], de) → GT
new_compare1([], [], de) → EQ
new_primCompAux1(xuu52000, xuu53000, xuu204, de) → new_primCompAux0(xuu204, new_compare31(xuu52000, xuu53000, de))
new_compare31(xuu52000, xuu53000, ty_Int) → new_compare6(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(ty_Maybe, dde)) → new_compare9(xuu52000, xuu53000, dde)
new_compare31(xuu52000, xuu53000, ty_@0) → new_compare27(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Float) → new_compare32(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Bool) → new_compare29(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Ordering) → new_compare30(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, ty_Integer) → new_compare14(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(app(app(ty_@3, dch), dda), ddb)) → new_compare8(xuu52000, xuu53000, dch, dda, ddb)
new_compare31(xuu52000, xuu53000, app(app(ty_Either, dce), dcf)) → new_compare19(xuu52000, xuu53000, dce, dcf)
new_compare31(xuu52000, xuu53000, app(app(ty_@2, ddc), ddd)) → new_compare17(xuu52000, xuu53000, ddc, ddd)
new_compare31(xuu52000, xuu53000, ty_Char) → new_compare15(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(ty_Ratio, dcg)) → new_compare7(xuu52000, xuu53000, dcg)
new_compare31(xuu52000, xuu53000, ty_Double) → new_compare13(xuu52000, xuu53000)
new_compare31(xuu52000, xuu53000, app(ty_[], ddf)) → new_compare1(xuu52000, xuu53000, ddf)
new_primCompAux0(xuu218, GT) → GT
new_primCompAux0(xuu218, LT) → LT
new_primCompAux0(xuu218, EQ) → xuu218
new_compare17(xuu52000, xuu53000, bad, bae) → new_compare26(xuu52000, xuu53000, new_esEs6(xuu52000, xuu53000, bad, bae), bad, bae)
new_esEs6(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), bfa, bfb) → new_asAs(new_esEs20(xuu50000, xuu4000, bfa), new_esEs19(xuu50001, xuu4001, bfb))
new_compare26(xuu52000, xuu53000, True, bad, bae) → EQ
new_compare26(xuu52000, xuu53000, False, bad, bae) → new_compare111(xuu52000, xuu53000, new_ltEs11(xuu52000, xuu53000, bad, bae), bad, bae)
new_compare111(xuu52000, xuu53000, False, bad, bae) → GT
new_compare111(xuu52000, xuu53000, True, bad, bae) → LT
new_esEs20(xuu50000, xuu4000, app(ty_Maybe, bhd)) → new_esEs7(xuu50000, xuu4000, bhd)
new_esEs20(xuu50000, xuu4000, app(app(ty_Either, bhb), bhc)) → new_esEs4(xuu50000, xuu4000, bhb, bhc)
new_esEs20(xuu50000, xuu4000, app(app(ty_@2, bhe), bhf)) → new_esEs6(xuu50000, xuu4000, bhe, bhf)
new_esEs20(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, app(ty_Ratio, bge)) → new_esEs10(xuu50000, xuu4000, bge)
new_esEs20(xuu50000, xuu4000, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs5(xuu50000, xuu4000, bgf, bgg, bgh)
new_esEs20(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, app(ty_[], bha)) → new_esEs15(xuu50000, xuu4000, bha)
new_esEs20(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs20(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs19(xuu50001, xuu4001, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs5(xuu50001, xuu4001, bfd, bfe, bff)
new_esEs19(xuu50001, xuu4001, app(ty_Maybe, bgb)) → new_esEs7(xuu50001, xuu4001, bgb)
new_esEs19(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, app(app(ty_@2, bgc), bgd)) → new_esEs6(xuu50001, xuu4001, bgc, bgd)
new_esEs19(xuu50001, xuu4001, app(ty_[], bfg)) → new_esEs15(xuu50001, xuu4001, bfg)
new_esEs19(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, app(ty_Ratio, bfc)) → new_esEs10(xuu50001, xuu4001, bfc)
new_esEs19(xuu50001, xuu4001, app(app(ty_Either, bfh), bga)) → new_esEs4(xuu50001, xuu4001, bfh, bga)
new_esEs19(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs19(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs8(EQ, EQ) → True
new_esEs8(LT, EQ) → False
new_esEs8(GT, EQ) → False
new_esEs11(@0, @0) → True
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_[], bbc), baf) → new_esEs15(xuu50000, xuu4000, bbc)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_[], bcf)) → new_esEs15(xuu50000, xuu4000, bcf)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_@2, bbg), bbh), baf) → new_esEs6(xuu50000, xuu4000, bbg, bbh)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Ratio, bag), baf) → new_esEs10(xuu50000, xuu4000, bag)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_@0, baf) → new_esEs11(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Ordering, baf) → new_esEs8(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Ratio, bcb)) → new_esEs10(xuu50000, xuu4000, bcb)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, bah), bba), bbb), baf) → new_esEs5(xuu50000, xuu4000, bah, bba, bbb)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Char, baf) → new_esEs17(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Bool, baf) → new_esEs9(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs5(xuu50000, xuu4000, bcc, bcd, bce)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Integer, baf) → new_esEs12(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Double, baf) → new_esEs16(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_@2, bdb), bdc)) → new_esEs6(xuu50000, xuu4000, bdb, bdc)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Int, baf) → new_esEs14(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Left(xuu4000), ty_Float, baf) → new_esEs13(xuu50000, xuu4000)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs4(Left(xuu50000), Right(xuu4000), bca, baf) → False
new_esEs4(Right(xuu50000), Left(xuu4000), bca, baf) → False
new_esEs4(Right(xuu50000), Right(xuu4000), bca, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_Either, hf), hg)) → new_esEs4(xuu50000, xuu4000, hf, hg)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(ty_Maybe, bda)) → new_esEs7(xuu50000, xuu4000, bda)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Maybe, hh)) → new_esEs7(xuu50000, xuu4000, hh)
new_esEs4(Right(xuu50000), Right(xuu4000), bca, app(app(ty_Either, bcg), bch)) → new_esEs4(xuu50000, xuu4000, bcg, bch)
new_esEs4(Left(xuu50000), Left(xuu4000), app(app(ty_Either, bbd), bbe), baf) → new_esEs4(xuu50000, xuu4000, bbd, bbe)
new_esEs4(Left(xuu50000), Left(xuu4000), app(ty_Maybe, bbf), baf) → new_esEs7(xuu50000, xuu4000, bbf)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_[], he)) → new_esEs15(xuu50000, xuu4000, he)
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(ty_@2, baa), bab)) → new_esEs6(xuu50000, xuu4000, baa, bab)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), app(ty_Ratio, ha)) → new_esEs10(xuu50000, xuu4000, ha)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs7(Nothing, Nothing, gh) → True
new_esEs7(Just(xuu50000), Nothing, gh) → False
new_esEs7(Nothing, Just(xuu4000), gh) → False
new_esEs7(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, hb), hc), hd)) → new_esEs5(xuu50000, xuu4000, hb, hc, hd)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs7(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs16(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_esEs14(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_primEqNat0(Succ(xuu500000), Zero) → False
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_esEs13(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs14(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_esEs17(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), bhg, bhh, caa) → new_asAs(new_esEs23(xuu50000, xuu4000, bhg), new_asAs(new_esEs22(xuu50001, xuu4001, bhh), new_esEs21(xuu50002, xuu4002, caa)))
new_esEs23(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Maybe, cde)) → new_esEs7(xuu50000, xuu4000, cde)
new_esEs23(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_[], cdb)) → new_esEs15(xuu50000, xuu4000, cdb)
new_esEs23(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Ratio, ccf)) → new_esEs10(xuu50000, xuu4000, ccf)
new_esEs23(xuu50000, xuu4000, app(app(ty_@2, cdf), cdg)) → new_esEs6(xuu50000, xuu4000, cdf, cdg)
new_esEs23(xuu50000, xuu4000, app(app(ty_Either, cdc), cdd)) → new_esEs4(xuu50000, xuu4000, cdc, cdd)
new_esEs23(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(app(app(ty_@3, ccg), cch), cda)) → new_esEs5(xuu50000, xuu4000, ccg, cch, cda)
new_esEs22(xuu50001, xuu4001, ty_Char) → new_esEs17(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(app(ty_Either, cca), ccb)) → new_esEs4(xuu50001, xuu4001, cca, ccb)
new_esEs22(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Bool) → new_esEs9(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_@0) → new_esEs11(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs5(xuu50001, xuu4001, cbe, cbf, cbg)
new_esEs22(xuu50001, xuu4001, app(app(ty_@2, ccd), cce)) → new_esEs6(xuu50001, xuu4001, ccd, cce)
new_esEs22(xuu50001, xuu4001, app(ty_[], cbh)) → new_esEs15(xuu50001, xuu4001, cbh)
new_esEs22(xuu50001, xuu4001, app(ty_Ratio, cbd)) → new_esEs10(xuu50001, xuu4001, cbd)
new_esEs22(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, ty_Double) → new_esEs16(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(ty_Maybe, ccc)) → new_esEs7(xuu50001, xuu4001, ccc)
new_esEs21(xuu50002, xuu4002, app(app(ty_@2, cbb), cbc)) → new_esEs6(xuu50002, xuu4002, cbb, cbc)
new_esEs21(xuu50002, xuu4002, ty_Int) → new_esEs14(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, app(ty_[], caf)) → new_esEs15(xuu50002, xuu4002, caf)
new_esEs21(xuu50002, xuu4002, ty_Double) → new_esEs16(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, app(app(ty_Either, cag), cah)) → new_esEs4(xuu50002, xuu4002, cag, cah)
new_esEs21(xuu50002, xuu4002, app(app(app(ty_@3, cac), cad), cae)) → new_esEs5(xuu50002, xuu4002, cac, cad, cae)
new_esEs21(xuu50002, xuu4002, app(ty_Maybe, cba)) → new_esEs7(xuu50002, xuu4002, cba)
new_esEs21(xuu50002, xuu4002, app(ty_Ratio, cab)) → new_esEs10(xuu50002, xuu4002, cab)
new_esEs21(xuu50002, xuu4002, ty_Bool) → new_esEs9(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Char) → new_esEs17(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Float) → new_esEs13(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Ordering) → new_esEs8(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_@0) → new_esEs11(xuu50002, xuu4002)
new_esEs21(xuu50002, xuu4002, ty_Integer) → new_esEs12(xuu50002, xuu4002)
new_esEs12(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_esEs9(True, True) → True
new_esEs9(False, True) → False
new_esEs9(True, False) → False
new_esEs9(False, False) → True
new_esEs10(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), dcd) → new_asAs(new_esEs28(xuu50000, xuu4000, dcd), new_esEs27(xuu50001, xuu4001, dcd))
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs12(xuu50001, xuu4001)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs14(xuu50001, xuu4001)
new_esEs15(:(xuu50000, xuu50001), :(xuu4000, xuu4001), bdf) → new_asAs(new_esEs18(xuu50000, xuu4000, bdf), new_esEs15(xuu50001, xuu4001, bdf))
new_esEs15([], [], bdf) → True
new_esEs15(:(xuu50000, xuu50001), [], bdf) → False
new_esEs15([], :(xuu4000, xuu4001), bdf) → False
new_esEs18(xuu50000, xuu4000, app(app(ty_@2, beg), beh)) → new_esEs6(xuu50000, xuu4000, beg, beh)
new_esEs18(xuu50000, xuu4000, ty_Int) → new_esEs14(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs5(xuu50000, xuu4000, bdh, bea, beb)
new_esEs18(xuu50000, xuu4000, ty_Bool) → new_esEs9(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Char) → new_esEs17(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(ty_Maybe, bef)) → new_esEs7(xuu50000, xuu4000, bef)
new_esEs18(xuu50000, xuu4000, ty_@0) → new_esEs11(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(app(ty_Either, bed), bee)) → new_esEs4(xuu50000, xuu4000, bed, bee)
new_esEs18(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Double) → new_esEs16(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Integer) → new_esEs12(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs18(xuu50000, xuu4000, app(ty_[], bec)) → new_esEs15(xuu50000, xuu4000, bec)
new_esEs18(xuu50000, xuu4000, app(ty_Ratio, bdg)) → new_esEs10(xuu50000, xuu4000, bdg)
new_compare19(xuu52000, xuu53000, bdd, bde) → new_compare23(xuu52000, xuu53000, new_esEs4(xuu52000, xuu53000, bdd, bde), bdd, bde)
new_compare23(Right(xuu5200), Left(xuu5300), False, ca, cb) → GT
new_compare23(Left(xuu5200), Right(xuu5300), False, ca, cb) → LT
new_compare23(Right(xuu5200), Right(xuu5300), False, ca, cb) → new_compare11(xuu5200, xuu5300, new_ltEs5(xuu5200, xuu5300, cb), ca, cb)
new_ltEs5(xuu5200, xuu5300, ty_Float) → new_ltEs13(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, app(app(app(ty_@3, ea), eb), ec)) → new_ltEs10(xuu5200, xuu5300, ea, eb, ec)
new_ltEs5(xuu5200, xuu5300, app(app(ty_Either, df), dg)) → new_ltEs8(xuu5200, xuu5300, df, dg)
new_ltEs5(xuu5200, xuu5300, ty_@0) → new_ltEs7(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, app(ty_Ratio, dh)) → new_ltEs9(xuu5200, xuu5300, dh)
new_ltEs5(xuu5200, xuu5300, ty_Ordering) → new_ltEs16(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Bool) → new_ltEs17(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Double) → new_ltEs15(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, app(app(ty_@2, ed), ee)) → new_ltEs11(xuu5200, xuu5300, ed, ee)
new_ltEs5(xuu5200, xuu5300, app(ty_Maybe, ef)) → new_ltEs12(xuu5200, xuu5300, ef)
new_ltEs5(xuu5200, xuu5300, app(ty_[], eg)) → new_ltEs14(xuu5200, xuu5300, eg)
new_ltEs5(xuu5200, xuu5300, ty_Char) → new_ltEs6(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Integer) → new_ltEs18(xuu5200, xuu5300)
new_ltEs5(xuu5200, xuu5300, ty_Int) → new_ltEs19(xuu5200, xuu5300)
new_compare11(xuu174, xuu175, True, cdh, cea) → LT
new_compare11(xuu174, xuu175, False, cdh, cea) → GT
new_ltEs7(xuu5200, xuu5300) → new_fsEs(new_compare27(xuu5200, xuu5300))
new_compare27(@0, @0) → EQ
new_compare8(xuu52000, xuu53000, fa, fb, fc) → new_compare24(xuu52000, xuu53000, new_esEs5(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_compare24(xuu52000, xuu53000, False, fa, fb, fc) → new_compare12(xuu52000, xuu53000, new_ltEs10(xuu52000, xuu53000, fa, fb, fc), fa, fb, fc)
new_compare24(xuu52000, xuu53000, True, fa, fb, fc) → EQ
new_compare12(xuu52000, xuu53000, True, fa, fb, fc) → LT
new_compare12(xuu52000, xuu53000, False, fa, fb, fc) → GT
new_compare30(xuu52000, xuu53000) → new_compare28(xuu52000, xuu53000, new_esEs8(xuu52000, xuu53000))
new_compare28(xuu52000, xuu53000, True) → EQ
new_compare28(xuu52000, xuu53000, False) → new_compare110(xuu52000, xuu53000, new_ltEs16(xuu52000, xuu53000))
new_compare110(xuu52000, xuu53000, True) → LT
new_compare110(xuu52000, xuu53000, False) → GT
new_compare29(xuu52000, xuu53000) → new_compare210(xuu52000, xuu53000, new_esEs9(xuu52000, xuu53000))
new_compare210(xuu52000, xuu53000, True) → EQ
new_compare210(xuu52000, xuu53000, False) → new_compare16(xuu52000, xuu53000, new_ltEs17(xuu52000, xuu53000))
new_compare16(xuu52000, xuu53000, True) → LT
new_compare16(xuu52000, xuu53000, False) → GT
new_compare9(xuu52000, xuu53000, gg) → new_compare25(xuu52000, xuu53000, new_esEs7(xuu52000, xuu53000, gg), gg)
new_compare25(xuu52000, xuu53000, True, gg) → EQ
new_compare25(xuu52000, xuu53000, False, gg) → new_compare18(xuu52000, xuu53000, new_ltEs12(xuu52000, xuu53000, gg), gg)
new_compare18(xuu52000, xuu53000, True, gg) → LT
new_compare18(xuu52000, xuu53000, False, gg) → GT
new_lt15(xuu52000, xuu53000, bad, bae) → new_esEs8(new_compare17(xuu52000, xuu53000, bad, bae), LT)
new_lt14(xuu52000, xuu53000) → new_esEs8(new_compare27(xuu52000, xuu53000), LT)
new_lt10(xuu52000, xuu53000, bdd, bde) → new_esEs8(new_compare19(xuu52000, xuu53000, bdd, bde), LT)
new_lt6(xuu52000, xuu53000) → new_esEs8(new_compare13(xuu52000, xuu53000), LT)
new_lt18(xuu52000, xuu53000) → new_esEs8(new_compare30(xuu52000, xuu53000), LT)
new_lt19(xuu52000, xuu53000) → new_esEs8(new_compare29(xuu52000, xuu53000), LT)
new_lt9(xuu52000, xuu53000, fa, fb, fc) → new_esEs8(new_compare8(xuu52000, xuu53000, fa, fb, fc), LT)
new_lt13(xuu52000, xuu53000) → new_esEs8(new_compare15(xuu52000, xuu53000), LT)
new_lt5(xuu52000, xuu53000, eh) → new_esEs8(new_compare7(xuu52000, xuu53000, eh), LT)
new_lt4(xuu520, xuu530) → new_esEs8(new_compare6(xuu520, xuu530), LT)
new_lt7(xuu52000, xuu53000) → new_esEs8(new_compare14(xuu52000, xuu53000), LT)
new_lt16(xuu52000, xuu53000, gg) → new_esEs8(new_compare9(xuu52000, xuu53000, gg), LT)
new_lt17(xuu52000, xuu53000) → new_esEs8(new_compare32(xuu52000, xuu53000), LT)
new_lt8(xuu52000, xuu53000, bac) → new_esEs8(new_compare1(xuu52000, xuu53000, bac), LT)
new_esEs29(xuu22, xuu17, app(app(ty_Either, ead), eae)) → new_esEs4(xuu22, xuu17, ead, eae)
new_esEs29(xuu22, xuu17, app(ty_Maybe, eaf)) → new_esEs7(xuu22, xuu17, eaf)
new_esEs29(xuu22, xuu17, ty_Bool) → new_esEs9(xuu22, xuu17)
new_esEs29(xuu22, xuu17, ty_Double) → new_esEs16(xuu22, xuu17)
new_esEs29(xuu22, xuu17, ty_Int) → new_esEs14(xuu22, xuu17)
new_esEs29(xuu22, xuu17, ty_Float) → new_esEs13(xuu22, xuu17)
new_esEs29(xuu22, xuu17, ty_Integer) → new_esEs12(xuu22, xuu17)
new_esEs29(xuu22, xuu17, app(app(ty_@2, eag), eah)) → new_esEs6(xuu22, xuu17, eag, eah)
new_esEs29(xuu22, xuu17, app(app(app(ty_@3, dhh), eaa), eab)) → new_esEs5(xuu22, xuu17, dhh, eaa, eab)
new_esEs29(xuu22, xuu17, ty_Char) → new_esEs17(xuu22, xuu17)
new_esEs29(xuu22, xuu17, app(ty_Ratio, dhg)) → new_esEs10(xuu22, xuu17, dhg)
new_esEs29(xuu22, xuu17, ty_@0) → new_esEs11(xuu22, xuu17)
new_esEs29(xuu22, xuu17, app(ty_[], eac)) → new_esEs15(xuu22, xuu17, eac)
new_esEs29(xuu22, xuu17, ty_Ordering) → new_esEs8(xuu22, xuu17)

The set Q consists of the following terms:

new_primCompAux0(x0, EQ)
new_ltEs4(x0, x1, ty_Bool)
new_ltEs5(x0, x1, ty_Float)
new_compare29(x0, x1)
new_fsEs(x0)
new_primCompAux0(x0, GT)
new_esEs19(x0, x1, ty_Bool)
new_esEs18(x0, x1, ty_@0)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare11(x0, x1, False, x2, x3)
new_compare16(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_compare9(x0, x1, x2)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, False)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Char)
new_compare8(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Double)
new_ltEs8(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare23(x0, x1, True, x2, x3)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1)
new_compare17(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs11(@0, @0)
new_compare10(x0, x1, True, x2, x3)
new_compare111(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_ltEs4(x0, x1, ty_Int)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs8(GT, GT)
new_lt11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_primCmpNat1(x0, Zero)
new_ltEs21(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs4(x0, x1, ty_Integer)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs8(Right(x0), Right(x1), x2, ty_Float)
new_ltEs4(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), ty_Bool, x2)
new_esEs19(x0, x1, ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_esEs8(LT, LT)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, x2)
new_esEs21(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Ordering)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_@0)
new_ltEs8(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, ty_Integer)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs7(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Float)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(False, False)
new_esEs7(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Integer)
new_ltEs4(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(ty_[], x2))
new_compare1(:(x0, x1), [], x2)
new_compare24(x0, x1, False, x2, x3, x4)
new_primEqNat0(Zero, Zero)
new_lt11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(Right(x0), Right(x1), x2, ty_Bool)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs8(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs9(True, True)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs29(x0, x1, ty_Double)
new_lt10(x0, x1, x2, x3)
new_primCmpNat1(x0, Succ(x1))
new_primMulNat0(Zero, Zero)
new_ltEs8(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs18(x0, x1)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Integer)
new_ltEs17(True, True)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs24(x0, x1, ty_@0)
new_ltEs8(Right(x0), Right(x1), x2, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare23(Left(x0), Left(x1), False, x2, x3)
new_esEs29(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, ty_Char)
new_lt12(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare14(Integer(x0), Integer(x1))
new_primCmpNat0(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Zero)
new_compare23(Right(x0), Right(x1), False, x2, x3)
new_esEs24(x0, x1, ty_Bool)
new_primCompAux1(x0, x1, x2, x3)
new_esEs7(Nothing, Nothing, x0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1)
new_ltEs4(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(x0, x1, ty_Integer)
new_pePe(False, x0)
new_ltEs8(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_compare1([], :(x0, x1), x2)
new_ltEs21(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_lt17(x0, x1)
new_ltEs6(x0, x1)
new_ltEs12(Just(x0), Nothing, x1)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare32(Float(x0, x1), Float(x2, x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2)
new_ltEs8(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs30(x0, x1, ty_Float)
new_lt12(x0, x1, ty_Int)
new_esEs17(Char(x0), Char(x1))
new_esEs19(x0, x1, ty_Char)
new_primPlusNat0(Zero, Zero)
new_ltEs8(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs16(EQ, EQ)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs8(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare25(x0, x1, True, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs15(:(x0, x1), :(x2, x3), x4)
new_esEs19(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_ltEs8(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs8(Left(x0), Left(x1), ty_Char, x2)
new_compare28(x0, x1, False)
new_esEs18(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Float)
new_compare16(x0, x1, True)
new_esEs23(x0, x1, ty_Float)
new_esEs18(x0, x1, ty_Int)
new_ltEs16(LT, GT)
new_ltEs16(GT, LT)
new_esEs25(x0, x1, ty_@0)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt7(x0, x1)
new_primPlusNat1(Succ(x0), x1)
new_pePe(True, x0)
new_lt11(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt11(x0, x1, ty_Ordering)
new_primCompAux0(x0, LT)
new_esEs25(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_lt12(x0, x1, ty_Bool)
new_ltEs11(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1)
new_compare10(x0, x1, False, x2, x3)
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1, x2)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Bool)
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt15(x0, x1, x2, x3)
new_primPlusNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs15(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs8(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare31(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_asAs(True, x0)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare26(x0, x1, True, x2, x3)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare31(x0, x1, ty_Char)
new_compare210(x0, x1, False)
new_ltEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_ltEs8(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Integer)
new_ltEs16(GT, GT)
new_esEs18(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_@0)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, ty_Double)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs13(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs5(x0, x1, ty_@0)
new_compare110(x0, x1, True)
new_primCmpNat2(Succ(x0), x1)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs14(x0, x1)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_compare18(x0, x1, True, x2)
new_esEs30(x0, x1, ty_Integer)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_compare13(Double(x0, x1), Double(x2, x3))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, x0)
new_compare31(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_lt11(x0, x1, app(ty_Ratio, x2))
new_compare15(Char(x0), Char(x1))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCmpNat0(Zero, Zero)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare23(Left(x0), Right(x1), False, x2, x3)
new_compare23(Right(x0), Left(x1), False, x2, x3)
new_ltEs12(Nothing, Nothing, x0)
new_esEs18(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Char)
new_ltEs12(Nothing, Just(x0), x1)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Int)
new_esEs9(False, False)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs21(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs18(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_ltEs8(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_compare6(x0, x1)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_Bool)
new_compare31(x0, x1, ty_Ordering)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs4(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_ltEs4(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Double)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_compare18(x0, x1, False, x2)
new_compare26(x0, x1, False, x2, x3)
new_esEs30(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_not(True)
new_ltEs19(x0, x1)
new_esEs20(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs21(x0, x1, ty_Float)
new_lt11(x0, x1, ty_Int)
new_lt9(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, x0)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_lt11(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs8(Right(x0), Right(x1), x2, ty_@0)
new_ltEs17(False, True)
new_ltEs17(True, False)
new_ltEs20(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Left(x0), Left(x1), ty_Integer, x2)
new_lt12(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, True)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt6(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Char)
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_compare28(x0, x1, True)
new_ltEs8(Left(x0), Right(x1), x2, x3)
new_ltEs8(Right(x0), Left(x1), x2, x3)
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs9(False, True)
new_esEs9(True, False)
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_ltEs20(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare31(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_lt11(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs15([], :(x0, x1), x2)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs15(:(x0, x1), [], x2)
new_esEs21(x0, x1, ty_Bool)
new_ltEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_compare27(@0, @0)
new_lt11(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs30(x0, x1, ty_@0)
new_lt11(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_ltEs9(x0, x1, x2)
new_compare25(x0, x1, False, x2)
new_esEs30(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Float)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt8(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs20(x0, x1, ty_Double)
new_lt12(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_esEs29(x0, x1, ty_Int)
new_esEs15([], [], x0)
new_lt12(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_lt11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, app(ty_[], x2))
new_ltEs8(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_Char)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_sr(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)

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, :(xuu50, xuu51), h, ba, bb) → new_foldl(xuu3, xuu51, h, ba, bb)

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: