YES 9.564 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 a => (b  ->  b  ->  b ->  FiniteMap (Maybe a) b  ->  [(Maybe a,b)]  ->  FiniteMap (Maybe a) b) :: Ord a => (b  ->  b  ->  b ->  FiniteMap (Maybe a) b  ->  [(Maybe a,b)]  ->  FiniteMap (Maybe a) b)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

  fmToList :: FiniteMap 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 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 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



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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
fmToList0 key elt rest (key,elt: rest

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



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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

  mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBranch which key elt fm_l fm_r 
let 
result Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result
 where 
balance_ok True
left_ok left_ok0 fm_l key fm_l
left_ok0 fm_l key EmptyFM True
left_ok0 fm_l key (Branch left_key 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 :: a  ->  b  ->  FiniteMap a b
unitFM key elt Branch key elt 1 emptyFM emptyFM


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

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

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

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_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_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_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

compare0 x y True = GT

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

compare3 x y = compare2 x y (x == y)

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

is transformed to
gcd' x 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 a => (b  ->  b  ->  b ->  FiniteMap (Maybe a) b  ->  [(Maybe a,b)]  ->  FiniteMap (Maybe a) b) :: Ord a => (b  ->  b  ->  b ->  FiniteMap (Maybe a) b  ->  [(Maybe a,b)]  ->  FiniteMap (Maybe a) b)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


  instance (Eq a, Eq b) => Eq (FiniteMap 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 add fm key_elt_pairs where 
add fmap (key,eltaddToFM_C combiner fmap key elt

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

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

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

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

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

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

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Let/Where Reductions:
The bindings of the following Let/Where expression
let 
result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result
where 
balance_ok  = True
left_ok  = left_ok0 fm_l key fm_l
left_ok0 fm_l key EmptyFM = True
left_ok0 fm_l key (Branch left_key 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_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

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

mkBranchBalance_ok wxw wxx wxy = True

mkBranchRight_size wxw wxx wxy = sizeFM wxy

mkBranchLeft_size wxw wxx wxy = sizeFM wxw

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

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

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

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

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
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)

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)

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

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)

mkBalBranch6Size_r wyx wyy wyz wzu = sizeFM wyz

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)

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)

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

mkBalBranch6Size_l wyx wyy wyz wzu = sizeFM wzu

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

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

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

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)

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

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)

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

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)

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 
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 wzw = fst (findMin wzw)

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 wzx = fst (findMax 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' x wuy = gcd0Gcd'2 x wuy
gcd0Gcd' x y = gcd0Gcd'0 x y

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

gcd0Gcd'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 => (b  ->  b  ->  b ->  FiniteMap (Maybe a) b  ->  [(Maybe a,b)]  ->  FiniteMap (Maybe a) b) :: Ord a => (b  ->  b  ->  b ->  FiniteMap (Maybe a) b  ->  [(Maybe a,b)]  ->  FiniteMap (Maybe a) b)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
addListToFM_CAdd wzv fmap (key,eltaddToFM_C wzv fmap key elt

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

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

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

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

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

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

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (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 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 < 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 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_l fm_r

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxw wxx wxw

  
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 wzx fst (findMax wzx)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxw

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

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxy wxx wxy

  
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 wzw fst (findMin wzw)

  
mkBranchRight_size wxw wxx wxy sizeFM wxy

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

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

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

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

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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (c  ->  b  ->  a  ->  a ->  a  ->  FiniteMap c b  ->  a
foldFM k z EmptyFM z
foldFM k z (Branch key elt vw fm_l fm_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 < 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_l fm_r

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxw wxx wxw

  
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 wzx fst (findMax wzx)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxw

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

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxy wxx wxy

  
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 wzw fst (findMin wzw)

  
mkBranchRight_size wxw wxx wxy sizeFM wxy

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

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

  sizeFM :: FiniteMap b a  ->  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(xuu3300), Succ(xuu3400)) → new_primCmpNat(xuu3300, xuu3400)

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(xuu28200), Succ(xuu9700)) → new_primMinusNat(xuu28200, xuu9700)

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(xuu28200), Succ(xuu9700)) → new_primPlusNat(xuu28200, xuu9700)

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(xuu5000000), Succ(xuu400000)) → new_primMulNat(xuu5000000, Succ(xuu400000))

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

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_ltEs2(Right(xuu33000), Right(xuu34000), bae, app(ty_Maybe, baf)) → new_ltEs(xuu33000, xuu34000, baf)
new_ltEs1(:(xuu33000, xuu33001), :(xuu34000, xuu34001), ga) → new_compare(xuu33001, xuu34001, ga)
new_compare2(Just(Just(xuu33000)), Just(Just(xuu34000)), False, app(ty_Maybe, app(app(ty_@2, bg), bh))) → new_ltEs3(xuu33000, xuu34000, bg, bh)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), app(app(ty_Either, bdg), bdh), bdb) → new_lt2(xuu33000, xuu34000, bdg, bdh)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, app(app(app(ty_@3, eh), fa), fb)), cb), df)) → new_compare20(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, eh, fa, fb), eh, fa, fb)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), app(app(app(ty_@3, eh), fa), fb), cb, df) → new_compare20(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, eh, fa, fb), eh, fa, fb)
new_compare2(Just(Left(xuu33000)), Just(Left(xuu34000)), False, app(app(ty_Either, app(app(ty_Either, baa), bab)), hd)) → new_ltEs2(xuu33000, xuu34000, baa, bab)
new_ltEs2(Left(xuu33000), Left(xuu34000), app(app(ty_Either, baa), bab), hd) → new_ltEs2(xuu33000, xuu34000, baa, bab)
new_lt3(xuu33000, xuu34000, fg, fh) → new_compare22(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, fg, fh), fg, fh)
new_primCompAux(xuu33000, xuu34000, xuu173, app(ty_[], gf)) → new_compare(xuu33000, xuu34000, gf)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ca, cb, app(app(ty_@2, dc), dd)) → new_ltEs3(xuu33002, xuu34002, dc, dd)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, ca), cb), app(ty_Maybe, cc))) → new_ltEs(xuu33002, xuu34002, cc)
new_compare2(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, app(app(ty_@2, bea), beb)), bdb)) → new_lt3(xuu33000, xuu34000, bea, beb)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), app(ty_[], fc), cb, df) → new_compare(xuu33000, xuu34000, fc)
new_compare2(Just(Just(xuu33000)), Just(Just(xuu34000)), False, app(ty_Maybe, app(app(app(ty_@3, ba), bb), bc))) → new_ltEs0(xuu33000, xuu34000, ba, bb, bc)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bbg, app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs0(xuu33001, xuu34001, bca, bcb, bcc)
new_compare2(Just(:(xuu33000, xuu33001)), Just(:(xuu34000, xuu34001)), False, app(ty_[], ga)) → new_primCompAux(xuu33000, xuu34000, new_compare0(xuu33001, xuu34001, ga), ga)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bbg, app(app(ty_@2, bcg), bch)) → new_ltEs3(xuu33001, xuu34001, bcg, bch)
new_compare2(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, app(app(app(ty_@3, bdc), bdd), bde)), bdb)) → new_lt0(xuu33000, xuu34000, bdc, bdd, bde)
new_ltEs2(Right(xuu33000), Right(xuu34000), bae, app(app(ty_@2, bbe), bbf)) → new_ltEs3(xuu33000, xuu34000, bbe, bbf)
new_lt0(xuu33000, xuu34000, eh, fa, fb) → new_compare20(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, eh, fa, fb), eh, fa, fb)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, app(ty_[], fc)), cb), df)) → new_compare(xuu33000, xuu34000, fc)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, app(app(ty_Either, fd), ff)), cb), df)) → new_compare21(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, fd, ff), fd, ff)
new_compare21(xuu33000, xuu34000, False, fd, ff) → new_ltEs2(xuu33000, xuu34000, fd, ff)
new_ltEs(Just(xuu33000), Just(xuu34000), app(app(app(ty_@3, ba), bb), bc)) → new_ltEs0(xuu33000, xuu34000, ba, bb, bc)
new_compare2(Just(Right(xuu33000)), Just(Right(xuu34000)), False, app(app(ty_Either, bae), app(ty_[], bbb))) → new_ltEs1(xuu33000, xuu34000, bbb)
new_compare2(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, bbg), app(ty_Maybe, bbh))) → new_ltEs(xuu33001, xuu34001, bbh)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, ca), app(app(ty_@2, ee), ef)), df)) → new_lt3(xuu33001, xuu34001, ee, ef)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ca, cb, app(app(app(ty_@3, cd), ce), cf)) → new_ltEs0(xuu33002, xuu34002, cd, ce, cf)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ca, cb, app(ty_[], cg)) → new_ltEs1(xuu33002, xuu34002, cg)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), app(app(ty_@2, bea), beb), bdb) → new_lt3(xuu33000, xuu34000, bea, beb)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, ca), app(app(app(ty_@3, dg), dh), ea)), df)) → new_lt0(xuu33001, xuu34001, dg, dh, ea)
new_compare2(Just(Just(xuu33000)), Just(Just(xuu34000)), False, app(ty_Maybe, app(ty_[], bd))) → new_ltEs1(xuu33000, xuu34000, bd)
new_primCompAux(xuu33000, xuu34000, xuu173, app(ty_Maybe, gb)) → new_compare1(xuu33000, xuu34000, gb)
new_ltEs(Just(xuu33000), Just(xuu34000), app(ty_[], bd)) → new_ltEs1(xuu33000, xuu34000, bd)
new_primCompAux(xuu33000, xuu34000, xuu173, app(app(app(ty_@3, gc), gd), ge)) → new_compare3(xuu33000, xuu34000, gc, gd, ge)
new_compare2(Just(Right(xuu33000)), Just(Right(xuu34000)), False, app(app(ty_Either, bae), app(app(app(ty_@3, bag), bah), bba))) → new_ltEs0(xuu33000, xuu34000, bag, bah, bba)
new_compare2(Just(Just(xuu33000)), Just(Just(xuu34000)), False, app(ty_Maybe, app(ty_Maybe, h))) → new_ltEs(xuu33000, xuu34000, h)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ca, cb, app(ty_Maybe, cc)) → new_ltEs(xuu33002, xuu34002, cc)
new_compare2(Just(:(xuu33000, xuu33001)), Just(:(xuu34000, xuu34001)), False, app(ty_[], ga)) → new_compare(xuu33001, xuu34001, ga)
new_compare2(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, app(ty_Maybe, bda)), bdb)) → new_lt(xuu33000, xuu34000, bda)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bbg, app(app(ty_Either, bce), bcf)) → new_ltEs2(xuu33001, xuu34001, bce, bcf)
new_compare20(xuu33000, xuu34000, False, eh, fa, fb) → new_ltEs0(xuu33000, xuu34000, eh, fa, fb)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, ca), app(ty_[], eb)), df)) → new_lt1(xuu33001, xuu34001, eb)
new_ltEs2(Left(xuu33000), Left(xuu34000), app(app(app(ty_@3, he), hf), hg), hd) → new_ltEs0(xuu33000, xuu34000, he, hf, hg)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ca, app(ty_[], eb), df) → new_lt1(xuu33001, xuu34001, eb)
new_compare4(xuu33000, xuu34000, fd, ff) → new_compare21(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, fd, ff), fd, ff)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, app(ty_Maybe, eg)), cb), df)) → new_compare2(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, eg), eg)
new_compare2(Just(Right(xuu33000)), Just(Right(xuu34000)), False, app(app(ty_Either, bae), app(ty_Maybe, baf))) → new_ltEs(xuu33000, xuu34000, baf)
new_compare2(Just(Left(xuu33000)), Just(Left(xuu34000)), False, app(app(ty_Either, app(ty_Maybe, hc)), hd)) → new_ltEs(xuu33000, xuu34000, hc)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), app(ty_[], bdf), bdb) → new_lt1(xuu33000, xuu34000, bdf)
new_compare2(Just(Left(xuu33000)), Just(Left(xuu34000)), False, app(app(ty_Either, app(app(ty_@2, bac), bad)), hd)) → new_ltEs3(xuu33000, xuu34000, bac, bad)
new_compare2(Just(Left(xuu33000)), Just(Left(xuu34000)), False, app(app(ty_Either, app(ty_[], hh)), hd)) → new_ltEs1(xuu33000, xuu34000, hh)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bbg, app(ty_[], bcd)) → new_ltEs1(xuu33001, xuu34001, bcd)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, ca), cb), app(app(app(ty_@3, cd), ce), cf))) → new_ltEs0(xuu33002, xuu34002, cd, ce, cf)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), app(app(ty_Either, fd), ff), cb, df) → new_compare21(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, fd, ff), fd, ff)
new_compare2(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, bbg), app(app(app(ty_@3, bca), bcb), bcc))) → new_ltEs0(xuu33001, xuu34001, bca, bcb, bcc)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, ca), app(ty_Maybe, de)), df)) → new_lt(xuu33001, xuu34001, de)
new_primCompAux(xuu33000, xuu34000, xuu173, app(app(ty_@2, ha), hb)) → new_compare5(xuu33000, xuu34000, ha, hb)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, app(app(ty_@2, fg), fh)), cb), df)) → new_compare22(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, fg, fh), fg, fh)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, ca), cb), app(app(ty_Either, da), db))) → new_ltEs2(xuu33002, xuu34002, da, db)
new_compare2(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, bbg), app(app(ty_Either, bce), bcf))) → new_ltEs2(xuu33001, xuu34001, bce, bcf)
new_compare22(xuu33000, xuu34000, False, fg, fh) → new_ltEs3(xuu33000, xuu34000, fg, fh)
new_compare1(xuu33000, xuu34000, eg) → new_compare2(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, eg), eg)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ca, app(app(ty_@2, ee), ef), df) → new_lt3(xuu33001, xuu34001, ee, ef)
new_ltEs2(Left(xuu33000), Left(xuu34000), app(ty_Maybe, hc), hd) → new_ltEs(xuu33000, xuu34000, hc)
new_compare2(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, app(app(ty_Either, bdg), bdh)), bdb)) → new_lt2(xuu33000, xuu34000, bdg, bdh)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ca, app(app(ty_Either, ec), ed), df) → new_lt2(xuu33001, xuu34001, ec, ed)
new_compare2(Just(Left(xuu33000)), Just(Left(xuu34000)), False, app(app(ty_Either, app(app(app(ty_@3, he), hf), hg)), hd)) → new_ltEs0(xuu33000, xuu34000, he, hf, hg)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, ca), app(app(ty_Either, ec), ed)), df)) → new_lt2(xuu33001, xuu34001, ec, ed)
new_ltEs(Just(xuu33000), Just(xuu34000), app(ty_Maybe, h)) → new_ltEs(xuu33000, xuu34000, h)
new_lt(xuu33000, xuu34000, eg) → new_compare2(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, eg), eg)
new_ltEs2(Right(xuu33000), Right(xuu34000), bae, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs0(xuu33000, xuu34000, bag, bah, bba)
new_ltEs2(Left(xuu33000), Left(xuu34000), app(app(ty_@2, bac), bad), hd) → new_ltEs3(xuu33000, xuu34000, bac, bad)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bbg, app(ty_Maybe, bbh)) → new_ltEs(xuu33001, xuu34001, bbh)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ca, app(app(app(ty_@3, dg), dh), ea), df) → new_lt0(xuu33001, xuu34001, dg, dh, ea)
new_compare3(xuu33000, xuu34000, eh, fa, fb) → new_compare20(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, eh, fa, fb), eh, fa, fb)
new_compare2(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, bbg), app(ty_[], bcd))) → new_ltEs1(xuu33001, xuu34001, bcd)
new_ltEs2(Right(xuu33000), Right(xuu34000), bae, app(ty_[], bbb)) → new_ltEs1(xuu33000, xuu34000, bbb)
new_primCompAux(xuu33000, xuu34000, xuu173, app(app(ty_Either, gg), gh)) → new_compare4(xuu33000, xuu34000, gg, gh)
new_ltEs2(Right(xuu33000), Right(xuu34000), bae, app(app(ty_Either, bbc), bbd)) → new_ltEs2(xuu33000, xuu34000, bbc, bbd)
new_ltEs(Just(xuu33000), Just(xuu34000), app(app(ty_Either, be), bf)) → new_ltEs2(xuu33000, xuu34000, be, bf)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ca, cb, app(app(ty_Either, da), db)) → new_ltEs2(xuu33002, xuu34002, da, db)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), app(ty_Maybe, eg), cb, df) → new_compare2(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, eg), eg)
new_lt1(xuu33000, xuu34000, fc) → new_compare(xuu33000, xuu34000, fc)
new_compare2(Just(Just(xuu33000)), Just(Just(xuu34000)), False, app(ty_Maybe, app(app(ty_Either, be), bf))) → new_ltEs2(xuu33000, xuu34000, be, bf)
new_lt2(xuu33000, xuu34000, fd, ff) → new_compare21(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, fd, ff), fd, ff)
new_compare2(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, bbg), app(app(ty_@2, bcg), bch))) → new_ltEs3(xuu33001, xuu34001, bcg, bch)
new_ltEs(Just(xuu33000), Just(xuu34000), app(app(ty_@2, bg), bh)) → new_ltEs3(xuu33000, xuu34000, bg, bh)
new_compare2(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, app(ty_[], bdf)), bdb)) → new_lt1(xuu33000, xuu34000, bdf)
new_compare(:(xuu33000, xuu33001), :(xuu34000, xuu34001), ga) → new_compare(xuu33001, xuu34001, ga)
new_compare5(xuu33000, xuu34000, fg, fh) → new_compare22(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, fg, fh), fg, fh)
new_compare(:(xuu33000, xuu33001), :(xuu34000, xuu34001), ga) → new_primCompAux(xuu33000, xuu34000, new_compare0(xuu33001, xuu34001, ga), ga)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), app(ty_Maybe, bda), bdb) → new_lt(xuu33000, xuu34000, bda)
new_ltEs1(:(xuu33000, xuu33001), :(xuu34000, xuu34001), ga) → new_primCompAux(xuu33000, xuu34000, new_compare0(xuu33001, xuu34001, ga), ga)
new_compare2(Just(Right(xuu33000)), Just(Right(xuu34000)), False, app(app(ty_Either, bae), app(app(ty_Either, bbc), bbd))) → new_ltEs2(xuu33000, xuu34000, bbc, bbd)
new_compare2(Just(Right(xuu33000)), Just(Right(xuu34000)), False, app(app(ty_Either, bae), app(app(ty_@2, bbe), bbf))) → new_ltEs3(xuu33000, xuu34000, bbe, bbf)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), app(app(ty_@2, fg), fh), cb, df) → new_compare22(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, fg, fh), fg, fh)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), app(app(app(ty_@3, bdc), bdd), bde), bdb) → new_lt0(xuu33000, xuu34000, bdc, bdd, bde)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, ca), cb), app(ty_[], cg))) → new_ltEs1(xuu33002, xuu34002, cg)
new_ltEs2(Left(xuu33000), Left(xuu34000), app(ty_[], hh), hd) → new_ltEs1(xuu33000, xuu34000, hh)
new_ltEs0(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ca, app(ty_Maybe, de), df) → new_lt(xuu33001, xuu34001, de)
new_compare2(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, ca), cb), app(app(ty_@2, dc), dd))) → new_ltEs3(xuu33002, xuu34002, dc, dd)

The TRS R consists of the following rules:

new_esEs4(Just(xuu50000), Just(xuu4000), app(ty_Maybe, cfh)) → new_esEs4(xuu50000, xuu4000, cfh)
new_ltEs19(xuu33002, xuu34002, app(app(ty_@2, dc), dd)) → new_ltEs5(xuu33002, xuu34002, dc, dd)
new_lt19(xuu33001, xuu34001, ty_Char) → new_lt7(xuu33001, xuu34001)
new_esEs16(EQ, GT) → False
new_esEs16(GT, EQ) → False
new_ltEs19(xuu33002, xuu34002, ty_Ordering) → new_ltEs16(xuu33002, xuu34002)
new_lt19(xuu33001, xuu34001, app(ty_Ratio, bef)) → new_lt10(xuu33001, xuu34001, bef)
new_ltEs16(GT, GT) → True
new_esEs20(xuu33000, xuu34000, ty_Ordering) → new_esEs16(xuu33000, xuu34000)
new_lt5(xuu33000, xuu34000) → new_esEs16(new_compare6(xuu33000, xuu34000), LT)
new_compare9(Char(xuu33000), Char(xuu34000)) → new_primCmpNat0(xuu33000, xuu34000)
new_esEs26(xuu50000, xuu4000, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_esEs24(xuu50000, xuu4000, app(app(app(ty_@3, ccd), cce), ccf)) → new_esEs5(xuu50000, xuu4000, ccd, cce, ccf)
new_ltEs10(xuu3300, xuu3400) → new_fsEs(new_compare16(xuu3300, xuu3400))
new_lt4(xuu33000, xuu34000, ty_Ordering) → new_lt14(xuu33000, xuu34000)
new_compare10(xuu33000, xuu34000, True, fd, ff) → LT
new_esEs4(Just(xuu50000), Nothing, cfe) → False
new_esEs4(Nothing, Just(xuu4000), cfe) → False
new_esEs24(xuu50000, xuu4000, app(ty_Maybe, cbg)) → new_esEs4(xuu50000, xuu4000, cbg)
new_lt19(xuu33001, xuu34001, ty_Integer) → new_lt5(xuu33001, xuu34001)
new_lt4(xuu33000, xuu34000, ty_Char) → new_lt7(xuu33000, xuu34000)
new_ltEs16(LT, GT) → True
new_lt14(xuu33000, xuu34000) → new_esEs16(new_compare8(xuu33000, xuu34000), LT)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs14(xuu50000, xuu4000)
new_lt4(xuu33000, xuu34000, app(app(ty_@2, bea), beb)) → new_lt18(xuu33000, xuu34000, bea, beb)
new_ltEs19(xuu33002, xuu34002, ty_Double) → new_ltEs11(xuu33002, xuu34002)
new_esEs20(xuu33000, xuu34000, ty_Double) → new_esEs12(xuu33000, xuu34000)
new_esEs23(xuu50000, xuu4000, app(ty_[], cae)) → new_esEs17(xuu50000, xuu4000, cae)
new_lt19(xuu33001, xuu34001, ty_Ordering) → new_lt14(xuu33001, xuu34001)
new_ltEs19(xuu33002, xuu34002, app(ty_Ratio, bee)) → new_ltEs12(xuu33002, xuu34002, bee)
new_primMulNat0(Zero, Zero) → Zero
new_esEs25(xuu50001, xuu4001, ty_Double) → new_esEs12(xuu50001, xuu4001)
new_compare16(Float(xuu33000, xuu33001), Float(xuu34000, xuu34001)) → new_compare7(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, app(app(ty_@2, cec), ced)) → new_esEs7(xuu50000, xuu4000, cec, ced)
new_esEs23(xuu50000, xuu4000, app(ty_Ratio, cah)) → new_esEs13(xuu50000, xuu4000, cah)
new_esEs25(xuu50001, xuu4001, app(app(ty_Either, chf), chg)) → new_esEs6(xuu50001, xuu4001, chf, chg)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs12(xuu50000, xuu4000)
new_esEs20(xuu33000, xuu34000, app(ty_Maybe, eg)) → new_esEs4(xuu33000, xuu34000, eg)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(app(ty_@2, bg), bh)) → new_ltEs5(xuu33000, xuu34000, bg, bh)
new_compare25(xuu330, xuu340, True, beh) → EQ
new_ltEs20(xuu3300, xuu3400, app(ty_Maybe, bfa)) → new_ltEs8(xuu3300, xuu3400, bfa)
new_esEs8(xuu33000, xuu34000, ty_Double) → new_esEs12(xuu33000, xuu34000)
new_esEs20(xuu33000, xuu34000, ty_Bool) → new_esEs18(xuu33000, xuu34000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, ty_Double) → new_ltEs11(xuu33000, xuu34000)
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_ltEs6(xuu33001, xuu34001, app(ty_Ratio, bec)) → new_ltEs12(xuu33001, xuu34001, bec)
new_esEs24(xuu50000, xuu4000, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Maybe, cad)) → new_esEs4(xuu50000, xuu4000, cad)
new_ltEs19(xuu33002, xuu34002, ty_Bool) → new_ltEs18(xuu33002, xuu34002)
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_esEs20(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_lt4(xuu33000, xuu34000, app(ty_[], bdf)) → new_lt15(xuu33000, xuu34000, bdf)
new_compare30(xuu33000, xuu34000, app(ty_Ratio, dbg)) → new_compare14(xuu33000, xuu34000, dbg)
new_ltEs19(xuu33002, xuu34002, ty_@0) → new_ltEs13(xuu33002, xuu34002)
new_esEs20(xuu33000, xuu34000, app(ty_Ratio, beg)) → new_esEs13(xuu33000, xuu34000, beg)
new_esEs21(xuu50002, xuu4002, ty_Int) → new_esEs15(xuu50002, xuu4002)
new_compare0(:(xuu33000, xuu33001), :(xuu34000, xuu34001), ga) → new_primCompAux0(xuu33000, xuu34000, new_compare0(xuu33001, xuu34001, ga), ga)
new_lt19(xuu33001, xuu34001, ty_Int) → new_lt12(xuu33001, xuu34001)
new_esEs20(xuu33000, xuu34000, ty_Char) → new_esEs10(xuu33000, xuu34000)
new_esEs22(xuu50001, xuu4001, ty_Integer) → new_esEs9(xuu50001, xuu4001)
new_esEs21(xuu50002, xuu4002, app(app(ty_Either, bgb), bgc)) → new_esEs6(xuu50002, xuu4002, bgb, bgc)
new_compare30(xuu33000, xuu34000, app(app(app(ty_@3, gc), gd), ge)) → new_compare15(xuu33000, xuu34000, gc, gd, ge)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(ty_Maybe, hc), hd) → new_ltEs8(xuu33000, xuu34000, hc)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Ordering) → new_ltEs16(xuu33000, xuu34000)
new_esEs8(xuu33000, xuu34000, app(app(ty_Either, bdg), bdh)) → new_esEs6(xuu33000, xuu34000, bdg, bdh)
new_esEs19(xuu33001, xuu34001, app(app(app(ty_@3, dg), dh), ea)) → new_esEs5(xuu33001, xuu34001, dg, dh, ea)
new_esEs19(xuu33001, xuu34001, ty_@0) → new_esEs14(xuu33001, xuu34001)
new_esEs26(xuu50000, xuu4000, app(ty_Maybe, daf)) → new_esEs4(xuu50000, xuu4000, daf)
new_esEs19(xuu33001, xuu34001, ty_Ordering) → new_esEs16(xuu33001, xuu34001)
new_lt4(xuu33000, xuu34000, app(ty_Maybe, bda)) → new_lt6(xuu33000, xuu34000, bda)
new_esEs20(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Float, cda) → new_esEs11(xuu50000, xuu4000)
new_ltEs19(xuu33002, xuu34002, app(app(ty_Either, da), db)) → new_ltEs4(xuu33002, xuu34002, da, db)
new_pePe(False, xuu162) → xuu162
new_esEs25(xuu50001, xuu4001, app(app(ty_@2, chb), chc)) → new_esEs7(xuu50001, xuu4001, chb, chc)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Double, hd) → new_ltEs11(xuu33000, xuu34000)
new_ltEs14(xuu3300, xuu3400) → new_fsEs(new_compare7(xuu3300, xuu3400))
new_ltEs19(xuu33002, xuu34002, ty_Float) → new_ltEs10(xuu33002, xuu34002)
new_esEs15(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_ltEs20(xuu3300, xuu3400, app(app(ty_Either, bae), hd)) → new_ltEs4(xuu3300, xuu3400, bae, hd)
new_ltEs16(EQ, GT) → True
new_lt20(xuu33000, xuu34000, app(app(app(ty_@3, eh), fa), fb)) → new_lt13(xuu33000, xuu34000, eh, fa, fb)
new_esEs7(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), cgh, cha) → new_asAs(new_esEs26(xuu50000, xuu4000, cgh), new_esEs25(xuu50001, xuu4001, cha))
new_esEs8(xuu33000, xuu34000, ty_Char) → new_esEs10(xuu33000, xuu34000)
new_compare25(Just(xuu3300), Just(xuu3400), False, beh) → new_compare12(xuu3300, xuu3400, new_ltEs20(xuu3300, xuu3400, beh), beh)
new_ltEs20(xuu3300, xuu3400, app(app(app(ty_@3, ca), cb), df)) → new_ltEs15(xuu3300, xuu3400, ca, cb, df)
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, app(app(ty_Either, bbc), bbd)) → new_ltEs4(xuu33000, xuu34000, bbc, bbd)
new_lt4(xuu33000, xuu34000, ty_Float) → new_lt8(xuu33000, xuu34000)
new_ltEs4(Left(xuu33000), Right(xuu34000), bae, hd) → True
new_primCmpNat0(Zero, Succ(xuu3400)) → LT
new_esEs26(xuu50000, xuu4000, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_ltEs8(Nothing, Just(xuu34000), bfa) → True
new_esEs6(Right(xuu50000), Left(xuu4000), ceb, cda) → False
new_esEs6(Left(xuu50000), Right(xuu4000), ceb, cda) → False
new_lt6(xuu33000, xuu34000, eg) → new_esEs16(new_compare31(xuu33000, xuu34000, eg), LT)
new_esEs19(xuu33001, xuu34001, app(ty_[], eb)) → new_esEs17(xuu33001, xuu34001, eb)
new_esEs19(xuu33001, xuu34001, app(ty_Maybe, de)) → new_esEs4(xuu33001, xuu34001, de)
new_esEs21(xuu50002, xuu4002, app(ty_Ratio, bgd)) → new_esEs13(xuu50002, xuu4002, bgd)
new_compare27(xuu33000, xuu34000, False, eh, fa, fb) → new_compare110(xuu33000, xuu34000, new_ltEs15(xuu33000, xuu34000, eh, fa, fb), eh, fa, fb)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs11(xuu50000, xuu4000)
new_esEs25(xuu50001, xuu4001, app(ty_Ratio, chh)) → new_esEs13(xuu50001, xuu4001, chh)
new_ltEs6(xuu33001, xuu34001, ty_Double) → new_ltEs11(xuu33001, xuu34001)
new_compare0([], [], ga) → EQ
new_pePe(True, xuu162) → True
new_primEqNat0(Zero, Zero) → True
new_lt20(xuu33000, xuu34000, app(ty_Maybe, eg)) → new_lt6(xuu33000, xuu34000, eg)
new_compare26(xuu33000, xuu34000, True) → EQ
new_esEs19(xuu33001, xuu34001, app(ty_Ratio, bef)) → new_esEs13(xuu33001, xuu34001, bef)
new_ltEs6(xuu33001, xuu34001, ty_Ordering) → new_ltEs16(xuu33001, xuu34001)
new_ltEs6(xuu33001, xuu34001, app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs15(xuu33001, xuu34001, bca, bcb, bcc)
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), bfc, bfd, bfe) → new_asAs(new_esEs23(xuu50000, xuu4000, bfc), new_asAs(new_esEs22(xuu50001, xuu4001, bfd), new_esEs21(xuu50002, xuu4002, bfe)))
new_compare17(@0, @0) → EQ
new_esEs23(xuu50000, xuu4000, app(app(ty_Either, caf), cag)) → new_esEs6(xuu50000, xuu4000, caf, cag)
new_esEs14(@0, @0) → True
new_primMulNat0(Succ(xuu5000000), Succ(xuu400000)) → new_primPlusNat1(new_primMulNat0(xuu5000000, Succ(xuu400000)), xuu400000)
new_esEs17(:(xuu50000, xuu50001), :(xuu4000, xuu4001), cbd) → new_asAs(new_esEs24(xuu50000, xuu4000, cbd), new_esEs17(xuu50001, xuu4001, cbd))
new_lt12(xuu330, xuu340) → new_esEs16(new_compare7(xuu330, xuu340), LT)
new_compare30(xuu33000, xuu34000, ty_Int) → new_compare7(xuu33000, xuu34000)
new_esEs25(xuu50001, xuu4001, ty_Bool) → new_esEs18(xuu50001, xuu4001)
new_esEs23(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_esEs16(LT, GT) → False
new_esEs16(GT, LT) → False
new_compare32(xuu33000, xuu34000, fd, ff) → new_compare23(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, fd, ff), fd, ff)
new_esEs26(xuu50000, xuu4000, app(ty_Ratio, dbb)) → new_esEs13(xuu50000, xuu4000, dbb)
new_compare30(xuu33000, xuu34000, ty_Ordering) → new_compare8(xuu33000, xuu34000)
new_esEs22(xuu50001, xuu4001, app(app(ty_@2, bgh), bha)) → new_esEs7(xuu50001, xuu4001, bgh, bha)
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, app(app(ty_Either, ceg), ceh)) → new_esEs6(xuu50000, xuu4000, ceg, ceh)
new_esEs25(xuu50001, xuu4001, ty_Int) → new_esEs15(xuu50001, xuu4001)
new_esEs24(xuu50000, xuu4000, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_ltEs16(EQ, LT) → False
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Char, hd) → new_ltEs9(xuu33000, xuu34000)
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_compare12(xuu129, xuu130, False, dbh) → GT
new_ltEs16(GT, EQ) → False
new_sr(xuu50000, xuu4000) → new_primMulInt(xuu50000, xuu4000)
new_compare7(xuu33, xuu34) → new_primCmpInt(xuu33, xuu34)
new_esEs24(xuu50000, xuu4000, app(app(ty_@2, cbe), cbf)) → new_esEs7(xuu50000, xuu4000, cbe, cbf)
new_esEs20(xuu33000, xuu34000, ty_Integer) → new_esEs9(xuu33000, xuu34000)
new_lt20(xuu33000, xuu34000, ty_Ordering) → new_lt14(xuu33000, xuu34000)
new_esEs23(xuu50000, xuu4000, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_esEs26(xuu50000, xuu4000, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_ltEs19(xuu33002, xuu34002, app(app(app(ty_@3, cd), ce), cf)) → new_ltEs15(xuu33002, xuu34002, cd, ce, cf)
new_lt20(xuu33000, xuu34000, app(app(ty_Either, fd), ff)) → new_lt17(xuu33000, xuu34000, fd, ff)
new_ltEs20(xuu3300, xuu3400, ty_Int) → new_ltEs14(xuu3300, xuu3400)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Int, cda) → new_esEs15(xuu50000, xuu4000)
new_lt20(xuu33000, xuu34000, app(app(ty_@2, fg), fh)) → new_lt18(xuu33000, xuu34000, fg, fh)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_esEs24(xuu50000, xuu4000, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_ltEs12(xuu3300, xuu3400, bfb) → new_fsEs(new_compare14(xuu3300, xuu3400, bfb))
new_ltEs20(xuu3300, xuu3400, ty_Char) → new_ltEs9(xuu3300, xuu3400)
new_ltEs16(LT, EQ) → True
new_esEs23(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_esEs19(xuu33001, xuu34001, ty_Bool) → new_esEs18(xuu33001, xuu34001)
new_compare25(Just(xuu3300), Nothing, False, beh) → GT
new_compare13(xuu33000, xuu34000, False) → GT
new_esEs22(xuu50001, xuu4001, ty_Int) → new_esEs15(xuu50001, xuu4001)
new_compare25(Nothing, Nothing, False, beh) → LT
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Float, hd) → new_ltEs10(xuu33000, xuu34000)
new_esEs20(xuu33000, xuu34000, ty_Int) → new_esEs15(xuu33000, xuu34000)
new_ltEs18(True, True) → True
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Integer, cda) → new_esEs9(xuu50000, xuu4000)
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt8(xuu33000, xuu34000) → new_esEs16(new_compare16(xuu33000, xuu34000), LT)
new_esEs21(xuu50002, xuu4002, app(app(ty_@2, bff), bfg)) → new_esEs7(xuu50002, xuu4002, bff, bfg)
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, ty_Integer) → new_ltEs7(xuu33000, xuu34000)
new_lt4(xuu33000, xuu34000, app(ty_Ratio, bed)) → new_lt10(xuu33000, xuu34000, bed)
new_esEs8(xuu33000, xuu34000, app(ty_Ratio, bed)) → new_esEs13(xuu33000, xuu34000, bed)
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_ltEs4(Left(xuu33000), Left(xuu34000), app(app(ty_Either, baa), bab), hd) → new_ltEs4(xuu33000, xuu34000, baa, bab)
new_ltEs18(False, False) → True
new_lt4(xuu33000, xuu34000, app(app(app(ty_@3, bdc), bdd), bde)) → new_lt13(xuu33000, xuu34000, bdc, bdd, bde)
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, app(ty_[], cef)) → new_esEs17(xuu50000, xuu4000, cef)
new_ltEs19(xuu33002, xuu34002, ty_Int) → new_ltEs14(xuu33002, xuu34002)
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_esEs24(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_lt9(xuu33000, xuu34000) → new_esEs16(new_compare29(xuu33000, xuu34000), LT)
new_ltEs17(xuu3300, xuu3400, ga) → new_fsEs(new_compare0(xuu3300, xuu3400, ga))
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Char, cda) → new_esEs10(xuu50000, xuu4000)
new_compare14(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Int) → new_compare7(new_sr(xuu33000, xuu34001), new_sr(xuu34000, xuu33001))
new_esEs22(xuu50001, xuu4001, app(app(app(ty_@3, bhg), bhh), caa)) → new_esEs5(xuu50001, xuu4001, bhg, bhh, caa)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Integer) → new_ltEs7(xuu33000, xuu34000)
new_esEs21(xuu50002, xuu4002, ty_Ordering) → new_esEs16(xuu50002, xuu4002)
new_ltEs13(xuu3300, xuu3400) → new_fsEs(new_compare17(xuu3300, xuu3400))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs8(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_ltEs20(xuu3300, xuu3400, ty_Bool) → new_ltEs18(xuu3300, xuu3400)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_ltEs16(GT, LT) → False
new_ltEs20(xuu3300, xuu3400, app(app(ty_@2, bbg), bdb)) → new_ltEs5(xuu3300, xuu3400, bbg, bdb)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Bool, hd) → new_ltEs18(xuu33000, xuu34000)
new_primCmpNat0(Succ(xuu3300), Succ(xuu3400)) → new_primCmpNat0(xuu3300, xuu3400)
new_esEs9(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_esEs22(xuu50001, xuu4001, app(ty_Maybe, bhb)) → new_esEs4(xuu50001, xuu4001, bhb)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Int, hd) → new_ltEs14(xuu33000, xuu34000)
new_esEs25(xuu50001, xuu4001, app(ty_Maybe, chd)) → new_esEs4(xuu50001, xuu4001, chd)
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_compare10(xuu33000, xuu34000, False, fd, ff) → GT
new_lt18(xuu33000, xuu34000, fg, fh) → new_esEs16(new_compare33(xuu33000, xuu34000, fg, fh), LT)
new_esEs4(Just(xuu50000), Just(xuu4000), app(app(ty_Either, cgb), cgc)) → new_esEs6(xuu50000, xuu4000, cgb, cgc)
new_esEs6(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, cdg), cdh), cea), cda) → new_esEs5(xuu50000, xuu4000, cdg, cdh, cea)
new_lt13(xuu33000, xuu34000, eh, fa, fb) → new_esEs16(new_compare15(xuu33000, xuu34000, eh, fa, fb), LT)
new_lt10(xuu33000, xuu34000, beg) → new_esEs16(new_compare14(xuu33000, xuu34000, beg), LT)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Float) → new_ltEs10(xuu33000, xuu34000)
new_esEs19(xuu33001, xuu34001, app(app(ty_Either, ec), ed)) → new_esEs6(xuu33001, xuu34001, ec, ed)
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, app(ty_Maybe, cee)) → new_esEs4(xuu50000, xuu4000, cee)
new_esEs25(xuu50001, xuu4001, ty_Char) → new_esEs10(xuu50001, xuu4001)
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs20(xuu3300, xuu3400, app(ty_[], ga)) → new_ltEs17(xuu3300, xuu3400, ga)
new_esEs6(Left(xuu50000), Left(xuu4000), app(ty_[], cdc), cda) → new_esEs17(xuu50000, xuu4000, cdc)
new_ltEs9(xuu3300, xuu3400) → new_fsEs(new_compare9(xuu3300, xuu3400))
new_esEs4(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, cge), cgf), cgg)) → new_esEs5(xuu50000, xuu4000, cge, cgf, cgg)
new_compare30(xuu33000, xuu34000, ty_@0) → new_compare17(xuu33000, xuu34000)
new_esEs8(xuu33000, xuu34000, ty_Bool) → new_esEs18(xuu33000, xuu34000)
new_primCompAux00(xuu179, LT) → LT
new_primCmpInt(Neg(Succ(xuu3300)), Neg(xuu340)) → new_primCmpNat0(xuu340, Succ(xuu3300))
new_ltEs19(xuu33002, xuu34002, app(ty_[], cg)) → new_ltEs17(xuu33002, xuu34002, cg)
new_ltEs8(Just(xuu33000), Nothing, bfa) → False
new_ltEs6(xuu33001, xuu34001, app(ty_[], bcd)) → new_ltEs17(xuu33001, xuu34001, bcd)
new_esEs8(xuu33000, xuu34000, app(app(ty_@2, bea), beb)) → new_esEs7(xuu33000, xuu34000, bea, beb)
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_ltEs5(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bbg, bdb) → new_pePe(new_lt4(xuu33000, xuu34000, bbg), new_asAs(new_esEs8(xuu33000, xuu34000, bbg), new_ltEs6(xuu33001, xuu34001, bdb)))
new_primPlusNat0(Succ(xuu28200), Zero) → Succ(xuu28200)
new_primPlusNat0(Zero, Succ(xuu9700)) → Succ(xuu9700)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu3300), Zero) → GT
new_esEs19(xuu33001, xuu34001, ty_Integer) → new_esEs9(xuu33001, xuu34001)
new_esEs8(xuu33000, xuu34000, app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs5(xuu33000, xuu34000, bdc, bdd, bde)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3400))) → LT
new_esEs6(Left(xuu50000), Left(xuu4000), ty_@0, cda) → new_esEs14(xuu50000, xuu4000)
new_esEs22(xuu50001, xuu4001, ty_Bool) → new_esEs18(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(ty_Ratio, bhf)) → new_esEs13(xuu50001, xuu4001, bhf)
new_compare31(xuu33000, xuu34000, eg) → new_compare25(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, eg), eg)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs9(xuu50001, xuu4001)
new_sr0(Integer(xuu340000), Integer(xuu330010)) → Integer(new_primMulInt(xuu340000, xuu330010))
new_compare13(xuu33000, xuu34000, True) → LT
new_compare6(Integer(xuu33000), Integer(xuu34000)) → new_primCmpInt(xuu33000, xuu34000)
new_compare12(xuu129, xuu130, True, dbh) → LT
new_compare28(xuu33000, xuu34000, True, fg, fh) → EQ
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_lt19(xuu33001, xuu34001, app(ty_Maybe, de)) → new_lt6(xuu33001, xuu34001, de)
new_esEs24(xuu50000, xuu4000, app(ty_Ratio, ccc)) → new_esEs13(xuu50000, xuu4000, ccc)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Bool, cda) → new_esEs18(xuu50000, xuu4000)
new_esEs6(Left(xuu50000), Left(xuu4000), app(ty_Maybe, cdb), cda) → new_esEs4(xuu50000, xuu4000, cdb)
new_ltEs6(xuu33001, xuu34001, app(ty_Maybe, bbh)) → new_ltEs8(xuu33001, xuu34001, bbh)
new_esEs12(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs15(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_compare30(xuu33000, xuu34000, app(app(ty_Either, gg), gh)) → new_compare32(xuu33000, xuu34000, gg, gh)
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_esEs10(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_esEs26(xuu50000, xuu4000, app(ty_[], dag)) → new_esEs17(xuu50000, xuu4000, dag)
new_primCompAux00(xuu179, EQ) → xuu179
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3400))) → new_primCmpNat0(Zero, Succ(xuu3400))
new_compare30(xuu33000, xuu34000, app(ty_Maybe, gb)) → new_compare31(xuu33000, xuu34000, gb)
new_compare15(xuu33000, xuu34000, eh, fa, fb) → new_compare27(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, eh, fa, fb), eh, fa, fb)
new_compare24(xuu33000, xuu34000, True) → EQ
new_esEs25(xuu50001, xuu4001, ty_@0) → new_esEs14(xuu50001, xuu4001)
new_esEs23(xuu50000, xuu4000, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(ty_[], hh), hd) → new_ltEs17(xuu33000, xuu34000, hh)
new_ltEs16(EQ, EQ) → True
new_lt19(xuu33001, xuu34001, ty_@0) → new_lt11(xuu33001, xuu34001)
new_compare25(Nothing, Just(xuu3400), False, beh) → LT
new_esEs21(xuu50002, xuu4002, app(ty_[], bga)) → new_esEs17(xuu50002, xuu4002, bga)
new_esEs8(xuu33000, xuu34000, ty_Int) → new_esEs15(xuu33000, xuu34000)
new_esEs6(Left(xuu50000), Left(xuu4000), app(app(ty_@2, ccg), cch), cda) → new_esEs7(xuu50000, xuu4000, ccg, cch)
new_esEs23(xuu50000, xuu4000, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_not(False) → True
new_ltEs4(Right(xuu33000), Left(xuu34000), bae, hd) → False
new_esEs6(Left(xuu50000), Left(xuu4000), app(app(ty_Either, cdd), cde), cda) → new_esEs6(xuu50000, xuu4000, cdd, cde)
new_ltEs6(xuu33001, xuu34001, ty_Char) → new_ltEs9(xuu33001, xuu34001)
new_esEs23(xuu50000, xuu4000, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_primCmpInt(Pos(Succ(xuu3300)), Pos(xuu340)) → new_primCmpNat0(Succ(xuu3300), xuu340)
new_esEs19(xuu33001, xuu34001, app(app(ty_@2, ee), ef)) → new_esEs7(xuu33001, xuu34001, ee, ef)
new_esEs22(xuu50001, xuu4001, ty_Float) → new_esEs11(xuu50001, xuu4001)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Double) → new_ltEs11(xuu33000, xuu34000)
new_esEs24(xuu50000, xuu4000, app(app(ty_Either, cca), ccb)) → new_esEs6(xuu50000, xuu4000, cca, ccb)
new_esEs16(LT, EQ) → False
new_esEs16(EQ, LT) → False
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, ty_Ordering) → new_ltEs16(xuu33000, xuu34000)
new_esEs19(xuu33001, xuu34001, ty_Double) → new_esEs12(xuu33001, xuu34001)
new_compare14(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Integer) → new_compare6(new_sr0(xuu33000, xuu34001), new_sr0(xuu34000, xuu33001))
new_lt4(xuu33000, xuu34000, ty_Double) → new_lt9(xuu33000, xuu34000)
new_compare0(:(xuu33000, xuu33001), [], ga) → GT
new_lt19(xuu33001, xuu34001, app(app(ty_@2, ee), ef)) → new_lt18(xuu33001, xuu34001, ee, ef)
new_esEs24(xuu50000, xuu4000, app(ty_[], cbh)) → new_esEs17(xuu50000, xuu4000, cbh)
new_lt4(xuu33000, xuu34000, app(app(ty_Either, bdg), bdh)) → new_lt17(xuu33000, xuu34000, bdg, bdh)
new_lt20(xuu33000, xuu34000, ty_Double) → new_lt9(xuu33000, xuu34000)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs15(xuu50000, xuu4000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, ty_Float) → new_ltEs10(xuu33000, xuu34000)
new_esEs24(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_esEs20(xuu33000, xuu34000, app(app(app(ty_@3, eh), fa), fb)) → new_esEs5(xuu33000, xuu34000, eh, fa, fb)
new_primCmpInt(Pos(Succ(xuu3300)), Neg(xuu340)) → GT
new_esEs21(xuu50002, xuu4002, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs5(xuu50002, xuu4002, bge, bgf, bgg)
new_lt19(xuu33001, xuu34001, app(ty_[], eb)) → new_lt15(xuu33001, xuu34001, eb)
new_ltEs6(xuu33001, xuu34001, ty_Integer) → new_ltEs7(xuu33001, xuu34001)
new_primMulInt(Pos(xuu500000), Pos(xuu40000)) → Pos(new_primMulNat0(xuu500000, xuu40000))
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, app(ty_[], bbb)) → new_ltEs17(xuu33000, xuu34000, bbb)
new_ltEs6(xuu33001, xuu34001, app(app(ty_Either, bce), bcf)) → new_ltEs4(xuu33001, xuu34001, bce, bcf)
new_primMulInt(Neg(xuu500000), Neg(xuu40000)) → Pos(new_primMulNat0(xuu500000, xuu40000))
new_ltEs19(xuu33002, xuu34002, app(ty_Maybe, cc)) → new_ltEs8(xuu33002, xuu34002, cc)
new_esEs21(xuu50002, xuu4002, ty_Char) → new_esEs10(xuu50002, xuu4002)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Ordering, cda) → new_esEs16(xuu50000, xuu4000)
new_esEs16(EQ, EQ) → True
new_esEs26(xuu50000, xuu4000, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_primEqNat0(Succ(xuu500000), Zero) → False
new_compare8(xuu33000, xuu34000) → new_compare24(xuu33000, xuu34000, new_esEs16(xuu33000, xuu34000))
new_primPlusNat0(Zero, Zero) → Zero
new_esEs26(xuu50000, xuu4000, app(app(ty_@2, dad), dae)) → new_esEs7(xuu50000, xuu4000, dad, dae)
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare23(xuu33000, xuu34000, False, fd, ff) → new_compare10(xuu33000, xuu34000, new_ltEs4(xuu33000, xuu34000, fd, ff), fd, ff)
new_esEs4(Nothing, Nothing, cfe) → True
new_esEs4(Just(xuu50000), Just(xuu4000), app(ty_Ratio, cgd)) → new_esEs13(xuu50000, xuu4000, cgd)
new_esEs20(xuu33000, xuu34000, app(ty_[], fc)) → new_esEs17(xuu33000, xuu34000, fc)
new_esEs20(xuu33000, xuu34000, app(app(ty_Either, fd), ff)) → new_esEs6(xuu33000, xuu34000, fd, ff)
new_ltEs6(xuu33001, xuu34001, ty_Float) → new_ltEs10(xuu33001, xuu34001)
new_esEs22(xuu50001, xuu4001, app(ty_[], bhc)) → new_esEs17(xuu50001, xuu4001, bhc)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(app(ty_Either, be), bf)) → new_ltEs4(xuu33000, xuu34000, be, bf)
new_ltEs20(xuu3300, xuu3400, ty_Ordering) → new_ltEs16(xuu3300, xuu3400)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Int) → new_ltEs14(xuu33000, xuu34000)
new_ltEs19(xuu33002, xuu34002, ty_Char) → new_ltEs9(xuu33002, xuu34002)
new_ltEs15(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ca, cb, df) → new_pePe(new_lt20(xuu33000, xuu34000, ca), new_asAs(new_esEs20(xuu33000, xuu34000, ca), new_pePe(new_lt19(xuu33001, xuu34001, cb), new_asAs(new_esEs19(xuu33001, xuu34001, cb), new_ltEs19(xuu33002, xuu34002, df)))))
new_esEs8(xuu33000, xuu34000, ty_Ordering) → new_esEs16(xuu33000, xuu34000)
new_lt20(xuu33000, xuu34000, ty_Int) → new_lt12(xuu33000, xuu34000)
new_lt19(xuu33001, xuu34001, app(app(ty_Either, ec), ed)) → new_lt17(xuu33001, xuu34001, ec, ed)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3400))) → new_primCmpNat0(Succ(xuu3400), Zero)
new_compare23(xuu33000, xuu34000, True, fd, ff) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3400))) → GT
new_lt4(xuu33000, xuu34000, ty_@0) → new_lt11(xuu33000, xuu34000)
new_lt20(xuu33000, xuu34000, ty_Char) → new_lt7(xuu33000, xuu34000)
new_esEs6(Left(xuu50000), Left(xuu4000), app(ty_Ratio, cdf), cda) → new_esEs13(xuu50000, xuu4000, cdf)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(ty_Ratio, dcb), hd) → new_ltEs12(xuu33000, xuu34000, dcb)
new_esEs26(xuu50000, xuu4000, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs15(xuu33000, xuu34000, bag, bah, bba)
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_esEs19(xuu33001, xuu34001, ty_Float) → new_esEs11(xuu33001, xuu34001)
new_compare30(xuu33000, xuu34000, ty_Float) → new_compare16(xuu33000, xuu34000)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Integer, hd) → new_ltEs7(xuu33000, xuu34000)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(ty_[], bd)) → new_ltEs17(xuu33000, xuu34000, bd)
new_esEs21(xuu50002, xuu4002, app(ty_Maybe, bfh)) → new_esEs4(xuu50002, xuu4002, bfh)
new_compare18(xuu33000, xuu34000, True, fg, fh) → LT
new_ltEs6(xuu33001, xuu34001, app(app(ty_@2, bcg), bch)) → new_ltEs5(xuu33001, xuu34001, bcg, bch)
new_esEs25(xuu50001, xuu4001, ty_Ordering) → new_esEs16(xuu50001, xuu4001)
new_compare19(xuu33000, xuu34000) → new_compare26(xuu33000, xuu34000, new_esEs18(xuu33000, xuu34000))
new_lt19(xuu33001, xuu34001, ty_Double) → new_lt9(xuu33001, xuu34001)
new_compare26(xuu33000, xuu34000, False) → new_compare13(xuu33000, xuu34000, new_ltEs18(xuu33000, xuu34000))
new_lt17(xuu33000, xuu34000, fd, ff) → new_esEs16(new_compare32(xuu33000, xuu34000, fd, ff), LT)
new_esEs23(xuu50000, xuu4000, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_primCompAux0(xuu33000, xuu34000, xuu173, ga) → new_primCompAux00(xuu173, new_compare30(xuu33000, xuu34000, ga))
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt20(xuu33000, xuu34000, app(ty_[], fc)) → new_lt15(xuu33000, xuu34000, fc)
new_esEs21(xuu50002, xuu4002, ty_@0) → new_esEs14(xuu50002, xuu4002)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Double, cda) → new_esEs12(xuu50000, xuu4000)
new_compare29(Double(xuu33000, xuu33001), Double(xuu34000, xuu34001)) → new_compare7(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_lt4(xuu33000, xuu34000, ty_Bool) → new_lt16(xuu33000, xuu34000)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(ty_Maybe, h)) → new_ltEs8(xuu33000, xuu34000, h)
new_esEs21(xuu50002, xuu4002, ty_Bool) → new_esEs18(xuu50002, xuu4002)
new_compare30(xuu33000, xuu34000, app(ty_[], gf)) → new_compare0(xuu33000, xuu34000, gf)
new_esEs24(xuu50000, xuu4000, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, app(app(ty_@2, bbe), bbf)) → new_ltEs5(xuu33000, xuu34000, bbe, bbf)
new_compare33(xuu33000, xuu34000, fg, fh) → new_compare28(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, fg, fh), fg, fh)
new_esEs16(LT, LT) → True
new_ltEs4(Left(xuu33000), Left(xuu34000), app(app(app(ty_@3, he), hf), hg), hd) → new_ltEs15(xuu33000, xuu34000, he, hf, hg)
new_esEs13(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), dca) → new_asAs(new_esEs28(xuu50000, xuu4000, dca), new_esEs27(xuu50001, xuu4001, dca))
new_asAs(False, xuu136) → False
new_esEs22(xuu50001, xuu4001, ty_Double) → new_esEs12(xuu50001, xuu4001)
new_lt20(xuu33000, xuu34000, ty_Bool) → new_lt16(xuu33000, xuu34000)
new_esEs11(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs15(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_primMulInt(Neg(xuu500000), Pos(xuu40000)) → Neg(new_primMulNat0(xuu500000, xuu40000))
new_primMulInt(Pos(xuu500000), Neg(xuu40000)) → Neg(new_primMulNat0(xuu500000, xuu40000))
new_lt4(xuu33000, xuu34000, ty_Int) → new_lt12(xuu33000, xuu34000)
new_primMulNat0(Succ(xuu5000000), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu400000)) → Zero
new_esEs22(xuu50001, xuu4001, ty_Ordering) → new_esEs16(xuu50001, xuu4001)
new_ltEs20(xuu3300, xuu3400, ty_Integer) → new_ltEs7(xuu3300, xuu3400)
new_esEs16(GT, GT) → True
new_esEs4(Just(xuu50000), Just(xuu4000), app(ty_[], cga)) → new_esEs17(xuu50000, xuu4000, cga)
new_ltEs20(xuu3300, xuu3400, ty_Double) → new_ltEs11(xuu3300, xuu3400)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_@0, hd) → new_ltEs13(xuu33000, xuu34000)
new_compare28(xuu33000, xuu34000, False, fg, fh) → new_compare18(xuu33000, xuu34000, new_ltEs5(xuu33000, xuu34000, fg, fh), fg, fh)
new_esEs18(True, True) → True
new_esEs23(xuu50000, xuu4000, app(app(ty_@2, cab), cac)) → new_esEs7(xuu50000, xuu4000, cab, cac)
new_lt19(xuu33001, xuu34001, ty_Float) → new_lt8(xuu33001, xuu34001)
new_esEs24(xuu50000, xuu4000, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_lt20(xuu33000, xuu34000, ty_Float) → new_lt8(xuu33000, xuu34000)
new_compare110(xuu33000, xuu34000, True, eh, fa, fb) → LT
new_esEs22(xuu50001, xuu4001, ty_Char) → new_esEs10(xuu50001, xuu4001)
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, ty_@0) → new_ltEs13(xuu33000, xuu34000)
new_lt16(xuu33000, xuu34000) → new_esEs16(new_compare19(xuu33000, xuu34000), LT)
new_lt19(xuu33001, xuu34001, ty_Bool) → new_lt16(xuu33001, xuu34001)
new_esEs25(xuu50001, xuu4001, app(ty_[], che)) → new_esEs17(xuu50001, xuu4001, che)
new_esEs21(xuu50002, xuu4002, ty_Integer) → new_esEs9(xuu50002, xuu4002)
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_ltEs20(xuu3300, xuu3400, app(ty_Ratio, bfb)) → new_ltEs12(xuu3300, xuu3400, bfb)
new_esEs26(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_compare18(xuu33000, xuu34000, False, fg, fh) → GT
new_lt11(xuu33000, xuu34000) → new_esEs16(new_compare17(xuu33000, xuu34000), LT)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Char) → new_ltEs9(xuu33000, xuu34000)
new_lt19(xuu33001, xuu34001, app(app(app(ty_@3, dg), dh), ea)) → new_lt13(xuu33001, xuu34001, dg, dh, ea)
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, ty_Int) → new_ltEs14(xuu33000, xuu34000)
new_compare30(xuu33000, xuu34000, app(app(ty_@2, ha), hb)) → new_compare33(xuu33000, xuu34000, ha, hb)
new_lt15(xuu33000, xuu34000, fc) → new_esEs16(new_compare0(xuu33000, xuu34000, fc), LT)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_esEs24(xuu50000, xuu4000, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_ltEs18(True, False) → False
new_ltEs20(xuu3300, xuu3400, ty_Float) → new_ltEs10(xuu3300, xuu3400)
new_lt20(xuu33000, xuu34000, ty_Integer) → new_lt5(xuu33000, xuu34000)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs15(xuu50001, xuu4001)
new_compare11(xuu33000, xuu34000, False) → GT
new_esEs8(xuu33000, xuu34000, app(ty_Maybe, bda)) → new_esEs4(xuu33000, xuu34000, bda)
new_ltEs8(Nothing, Nothing, bfa) → True
new_compare11(xuu33000, xuu34000, True) → LT
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_@0) → new_ltEs13(xuu33000, xuu34000)
new_esEs22(xuu50001, xuu4001, ty_@0) → new_esEs14(xuu50001, xuu4001)
new_fsEs(xuu146) → new_not(new_esEs16(xuu146, GT))
new_esEs25(xuu50001, xuu4001, app(app(app(ty_@3, daa), dab), dac)) → new_esEs5(xuu50001, xuu4001, daa, dab, dac)
new_esEs26(xuu50000, xuu4000, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_esEs22(xuu50001, xuu4001, app(app(ty_Either, bhd), bhe)) → new_esEs6(xuu50001, xuu4001, bhd, bhe)
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, ty_Char) → new_ltEs9(xuu33000, xuu34000)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Ordering, hd) → new_ltEs16(xuu33000, xuu34000)
new_esEs21(xuu50002, xuu4002, ty_Double) → new_esEs12(xuu50002, xuu4002)
new_esEs18(False, True) → False
new_esEs18(True, False) → False
new_esEs4(Just(xuu50000), Just(xuu4000), app(app(ty_@2, cff), cfg)) → new_esEs7(xuu50000, xuu4000, cff, cfg)
new_esEs8(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, app(ty_Ratio, dcc)) → new_ltEs12(xuu33000, xuu34000, dcc)
new_ltEs11(xuu3300, xuu3400) → new_fsEs(new_compare29(xuu3300, xuu3400))
new_esEs21(xuu50002, xuu4002, ty_Float) → new_esEs11(xuu50002, xuu4002)
new_ltEs6(xuu33001, xuu34001, ty_Int) → new_ltEs14(xuu33001, xuu34001)
new_ltEs19(xuu33002, xuu34002, ty_Integer) → new_ltEs7(xuu33002, xuu34002)
new_esEs8(xuu33000, xuu34000, app(ty_[], bdf)) → new_esEs17(xuu33000, xuu34000, bdf)
new_compare30(xuu33000, xuu34000, ty_Bool) → new_compare19(xuu33000, xuu34000)
new_esEs23(xuu50000, xuu4000, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_esEs20(xuu33000, xuu34000, app(app(ty_@2, fg), fh)) → new_esEs7(xuu33000, xuu34000, fg, fh)
new_ltEs18(False, True) → True
new_primPlusNat0(Succ(xuu28200), Succ(xuu9700)) → Succ(Succ(new_primPlusNat0(xuu28200, xuu9700)))
new_esEs26(xuu50000, xuu4000, app(app(ty_Either, dah), dba)) → new_esEs6(xuu50000, xuu4000, dah, dba)
new_ltEs7(xuu3300, xuu3400) → new_fsEs(new_compare6(xuu3300, xuu3400))
new_ltEs4(Right(xuu33000), Right(xuu34000), bae, app(ty_Maybe, baf)) → new_ltEs8(xuu33000, xuu34000, baf)
new_compare0([], :(xuu34000, xuu34001), ga) → LT
new_asAs(True, xuu136) → xuu136
new_esEs26(xuu50000, xuu4000, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs5(xuu50000, xuu4000, dbc, dbd, dbe)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(app(ty_@2, bac), bad), hd) → new_ltEs5(xuu33000, xuu34000, bac, bad)
new_esEs25(xuu50001, xuu4001, ty_Float) → new_esEs11(xuu50001, xuu4001)
new_lt20(xuu33000, xuu34000, app(ty_Ratio, beg)) → new_lt10(xuu33000, xuu34000, beg)
new_ltEs16(LT, LT) → True
new_primPlusNat1(xuu107, xuu400000) → new_primPlusNat0(xuu107, Succ(xuu400000))
new_compare27(xuu33000, xuu34000, True, eh, fa, fb) → EQ
new_esEs19(xuu33001, xuu34001, ty_Char) → new_esEs10(xuu33001, xuu34001)
new_esEs17([], [], cbd) → True
new_esEs17([], :(xuu4000, xuu4001), cbd) → False
new_esEs17(:(xuu50000, xuu50001), [], cbd) → False
new_esEs19(xuu33001, xuu34001, ty_Int) → new_esEs15(xuu33001, xuu34001)
new_lt20(xuu33000, xuu34000, ty_@0) → new_lt11(xuu33000, xuu34000)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(ty_Ratio, dbf)) → new_ltEs12(xuu33000, xuu34000, dbf)
new_esEs23(xuu50000, xuu4000, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs5(xuu50000, xuu4000, cba, cbb, cbc)
new_esEs8(xuu33000, xuu34000, ty_Integer) → new_esEs9(xuu33000, xuu34000)
new_compare30(xuu33000, xuu34000, ty_Char) → new_compare9(xuu33000, xuu34000)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs10(xuu50000, xuu4000)
new_compare24(xuu33000, xuu34000, False) → new_compare11(xuu33000, xuu34000, new_ltEs16(xuu33000, xuu34000))
new_ltEs20(xuu3300, xuu3400, ty_@0) → new_ltEs13(xuu3300, xuu3400)
new_lt4(xuu33000, xuu34000, ty_Integer) → new_lt5(xuu33000, xuu34000)
new_esEs26(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_compare110(xuu33000, xuu34000, False, eh, fa, fb) → GT
new_compare30(xuu33000, xuu34000, ty_Integer) → new_compare6(xuu33000, xuu34000)
new_primCompAux00(xuu179, GT) → GT
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, app(ty_Ratio, cfa)) → new_esEs13(xuu50000, xuu4000, cfa)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(app(app(ty_@3, ba), bb), bc)) → new_ltEs15(xuu33000, xuu34000, ba, bb, bc)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_compare30(xuu33000, xuu34000, ty_Double) → new_compare29(xuu33000, xuu34000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs5(xuu50000, xuu4000, cfb, cfc, cfd)
new_ltEs6(xuu33001, xuu34001, ty_@0) → new_ltEs13(xuu33001, xuu34001)
new_lt7(xuu33000, xuu34000) → new_esEs16(new_compare9(xuu33000, xuu34000), LT)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs6(xuu33001, xuu34001, ty_Bool) → new_ltEs18(xuu33001, xuu34001)
new_esEs6(Right(xuu50000), Right(xuu4000), ceb, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_primCmpInt(Neg(Succ(xuu3300)), Pos(xuu340)) → LT
new_not(True) → False
new_esEs25(xuu50001, xuu4001, ty_Integer) → new_esEs9(xuu50001, xuu4001)
new_esEs18(False, False) → True

The set Q consists of the following terms:

new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_@0)
new_compare30(x0, x1, app(ty_[], x2))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_ltEs8(Nothing, Nothing, x0)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Just(x0), Nothing, x1)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs12(Double(x0, x1), Double(x2, x3))
new_compare12(x0, x1, False, x2)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs25(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Char)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_esEs23(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_compare25(Just(x0), Just(x1), False, x2)
new_ltEs12(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, False)
new_asAs(False, x0)
new_esEs21(x0, x1, ty_Integer)
new_esEs10(Char(x0), Char(x1))
new_primMulInt(Pos(x0), Pos(x1))
new_esEs26(x0, x1, ty_Char)
new_ltEs17(x0, x1, x2)
new_compare0([], :(x0, x1), x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs9(x0, x1)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt5(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs19(x0, x1, ty_Ordering)
new_esEs18(True, True)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Ordering)
new_esEs16(LT, GT)
new_esEs16(GT, LT)
new_compare28(x0, x1, True, x2, x3)
new_ltEs11(x0, x1)
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs6(x0, x1, ty_Bool)
new_compare17(@0, @0)
new_esEs26(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, ty_@0)
new_ltEs7(x0, x1)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, x2, x3, x4)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt17(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare11(x0, x1, True)
new_primPlusNat1(x0, x1)
new_esEs28(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs6(x0, x1, ty_Ordering)
new_esEs4(Nothing, Nothing, x0)
new_esEs8(x0, x1, ty_Char)
new_primEqNat0(Zero, Zero)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primCompAux0(x0, x1, x2, x3)
new_compare10(x0, x1, True, x2, x3)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs19(x0, x1, ty_Int)
new_compare26(x0, x1, True)
new_ltEs6(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs6(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_compare26(x0, x1, False)
new_ltEs20(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Int)
new_primMulNat0(Zero, Zero)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs24(x0, x1, ty_Char)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Int)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare25(Just(x0), Nothing, False, x1)
new_compare6(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_lt15(x0, x1, x2)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs27(x0, x1, ty_Integer)
new_compare8(x0, x1)
new_lt20(x0, x1, ty_Double)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs16(GT, GT)
new_lt7(x0, x1)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_sr(x0, x1)
new_esEs22(x0, x1, ty_Integer)
new_esEs14(@0, @0)
new_compare19(x0, x1)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(False, False)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_compare27(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, ty_@0)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare33(x0, x1, x2, x3)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Integer)
new_ltEs14(x0, x1)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_compare7(x0, x1)
new_compare23(x0, x1, False, x2, x3)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs21(x0, x1, ty_@0)
new_ltEs18(True, True)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat0(Zero, Zero)
new_compare11(x0, x1, False)
new_ltEs16(EQ, EQ)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_lt4(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, ty_Ordering)
new_compare24(x0, x1, True)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare25(Nothing, Just(x0), False, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Float)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs6(x0, x1, ty_Int)
new_pePe(False, x0)
new_esEs15(x0, x1)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs17(:(x0, x1), [], x2)
new_compare9(Char(x0), Char(x1))
new_lt18(x0, x1, x2, x3)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs23(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Double)
new_ltEs16(GT, LT)
new_ltEs16(LT, GT)
new_ltEs13(x0, x1)
new_lt14(x0, x1)
new_lt20(x0, x1, ty_@0)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_compare15(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, ty_Int)
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_pePe(True, x0)
new_primCompAux00(x0, LT)
new_ltEs18(False, False)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs8(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Float)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_Bool)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_lt11(x0, x1)
new_compare30(x0, x1, ty_Char)
new_primCompAux00(x0, EQ)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_lt4(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare0(:(x0, x1), [], x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt12(x0, x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1, False, x2, x3, x4)
new_lt20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs20(x0, x1, ty_Int)
new_compare18(x0, x1, True, x2, x3)
new_esEs16(LT, LT)
new_esEs26(x0, x1, ty_Bool)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs17([], [], x0)
new_esEs26(x0, x1, ty_Double)
new_ltEs8(Nothing, Just(x0), x1)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs16(GT, GT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Float)
new_compare30(x0, x1, ty_Ordering)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs8(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Char)
new_primPlusNat0(Zero, Succ(x0))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_compare18(x0, x1, False, x2, x3)
new_compare13(x0, x1, True)
new_compare30(x0, x1, ty_Bool)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs21(x0, x1, app(ty_[], x2))
new_compare12(x0, x1, True, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs20(x0, x1, ty_@0)
new_primCmpNat0(Zero, Zero)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Char)
new_compare23(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1)
new_esEs17([], :(x0, x1), x2)
new_ltEs8(Just(x0), Nothing, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, ty_@0)
new_primCmpNat0(Zero, Succ(x0))
new_fsEs(x0)
new_esEs8(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_lt4(x0, x1, ty_Int)
new_lt9(x0, x1)
new_esEs8(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs25(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_compare110(x0, x1, True, x2, x3, x4)
new_primEqNat0(Zero, Succ(x0))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_not(True)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs21(x0, x1, ty_Double)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_esEs16(EQ, LT)
new_esEs16(LT, EQ)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs16(EQ, EQ)
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(False, True)
new_ltEs18(True, False)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_asAs(True, x0)
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare25(x0, x1, True, x2)
new_lt4(x0, x1, ty_Double)
new_lt4(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_lt19(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs26(x0, x1, ty_@0)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Char)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare13(x0, x1, False)
new_ltEs20(x0, x1, ty_Float)
new_compare16(Float(x0, x1), Float(x2, x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt4(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Int)
new_esEs16(EQ, GT)
new_esEs16(GT, EQ)
new_esEs9(Integer(x0), Integer(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0([], [], x0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs10(x0, x1)
new_esEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare29(Double(x0, x1), Double(x2, x3))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Int)
new_primMulNat0(Zero, Succ(x0))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Double)
new_compare25(Nothing, Nothing, False, x0)
new_compare30(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, ty_Double)
new_compare10(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare28(x0, x1, False, x2, x3)
new_lt10(x0, x1, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_lt6(x0, x1, x2)
new_esEs19(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs20(x0, x1, ty_Bool)
new_compare30(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare31(x0, x1, x2)
new_esEs24(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt8(x0, x1)
new_primCmpNat0(Succ(x0), Zero)
new_compare30(x0, x1, ty_@0)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))

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_C11(xuu3, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu44, Just(xuu5000), xuu501, h, ba)
new_addToFM_C21(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, bb, bc) → new_addToFM_C(xuu16, xuu20, Just(xuu22), xuu23, bb, bc)
new_addToFM_C(xuu3, Branch(Nothing, xuu41, xuu42, xuu43, xuu44), Just(xuu5000), xuu501, h, ba) → new_addToFM_C20(xuu3, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs16(new_compare25(Just(xuu5000), Nothing, False, h), LT), h, ba)
new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, False, h, ba) → new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, new_esEs16(new_compare25(Nothing, Just(xuu400), False, h), GT), h, ba)
new_addToFM_C1(xuu3, xuu41, xuu42, xuu43, xuu44, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu44, Nothing, xuu501, h, ba)
new_addToFM_C(xuu3, Branch(Nothing, xuu41, xuu42, xuu43, xuu44), Nothing, xuu501, h, ba) → new_addToFM_C1(xuu3, xuu41, xuu42, xuu43, xuu44, xuu501, new_esEs16(new_compare25(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C20(xuu3, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu43, Just(xuu5000), xuu501, h, ba)
new_addToFM_C(xuu3, Branch(Just(xuu400), xuu41, xuu42, xuu43, xuu44), Nothing, xuu501, h, ba) → new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, new_esEs16(new_compare25(Nothing, Just(xuu400), False, h), LT), h, ba)
new_addToFM_C12(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, bb, bc) → new_addToFM_C(xuu16, xuu21, Just(xuu22), xuu23, bb, bc)
new_addToFM_C(xuu3, Branch(Just(xuu400), xuu41, xuu42, xuu43, xuu44), Just(xuu5000), xuu501, h, ba) → new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs16(new_compare25(Just(xuu5000), Just(xuu400), new_esEs29(xuu5000, xuu400, h), h), LT), h, ba)
new_addToFM_C21(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, False, bb, bc) → new_addToFM_C12(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, new_esEs16(new_compare25(Just(xuu22), Just(xuu17), new_esEs30(xuu22, xuu17, bb), bb), GT), bb, bc)
new_addToFM_C20(xuu3, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, False, h, ba) → new_addToFM_C11(xuu3, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs16(new_compare25(Just(xuu5000), Nothing, False, h), GT), h, ba)
new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu44, Nothing, xuu501, h, ba)
new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu43, Nothing, xuu501, h, ba)

The TRS R consists of the following rules:

new_esEs4(Just(xuu50000), Just(xuu4000), app(ty_Maybe, cbh)) → new_esEs4(xuu50000, xuu4000, cbh)
new_ltEs19(xuu33002, xuu34002, app(app(ty_@2, gb), gc)) → new_ltEs5(xuu33002, xuu34002, gb, gc)
new_lt19(xuu33001, xuu34001, ty_Char) → new_lt7(xuu33001, xuu34001)
new_esEs16(EQ, GT) → False
new_esEs16(GT, EQ) → False
new_ltEs19(xuu33002, xuu34002, ty_Ordering) → new_ltEs16(xuu33002, xuu34002)
new_lt19(xuu33001, xuu34001, app(ty_Ratio, ge)) → new_lt10(xuu33001, xuu34001, ge)
new_ltEs16(GT, GT) → True
new_esEs20(xuu33000, xuu34000, ty_Ordering) → new_esEs16(xuu33000, xuu34000)
new_lt5(xuu33000, xuu34000) → new_esEs16(new_compare6(xuu33000, xuu34000), LT)
new_compare9(Char(xuu33000), Char(xuu34000)) → new_primCmpNat0(xuu33000, xuu34000)
new_esEs26(xuu50000, xuu4000, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_esEs24(xuu50000, xuu4000, app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs5(xuu50000, xuu4000, bgd, bge, bgf)
new_ltEs10(xuu3300, xuu3400) → new_fsEs(new_compare16(xuu3300, xuu3400))
new_lt4(xuu33000, xuu34000, ty_Ordering) → new_lt14(xuu33000, xuu34000)
new_compare10(xuu33000, xuu34000, True, ed, ee) → LT
new_esEs4(Just(xuu50000), Nothing, cbe) → False
new_esEs4(Nothing, Just(xuu4000), cbe) → False
new_esEs24(xuu50000, xuu4000, app(ty_Maybe, bfg)) → new_esEs4(xuu50000, xuu4000, bfg)
new_lt19(xuu33001, xuu34001, ty_Integer) → new_lt5(xuu33001, xuu34001)
new_lt4(xuu33000, xuu34000, ty_Char) → new_lt7(xuu33000, xuu34000)
new_ltEs16(LT, GT) → True
new_lt14(xuu33000, xuu34000) → new_esEs16(new_compare8(xuu33000, xuu34000), LT)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs14(xuu50000, xuu4000)
new_lt4(xuu33000, xuu34000, app(app(ty_@2, eb), ec)) → new_lt18(xuu33000, xuu34000, eb, ec)
new_ltEs19(xuu33002, xuu34002, ty_Double) → new_ltEs11(xuu33002, xuu34002)
new_esEs20(xuu33000, xuu34000, ty_Double) → new_esEs12(xuu33000, xuu34000)
new_esEs29(xuu5000, xuu400, ty_Ordering) → new_esEs16(xuu5000, xuu400)
new_esEs23(xuu50000, xuu4000, app(ty_[], bee)) → new_esEs17(xuu50000, xuu4000, bee)
new_lt19(xuu33001, xuu34001, ty_Ordering) → new_lt14(xuu33001, xuu34001)
new_ltEs19(xuu33002, xuu34002, app(ty_Ratio, fb)) → new_ltEs12(xuu33002, xuu34002, fb)
new_primMulNat0(Zero, Zero) → Zero
new_esEs25(xuu50001, xuu4001, ty_Double) → new_esEs12(xuu50001, xuu4001)
new_compare16(Float(xuu33000, xuu33001), Float(xuu34000, xuu34001)) → new_compare7(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(app(ty_@2, cac), cad)) → new_esEs7(xuu50000, xuu4000, cac, cad)
new_esEs23(xuu50000, xuu4000, app(ty_Ratio, beh)) → new_esEs13(xuu50000, xuu4000, beh)
new_esEs25(xuu50001, xuu4001, app(app(ty_Either, cdf), cdg)) → new_esEs6(xuu50001, xuu4001, cdf, cdg)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs12(xuu50000, xuu4000)
new_esEs20(xuu33000, xuu34000, app(ty_Maybe, hf)) → new_esEs4(xuu33000, xuu34000, hf)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(app(ty_@2, cgf), cgg)) → new_ltEs5(xuu33000, xuu34000, cgf, cgg)
new_compare25(xuu330, xuu340, True, baf) → EQ
new_ltEs20(xuu3300, xuu3400, app(ty_Maybe, bag)) → new_ltEs8(xuu3300, xuu3400, bag)
new_esEs8(xuu33000, xuu34000, ty_Double) → new_esEs12(xuu33000, xuu34000)
new_esEs20(xuu33000, xuu34000, ty_Bool) → new_esEs18(xuu33000, xuu34000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Double) → new_ltEs11(xuu33000, xuu34000)
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_ltEs6(xuu33001, xuu34001, app(ty_Ratio, bh)) → new_ltEs12(xuu33001, xuu34001, bh)
new_esEs24(xuu50000, xuu4000, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Maybe, bed)) → new_esEs4(xuu50000, xuu4000, bed)
new_ltEs19(xuu33002, xuu34002, ty_Bool) → new_ltEs18(xuu33002, xuu34002)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_esEs20(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_lt4(xuu33000, xuu34000, app(ty_[], dg)) → new_lt15(xuu33000, xuu34000, dg)
new_compare30(xuu33000, xuu34000, app(ty_Ratio, cha)) → new_compare14(xuu33000, xuu34000, cha)
new_ltEs19(xuu33002, xuu34002, ty_@0) → new_ltEs13(xuu33002, xuu34002)
new_esEs20(xuu33000, xuu34000, app(ty_Ratio, hg)) → new_esEs13(xuu33000, xuu34000, hg)
new_esEs21(xuu50002, xuu4002, ty_Int) → new_esEs15(xuu50002, xuu4002)
new_compare0(:(xuu33000, xuu33001), :(xuu34000, xuu34001), bd) → new_primCompAux0(xuu33000, xuu34000, new_compare0(xuu33001, xuu34001, bd), bd)
new_lt19(xuu33001, xuu34001, ty_Int) → new_lt12(xuu33001, xuu34001)
new_esEs20(xuu33000, xuu34000, ty_Char) → new_esEs10(xuu33000, xuu34000)
new_esEs22(xuu50001, xuu4001, ty_Integer) → new_esEs9(xuu50001, xuu4001)
new_esEs21(xuu50002, xuu4002, app(app(ty_Either, bcb), bcc)) → new_esEs6(xuu50002, xuu4002, bcb, bcc)
new_compare30(xuu33000, xuu34000, app(app(app(ty_@3, chb), chc), chd)) → new_compare15(xuu33000, xuu34000, chb, chc, chd)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(ty_Maybe, dbf), bbb) → new_ltEs8(xuu33000, xuu34000, dbf)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Ordering) → new_ltEs16(xuu33000, xuu34000)
new_esEs8(xuu33000, xuu34000, app(app(ty_Either, dh), ea)) → new_esEs6(xuu33000, xuu34000, dh, ea)
new_esEs19(xuu33001, xuu34001, app(app(app(ty_@3, gf), gg), gh)) → new_esEs5(xuu33001, xuu34001, gf, gg, gh)
new_esEs19(xuu33001, xuu34001, ty_@0) → new_esEs14(xuu33001, xuu34001)
new_esEs26(xuu50000, xuu4000, app(ty_Maybe, cef)) → new_esEs4(xuu50000, xuu4000, cef)
new_esEs19(xuu33001, xuu34001, ty_Ordering) → new_esEs16(xuu33001, xuu34001)
new_lt4(xuu33000, xuu34000, app(ty_Maybe, db)) → new_lt6(xuu33000, xuu34000, db)
new_esEs20(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Float, bha) → new_esEs11(xuu50000, xuu4000)
new_ltEs19(xuu33002, xuu34002, app(app(ty_Either, fh), ga)) → new_ltEs4(xuu33002, xuu34002, fh, ga)
new_pePe(False, xuu162) → xuu162
new_esEs25(xuu50001, xuu4001, app(app(ty_@2, cdb), cdc)) → new_esEs7(xuu50001, xuu4001, cdb, cdc)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Double, bbb) → new_ltEs11(xuu33000, xuu34000)
new_ltEs14(xuu3300, xuu3400) → new_fsEs(new_compare7(xuu3300, xuu3400))
new_ltEs19(xuu33002, xuu34002, ty_Float) → new_ltEs10(xuu33002, xuu34002)
new_esEs15(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_ltEs20(xuu3300, xuu3400, app(app(ty_Either, bba), bbb)) → new_ltEs4(xuu3300, xuu3400, bba, bbb)
new_ltEs16(EQ, GT) → True
new_lt20(xuu33000, xuu34000, app(app(app(ty_@3, hh), baa), bab)) → new_lt13(xuu33000, xuu34000, hh, baa, bab)
new_esEs7(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), cch, cda) → new_asAs(new_esEs26(xuu50000, xuu4000, cch), new_esEs25(xuu50001, xuu4001, cda))
new_esEs8(xuu33000, xuu34000, ty_Char) → new_esEs10(xuu33000, xuu34000)
new_compare25(Just(xuu3300), Just(xuu3400), False, baf) → new_compare12(xuu3300, xuu3400, new_ltEs20(xuu3300, xuu3400, baf), baf)
new_ltEs20(xuu3300, xuu3400, app(app(app(ty_@3, ef), eg), eh)) → new_ltEs15(xuu3300, xuu3400, ef, eg, eh)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(app(ty_Either, ddf), ddg)) → new_ltEs4(xuu33000, xuu34000, ddf, ddg)
new_lt4(xuu33000, xuu34000, ty_Float) → new_lt8(xuu33000, xuu34000)
new_esEs29(xuu5000, xuu400, app(ty_Ratio, dac)) → new_esEs13(xuu5000, xuu400, dac)
new_ltEs4(Left(xuu33000), Right(xuu34000), bba, bbb) → True
new_primCmpNat0(Zero, Succ(xuu3400)) → LT
new_esEs26(xuu50000, xuu4000, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_ltEs8(Nothing, Just(xuu34000), bag) → True
new_esEs6(Right(xuu50000), Left(xuu4000), cab, bha) → False
new_esEs6(Left(xuu50000), Right(xuu4000), cab, bha) → False
new_lt6(xuu33000, xuu34000, hf) → new_esEs16(new_compare31(xuu33000, xuu34000, hf), LT)
new_esEs19(xuu33001, xuu34001, app(ty_[], ha)) → new_esEs17(xuu33001, xuu34001, ha)
new_esEs19(xuu33001, xuu34001, app(ty_Maybe, gd)) → new_esEs4(xuu33001, xuu34001, gd)
new_esEs21(xuu50002, xuu4002, app(ty_Ratio, bcd)) → new_esEs13(xuu50002, xuu4002, bcd)
new_compare27(xuu33000, xuu34000, False, hh, baa, bab) → new_compare110(xuu33000, xuu34000, new_ltEs15(xuu33000, xuu34000, hh, baa, bab), hh, baa, bab)
new_esEs29(xuu5000, xuu400, app(app(ty_@2, cch), cda)) → new_esEs7(xuu5000, xuu400, cch, cda)
new_esEs29(xuu5000, xuu400, ty_Char) → new_esEs10(xuu5000, xuu400)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs11(xuu50000, xuu4000)
new_esEs25(xuu50001, xuu4001, app(ty_Ratio, cdh)) → new_esEs13(xuu50001, xuu4001, cdh)
new_ltEs6(xuu33001, xuu34001, ty_Double) → new_ltEs11(xuu33001, xuu34001)
new_compare0([], [], bd) → EQ
new_pePe(True, xuu162) → True
new_primEqNat0(Zero, Zero) → True
new_lt20(xuu33000, xuu34000, app(ty_Maybe, hf)) → new_lt6(xuu33000, xuu34000, hf)
new_compare26(xuu33000, xuu34000, True) → EQ
new_esEs19(xuu33001, xuu34001, app(ty_Ratio, ge)) → new_esEs13(xuu33001, xuu34001, ge)
new_ltEs6(xuu33001, xuu34001, ty_Ordering) → new_ltEs16(xuu33001, xuu34001)
new_ltEs6(xuu33001, xuu34001, app(app(app(ty_@3, ca), cb), cc)) → new_ltEs15(xuu33001, xuu34001, ca, cb, cc)
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), bbc, bbd, bbe) → new_asAs(new_esEs23(xuu50000, xuu4000, bbc), new_asAs(new_esEs22(xuu50001, xuu4001, bbd), new_esEs21(xuu50002, xuu4002, bbe)))
new_compare17(@0, @0) → EQ
new_esEs23(xuu50000, xuu4000, app(app(ty_Either, bef), beg)) → new_esEs6(xuu50000, xuu4000, bef, beg)
new_esEs14(@0, @0) → True
new_primMulNat0(Succ(xuu5000000), Succ(xuu400000)) → new_primPlusNat1(new_primMulNat0(xuu5000000, Succ(xuu400000)), xuu400000)
new_esEs17(:(xuu50000, xuu50001), :(xuu4000, xuu4001), bfd) → new_asAs(new_esEs24(xuu50000, xuu4000, bfd), new_esEs17(xuu50001, xuu4001, bfd))
new_lt12(xuu330, xuu340) → new_esEs16(new_compare7(xuu330, xuu340), LT)
new_compare30(xuu33000, xuu34000, ty_Int) → new_compare7(xuu33000, xuu34000)
new_esEs25(xuu50001, xuu4001, ty_Bool) → new_esEs18(xuu50001, xuu4001)
new_esEs23(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_esEs16(LT, GT) → False
new_esEs16(GT, LT) → False
new_compare32(xuu33000, xuu34000, ed, ee) → new_compare23(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, ed, ee), ed, ee)
new_esEs26(xuu50000, xuu4000, app(ty_Ratio, cfb)) → new_esEs13(xuu50000, xuu4000, cfb)
new_compare30(xuu33000, xuu34000, ty_Ordering) → new_compare8(xuu33000, xuu34000)
new_esEs22(xuu50001, xuu4001, app(app(ty_@2, bch), bda)) → new_esEs7(xuu50001, xuu4001, bch, bda)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(app(ty_Either, cag), cah)) → new_esEs6(xuu50000, xuu4000, cag, cah)
new_esEs25(xuu50001, xuu4001, ty_Int) → new_esEs15(xuu50001, xuu4001)
new_esEs24(xuu50000, xuu4000, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_ltEs16(EQ, LT) → False
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Char, bbb) → new_ltEs9(xuu33000, xuu34000)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_compare12(xuu129, xuu130, False, dab) → GT
new_ltEs16(GT, EQ) → False
new_sr(xuu50000, xuu4000) → new_primMulInt(xuu50000, xuu4000)
new_compare7(xuu33, xuu34) → new_primCmpInt(xuu33, xuu34)
new_esEs24(xuu50000, xuu4000, app(app(ty_@2, bfe), bff)) → new_esEs7(xuu50000, xuu4000, bfe, bff)
new_esEs20(xuu33000, xuu34000, ty_Integer) → new_esEs9(xuu33000, xuu34000)
new_lt20(xuu33000, xuu34000, ty_Ordering) → new_lt14(xuu33000, xuu34000)
new_esEs23(xuu50000, xuu4000, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_esEs26(xuu50000, xuu4000, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_ltEs19(xuu33002, xuu34002, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs15(xuu33002, xuu34002, fc, fd, ff)
new_lt20(xuu33000, xuu34000, app(app(ty_Either, ed), ee)) → new_lt17(xuu33000, xuu34000, ed, ee)
new_ltEs20(xuu3300, xuu3400, ty_Int) → new_ltEs14(xuu3300, xuu3400)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Int, bha) → new_esEs15(xuu50000, xuu4000)
new_lt20(xuu33000, xuu34000, app(app(ty_@2, bad), bae)) → new_lt18(xuu33000, xuu34000, bad, bae)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_esEs24(xuu50000, xuu4000, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_ltEs12(xuu3300, xuu3400, bah) → new_fsEs(new_compare14(xuu3300, xuu3400, bah))
new_ltEs20(xuu3300, xuu3400, ty_Char) → new_ltEs9(xuu3300, xuu3400)
new_ltEs16(LT, EQ) → True
new_esEs23(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_esEs19(xuu33001, xuu34001, ty_Bool) → new_esEs18(xuu33001, xuu34001)
new_esEs30(xuu22, xuu17, app(ty_Maybe, daf)) → new_esEs4(xuu22, xuu17, daf)
new_compare25(Just(xuu3300), Nothing, False, baf) → GT
new_compare13(xuu33000, xuu34000, False) → GT
new_esEs22(xuu50001, xuu4001, ty_Int) → new_esEs15(xuu50001, xuu4001)
new_compare25(Nothing, Nothing, False, baf) → LT
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Float, bbb) → new_ltEs10(xuu33000, xuu34000)
new_esEs20(xuu33000, xuu34000, ty_Int) → new_esEs15(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, ty_Integer) → new_esEs9(xuu22, xuu17)
new_ltEs18(True, True) → True
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Integer, bha) → new_esEs9(xuu50000, xuu4000)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt8(xuu33000, xuu34000) → new_esEs16(new_compare16(xuu33000, xuu34000), LT)
new_esEs21(xuu50002, xuu4002, app(app(ty_@2, bbf), bbg)) → new_esEs7(xuu50002, xuu4002, bbf, bbg)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Integer) → new_ltEs7(xuu33000, xuu34000)
new_lt4(xuu33000, xuu34000, app(ty_Ratio, dc)) → new_lt10(xuu33000, xuu34000, dc)
new_esEs8(xuu33000, xuu34000, app(ty_Ratio, dc)) → new_esEs13(xuu33000, xuu34000, dc)
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_ltEs4(Left(xuu33000), Left(xuu34000), app(app(ty_Either, dcd), dce), bbb) → new_ltEs4(xuu33000, xuu34000, dcd, dce)
new_ltEs18(False, False) → True
new_lt4(xuu33000, xuu34000, app(app(app(ty_@3, dd), de), df)) → new_lt13(xuu33000, xuu34000, dd, de, df)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(ty_[], caf)) → new_esEs17(xuu50000, xuu4000, caf)
new_ltEs19(xuu33002, xuu34002, ty_Int) → new_ltEs14(xuu33002, xuu34002)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_esEs24(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_lt9(xuu33000, xuu34000) → new_esEs16(new_compare29(xuu33000, xuu34000), LT)
new_ltEs17(xuu3300, xuu3400, bd) → new_fsEs(new_compare0(xuu3300, xuu3400, bd))
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Char, bha) → new_esEs10(xuu50000, xuu4000)
new_compare14(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Int) → new_compare7(new_sr(xuu33000, xuu34001), new_sr(xuu34000, xuu33001))
new_esEs22(xuu50001, xuu4001, app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs5(xuu50001, xuu4001, bdg, bdh, bea)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Integer) → new_ltEs7(xuu33000, xuu34000)
new_esEs21(xuu50002, xuu4002, ty_Ordering) → new_esEs16(xuu50002, xuu4002)
new_ltEs13(xuu3300, xuu3400) → new_fsEs(new_compare17(xuu3300, xuu3400))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs8(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_ltEs20(xuu3300, xuu3400, ty_Bool) → new_ltEs18(xuu3300, xuu3400)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_ltEs16(GT, LT) → False
new_ltEs20(xuu3300, xuu3400, app(app(ty_@2, be), bf)) → new_ltEs5(xuu3300, xuu3400, be, bf)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Bool, bbb) → new_ltEs18(xuu33000, xuu34000)
new_primCmpNat0(Succ(xuu3300), Succ(xuu3400)) → new_primCmpNat0(xuu3300, xuu3400)
new_esEs9(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_esEs22(xuu50001, xuu4001, app(ty_Maybe, bdb)) → new_esEs4(xuu50001, xuu4001, bdb)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Int, bbb) → new_ltEs14(xuu33000, xuu34000)
new_esEs25(xuu50001, xuu4001, app(ty_Maybe, cdd)) → new_esEs4(xuu50001, xuu4001, cdd)
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_compare10(xuu33000, xuu34000, False, ed, ee) → GT
new_lt18(xuu33000, xuu34000, bad, bae) → new_esEs16(new_compare33(xuu33000, xuu34000, bad, bae), LT)
new_esEs4(Just(xuu50000), Just(xuu4000), app(app(ty_Either, ccb), ccc)) → new_esEs6(xuu50000, xuu4000, ccb, ccc)
new_esEs6(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, bhg), bhh), caa), bha) → new_esEs5(xuu50000, xuu4000, bhg, bhh, caa)
new_lt13(xuu33000, xuu34000, hh, baa, bab) → new_esEs16(new_compare15(xuu33000, xuu34000, hh, baa, bab), LT)
new_lt10(xuu33000, xuu34000, hg) → new_esEs16(new_compare14(xuu33000, xuu34000, hg), LT)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Float) → new_ltEs10(xuu33000, xuu34000)
new_esEs19(xuu33001, xuu34001, app(app(ty_Either, hb), hc)) → new_esEs6(xuu33001, xuu34001, hb, hc)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(ty_Maybe, cae)) → new_esEs4(xuu50000, xuu4000, cae)
new_esEs25(xuu50001, xuu4001, ty_Char) → new_esEs10(xuu50001, xuu4001)
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs20(xuu3300, xuu3400, app(ty_[], bd)) → new_ltEs17(xuu3300, xuu3400, bd)
new_esEs6(Left(xuu50000), Left(xuu4000), app(ty_[], bhc), bha) → new_esEs17(xuu50000, xuu4000, bhc)
new_ltEs9(xuu3300, xuu3400) → new_fsEs(new_compare9(xuu3300, xuu3400))
new_esEs4(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, cce), ccf), ccg)) → new_esEs5(xuu50000, xuu4000, cce, ccf, ccg)
new_compare30(xuu33000, xuu34000, ty_@0) → new_compare17(xuu33000, xuu34000)
new_esEs8(xuu33000, xuu34000, ty_Bool) → new_esEs18(xuu33000, xuu34000)
new_primCompAux00(xuu179, LT) → LT
new_primCmpInt(Neg(Succ(xuu3300)), Neg(xuu340)) → new_primCmpNat0(xuu340, Succ(xuu3300))
new_ltEs19(xuu33002, xuu34002, app(ty_[], fg)) → new_ltEs17(xuu33002, xuu34002, fg)
new_ltEs8(Just(xuu33000), Nothing, bag) → False
new_ltEs6(xuu33001, xuu34001, app(ty_[], cd)) → new_ltEs17(xuu33001, xuu34001, cd)
new_esEs8(xuu33000, xuu34000, app(app(ty_@2, eb), ec)) → new_esEs7(xuu33000, xuu34000, eb, ec)
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_ltEs5(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), be, bf) → new_pePe(new_lt4(xuu33000, xuu34000, be), new_asAs(new_esEs8(xuu33000, xuu34000, be), new_ltEs6(xuu33001, xuu34001, bf)))
new_primPlusNat0(Succ(xuu28200), Zero) → Succ(xuu28200)
new_primPlusNat0(Zero, Succ(xuu9700)) → Succ(xuu9700)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu3300), Zero) → GT
new_esEs19(xuu33001, xuu34001, ty_Integer) → new_esEs9(xuu33001, xuu34001)
new_esEs8(xuu33000, xuu34000, app(app(app(ty_@3, dd), de), df)) → new_esEs5(xuu33000, xuu34000, dd, de, df)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3400))) → LT
new_esEs6(Left(xuu50000), Left(xuu4000), ty_@0, bha) → new_esEs14(xuu50000, xuu4000)
new_esEs22(xuu50001, xuu4001, ty_Bool) → new_esEs18(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(ty_Ratio, bdf)) → new_esEs13(xuu50001, xuu4001, bdf)
new_compare31(xuu33000, xuu34000, hf) → new_compare25(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, hf), hf)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs9(xuu50001, xuu4001)
new_esEs30(xuu22, xuu17, ty_Bool) → new_esEs18(xuu22, xuu17)
new_sr0(Integer(xuu340000), Integer(xuu330010)) → Integer(new_primMulInt(xuu340000, xuu330010))
new_compare13(xuu33000, xuu34000, True) → LT
new_compare6(Integer(xuu33000), Integer(xuu34000)) → new_primCmpInt(xuu33000, xuu34000)
new_compare12(xuu129, xuu130, True, dab) → LT
new_compare28(xuu33000, xuu34000, True, bad, bae) → EQ
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_lt19(xuu33001, xuu34001, app(ty_Maybe, gd)) → new_lt6(xuu33001, xuu34001, gd)
new_esEs24(xuu50000, xuu4000, app(ty_Ratio, bgc)) → new_esEs13(xuu50000, xuu4000, bgc)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Bool, bha) → new_esEs18(xuu50000, xuu4000)
new_esEs6(Left(xuu50000), Left(xuu4000), app(ty_Maybe, bhb), bha) → new_esEs4(xuu50000, xuu4000, bhb)
new_ltEs6(xuu33001, xuu34001, app(ty_Maybe, bg)) → new_ltEs8(xuu33001, xuu34001, bg)
new_esEs29(xuu5000, xuu400, ty_@0) → new_esEs14(xuu5000, xuu400)
new_esEs12(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs15(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_compare30(xuu33000, xuu34000, app(app(ty_Either, chf), chg)) → new_compare32(xuu33000, xuu34000, chf, chg)
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_esEs10(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_esEs26(xuu50000, xuu4000, app(ty_[], ceg)) → new_esEs17(xuu50000, xuu4000, ceg)
new_primCompAux00(xuu179, EQ) → xuu179
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3400))) → new_primCmpNat0(Zero, Succ(xuu3400))
new_compare30(xuu33000, xuu34000, app(ty_Maybe, cgh)) → new_compare31(xuu33000, xuu34000, cgh)
new_compare15(xuu33000, xuu34000, hh, baa, bab) → new_compare27(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, hh, baa, bab), hh, baa, bab)
new_compare24(xuu33000, xuu34000, True) → EQ
new_esEs25(xuu50001, xuu4001, ty_@0) → new_esEs14(xuu50001, xuu4001)
new_esEs23(xuu50000, xuu4000, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(ty_[], dcc), bbb) → new_ltEs17(xuu33000, xuu34000, dcc)
new_ltEs16(EQ, EQ) → True
new_lt19(xuu33001, xuu34001, ty_@0) → new_lt11(xuu33001, xuu34001)
new_compare25(Nothing, Just(xuu3400), False, baf) → LT
new_esEs29(xuu5000, xuu400, ty_Double) → new_esEs12(xuu5000, xuu400)
new_esEs21(xuu50002, xuu4002, app(ty_[], bca)) → new_esEs17(xuu50002, xuu4002, bca)
new_esEs8(xuu33000, xuu34000, ty_Int) → new_esEs15(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, app(app(ty_Either, dah), dba)) → new_esEs6(xuu22, xuu17, dah, dba)
new_esEs6(Left(xuu50000), Left(xuu4000), app(app(ty_@2, bgg), bgh), bha) → new_esEs7(xuu50000, xuu4000, bgg, bgh)
new_esEs23(xuu50000, xuu4000, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_esEs30(xuu22, xuu17, ty_Int) → new_esEs15(xuu22, xuu17)
new_not(False) → True
new_ltEs4(Right(xuu33000), Left(xuu34000), bba, bbb) → False
new_esEs6(Left(xuu50000), Left(xuu4000), app(app(ty_Either, bhd), bhe), bha) → new_esEs6(xuu50000, xuu4000, bhd, bhe)
new_ltEs6(xuu33001, xuu34001, ty_Char) → new_ltEs9(xuu33001, xuu34001)
new_esEs30(xuu22, xuu17, ty_@0) → new_esEs14(xuu22, xuu17)
new_esEs23(xuu50000, xuu4000, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_esEs30(xuu22, xuu17, ty_Double) → new_esEs12(xuu22, xuu17)
new_primCmpInt(Pos(Succ(xuu3300)), Pos(xuu340)) → new_primCmpNat0(Succ(xuu3300), xuu340)
new_esEs19(xuu33001, xuu34001, app(app(ty_@2, hd), he)) → new_esEs7(xuu33001, xuu34001, hd, he)
new_esEs22(xuu50001, xuu4001, ty_Float) → new_esEs11(xuu50001, xuu4001)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Double) → new_ltEs11(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, app(app(ty_@2, dad), dae)) → new_esEs7(xuu22, xuu17, dad, dae)
new_esEs29(xuu5000, xuu400, app(ty_[], bfd)) → new_esEs17(xuu5000, xuu400, bfd)
new_esEs24(xuu50000, xuu4000, app(app(ty_Either, bga), bgb)) → new_esEs6(xuu50000, xuu4000, bga, bgb)
new_esEs16(LT, EQ) → False
new_esEs16(EQ, LT) → False
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Ordering) → new_ltEs16(xuu33000, xuu34000)
new_esEs19(xuu33001, xuu34001, ty_Double) → new_esEs12(xuu33001, xuu34001)
new_compare14(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Integer) → new_compare6(new_sr0(xuu33000, xuu34001), new_sr0(xuu34000, xuu33001))
new_lt4(xuu33000, xuu34000, ty_Double) → new_lt9(xuu33000, xuu34000)
new_compare0(:(xuu33000, xuu33001), [], bd) → GT
new_lt19(xuu33001, xuu34001, app(app(ty_@2, hd), he)) → new_lt18(xuu33001, xuu34001, hd, he)
new_esEs24(xuu50000, xuu4000, app(ty_[], bfh)) → new_esEs17(xuu50000, xuu4000, bfh)
new_esEs29(xuu5000, xuu400, ty_Int) → new_esEs15(xuu5000, xuu400)
new_lt4(xuu33000, xuu34000, app(app(ty_Either, dh), ea)) → new_lt17(xuu33000, xuu34000, dh, ea)
new_lt20(xuu33000, xuu34000, ty_Double) → new_lt9(xuu33000, xuu34000)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs15(xuu50000, xuu4000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Float) → new_ltEs10(xuu33000, xuu34000)
new_esEs24(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_esEs30(xuu22, xuu17, app(ty_[], dag)) → new_esEs17(xuu22, xuu17, dag)
new_esEs20(xuu33000, xuu34000, app(app(app(ty_@3, hh), baa), bab)) → new_esEs5(xuu33000, xuu34000, hh, baa, bab)
new_primCmpInt(Pos(Succ(xuu3300)), Neg(xuu340)) → GT
new_esEs21(xuu50002, xuu4002, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs5(xuu50002, xuu4002, bce, bcf, bcg)
new_esEs29(xuu5000, xuu400, ty_Integer) → new_esEs9(xuu5000, xuu400)
new_lt19(xuu33001, xuu34001, app(ty_[], ha)) → new_lt15(xuu33001, xuu34001, ha)
new_ltEs6(xuu33001, xuu34001, ty_Integer) → new_ltEs7(xuu33001, xuu34001)
new_primMulInt(Pos(xuu500000), Pos(xuu40000)) → Pos(new_primMulNat0(xuu500000, xuu40000))
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(ty_[], dde)) → new_ltEs17(xuu33000, xuu34000, dde)
new_ltEs6(xuu33001, xuu34001, app(app(ty_Either, ce), cf)) → new_ltEs4(xuu33001, xuu34001, ce, cf)
new_primMulInt(Neg(xuu500000), Neg(xuu40000)) → Pos(new_primMulNat0(xuu500000, xuu40000))
new_ltEs19(xuu33002, xuu34002, app(ty_Maybe, fa)) → new_ltEs8(xuu33002, xuu34002, fa)
new_esEs21(xuu50002, xuu4002, ty_Char) → new_esEs10(xuu50002, xuu4002)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Ordering, bha) → new_esEs16(xuu50000, xuu4000)
new_esEs16(EQ, EQ) → True
new_esEs26(xuu50000, xuu4000, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_primEqNat0(Succ(xuu500000), Zero) → False
new_compare8(xuu33000, xuu34000) → new_compare24(xuu33000, xuu34000, new_esEs16(xuu33000, xuu34000))
new_primPlusNat0(Zero, Zero) → Zero
new_esEs26(xuu50000, xuu4000, app(app(ty_@2, ced), cee)) → new_esEs7(xuu50000, xuu4000, ced, cee)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare23(xuu33000, xuu34000, False, ed, ee) → new_compare10(xuu33000, xuu34000, new_ltEs4(xuu33000, xuu34000, ed, ee), ed, ee)
new_esEs4(Nothing, Nothing, cbe) → True
new_esEs4(Just(xuu50000), Just(xuu4000), app(ty_Ratio, ccd)) → new_esEs13(xuu50000, xuu4000, ccd)
new_esEs20(xuu33000, xuu34000, app(ty_[], bac)) → new_esEs17(xuu33000, xuu34000, bac)
new_esEs20(xuu33000, xuu34000, app(app(ty_Either, ed), ee)) → new_esEs6(xuu33000, xuu34000, ed, ee)
new_ltEs6(xuu33001, xuu34001, ty_Float) → new_ltEs10(xuu33001, xuu34001)
new_esEs22(xuu50001, xuu4001, app(ty_[], bdc)) → new_esEs17(xuu50001, xuu4001, bdc)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(app(ty_Either, cgd), cge)) → new_ltEs4(xuu33000, xuu34000, cgd, cge)
new_esEs29(xuu5000, xuu400, app(app(ty_Either, cab), bha)) → new_esEs6(xuu5000, xuu400, cab, bha)
new_ltEs20(xuu3300, xuu3400, ty_Ordering) → new_ltEs16(xuu3300, xuu3400)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Int) → new_ltEs14(xuu33000, xuu34000)
new_ltEs19(xuu33002, xuu34002, ty_Char) → new_ltEs9(xuu33002, xuu34002)
new_ltEs15(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ef, eg, eh) → new_pePe(new_lt20(xuu33000, xuu34000, ef), new_asAs(new_esEs20(xuu33000, xuu34000, ef), new_pePe(new_lt19(xuu33001, xuu34001, eg), new_asAs(new_esEs19(xuu33001, xuu34001, eg), new_ltEs19(xuu33002, xuu34002, eh)))))
new_esEs8(xuu33000, xuu34000, ty_Ordering) → new_esEs16(xuu33000, xuu34000)
new_lt20(xuu33000, xuu34000, ty_Int) → new_lt12(xuu33000, xuu34000)
new_esEs29(xuu5000, xuu400, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs5(xuu5000, xuu400, bbc, bbd, bbe)
new_lt19(xuu33001, xuu34001, app(app(ty_Either, hb), hc)) → new_lt17(xuu33001, xuu34001, hb, hc)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3400))) → new_primCmpNat0(Succ(xuu3400), Zero)
new_compare23(xuu33000, xuu34000, True, ed, ee) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3400))) → GT
new_lt4(xuu33000, xuu34000, ty_@0) → new_lt11(xuu33000, xuu34000)
new_lt20(xuu33000, xuu34000, ty_Char) → new_lt7(xuu33000, xuu34000)
new_esEs6(Left(xuu50000), Left(xuu4000), app(ty_Ratio, bhf), bha) → new_esEs13(xuu50000, xuu4000, bhf)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(ty_Ratio, dbg), bbb) → new_ltEs12(xuu33000, xuu34000, dbg)
new_esEs26(xuu50000, xuu4000, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(app(app(ty_@3, ddb), ddc), ddd)) → new_ltEs15(xuu33000, xuu34000, ddb, ddc, ddd)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_esEs19(xuu33001, xuu34001, ty_Float) → new_esEs11(xuu33001, xuu34001)
new_compare30(xuu33000, xuu34000, ty_Float) → new_compare16(xuu33000, xuu34000)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Integer, bbb) → new_ltEs7(xuu33000, xuu34000)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(ty_[], cgc)) → new_ltEs17(xuu33000, xuu34000, cgc)
new_esEs21(xuu50002, xuu4002, app(ty_Maybe, bbh)) → new_esEs4(xuu50002, xuu4002, bbh)
new_compare18(xuu33000, xuu34000, True, bad, bae) → LT
new_ltEs6(xuu33001, xuu34001, app(app(ty_@2, cg), da)) → new_ltEs5(xuu33001, xuu34001, cg, da)
new_esEs25(xuu50001, xuu4001, ty_Ordering) → new_esEs16(xuu50001, xuu4001)
new_compare19(xuu33000, xuu34000) → new_compare26(xuu33000, xuu34000, new_esEs18(xuu33000, xuu34000))
new_lt19(xuu33001, xuu34001, ty_Double) → new_lt9(xuu33001, xuu34001)
new_compare26(xuu33000, xuu34000, False) → new_compare13(xuu33000, xuu34000, new_ltEs18(xuu33000, xuu34000))
new_lt17(xuu33000, xuu34000, ed, ee) → new_esEs16(new_compare32(xuu33000, xuu34000, ed, ee), LT)
new_esEs23(xuu50000, xuu4000, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_primCompAux0(xuu33000, xuu34000, xuu173, bd) → new_primCompAux00(xuu173, new_compare30(xuu33000, xuu34000, bd))
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt20(xuu33000, xuu34000, app(ty_[], bac)) → new_lt15(xuu33000, xuu34000, bac)
new_esEs21(xuu50002, xuu4002, ty_@0) → new_esEs14(xuu50002, xuu4002)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Double, bha) → new_esEs12(xuu50000, xuu4000)
new_compare29(Double(xuu33000, xuu33001), Double(xuu34000, xuu34001)) → new_compare7(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_lt4(xuu33000, xuu34000, ty_Bool) → new_lt16(xuu33000, xuu34000)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(ty_Maybe, cff)) → new_ltEs8(xuu33000, xuu34000, cff)
new_esEs21(xuu50002, xuu4002, ty_Bool) → new_esEs18(xuu50002, xuu4002)
new_compare30(xuu33000, xuu34000, app(ty_[], che)) → new_compare0(xuu33000, xuu34000, che)
new_esEs24(xuu50000, xuu4000, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_esEs30(xuu22, xuu17, ty_Ordering) → new_esEs16(xuu22, xuu17)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(app(ty_@2, ddh), dea)) → new_ltEs5(xuu33000, xuu34000, ddh, dea)
new_compare33(xuu33000, xuu34000, bad, bae) → new_compare28(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, bad, bae), bad, bae)
new_esEs16(LT, LT) → True
new_ltEs4(Left(xuu33000), Left(xuu34000), app(app(app(ty_@3, dbh), dca), dcb), bbb) → new_ltEs15(xuu33000, xuu34000, dbh, dca, dcb)
new_esEs13(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), dac) → new_asAs(new_esEs28(xuu50000, xuu4000, dac), new_esEs27(xuu50001, xuu4001, dac))
new_asAs(False, xuu136) → False
new_esEs22(xuu50001, xuu4001, ty_Double) → new_esEs12(xuu50001, xuu4001)
new_lt20(xuu33000, xuu34000, ty_Bool) → new_lt16(xuu33000, xuu34000)
new_esEs11(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs15(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_primMulInt(Neg(xuu500000), Pos(xuu40000)) → Neg(new_primMulNat0(xuu500000, xuu40000))
new_primMulInt(Pos(xuu500000), Neg(xuu40000)) → Neg(new_primMulNat0(xuu500000, xuu40000))
new_lt4(xuu33000, xuu34000, ty_Int) → new_lt12(xuu33000, xuu34000)
new_primMulNat0(Succ(xuu5000000), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu400000)) → Zero
new_esEs22(xuu50001, xuu4001, ty_Ordering) → new_esEs16(xuu50001, xuu4001)
new_ltEs20(xuu3300, xuu3400, ty_Integer) → new_ltEs7(xuu3300, xuu3400)
new_esEs16(GT, GT) → True
new_esEs29(xuu5000, xuu400, ty_Float) → new_esEs11(xuu5000, xuu400)
new_esEs4(Just(xuu50000), Just(xuu4000), app(ty_[], cca)) → new_esEs17(xuu50000, xuu4000, cca)
new_ltEs20(xuu3300, xuu3400, ty_Double) → new_ltEs11(xuu3300, xuu3400)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_@0, bbb) → new_ltEs13(xuu33000, xuu34000)
new_compare28(xuu33000, xuu34000, False, bad, bae) → new_compare18(xuu33000, xuu34000, new_ltEs5(xuu33000, xuu34000, bad, bae), bad, bae)
new_esEs18(True, True) → True
new_esEs23(xuu50000, xuu4000, app(app(ty_@2, beb), bec)) → new_esEs7(xuu50000, xuu4000, beb, bec)
new_esEs30(xuu22, xuu17, app(ty_Ratio, dbb)) → new_esEs13(xuu22, xuu17, dbb)
new_lt19(xuu33001, xuu34001, ty_Float) → new_lt8(xuu33001, xuu34001)
new_esEs24(xuu50000, xuu4000, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_lt20(xuu33000, xuu34000, ty_Float) → new_lt8(xuu33000, xuu34000)
new_compare110(xuu33000, xuu34000, True, hh, baa, bab) → LT
new_esEs22(xuu50001, xuu4001, ty_Char) → new_esEs10(xuu50001, xuu4001)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_@0) → new_ltEs13(xuu33000, xuu34000)
new_lt16(xuu33000, xuu34000) → new_esEs16(new_compare19(xuu33000, xuu34000), LT)
new_lt19(xuu33001, xuu34001, ty_Bool) → new_lt16(xuu33001, xuu34001)
new_esEs25(xuu50001, xuu4001, app(ty_[], cde)) → new_esEs17(xuu50001, xuu4001, cde)
new_esEs21(xuu50002, xuu4002, ty_Integer) → new_esEs9(xuu50002, xuu4002)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_ltEs20(xuu3300, xuu3400, app(ty_Ratio, bah)) → new_ltEs12(xuu3300, xuu3400, bah)
new_esEs26(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_compare18(xuu33000, xuu34000, False, bad, bae) → GT
new_lt11(xuu33000, xuu34000) → new_esEs16(new_compare17(xuu33000, xuu34000), LT)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Char) → new_ltEs9(xuu33000, xuu34000)
new_lt19(xuu33001, xuu34001, app(app(app(ty_@3, gf), gg), gh)) → new_lt13(xuu33001, xuu34001, gf, gg, gh)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Int) → new_ltEs14(xuu33000, xuu34000)
new_compare30(xuu33000, xuu34000, app(app(ty_@2, chh), daa)) → new_compare33(xuu33000, xuu34000, chh, daa)
new_lt15(xuu33000, xuu34000, bac) → new_esEs16(new_compare0(xuu33000, xuu34000, bac), LT)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_esEs24(xuu50000, xuu4000, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_ltEs18(True, False) → False
new_ltEs20(xuu3300, xuu3400, ty_Float) → new_ltEs10(xuu3300, xuu3400)
new_lt20(xuu33000, xuu34000, ty_Integer) → new_lt5(xuu33000, xuu34000)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs15(xuu50001, xuu4001)
new_compare11(xuu33000, xuu34000, False) → GT
new_esEs8(xuu33000, xuu34000, app(ty_Maybe, db)) → new_esEs4(xuu33000, xuu34000, db)
new_ltEs8(Nothing, Nothing, bag) → True
new_compare11(xuu33000, xuu34000, True) → LT
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_@0) → new_ltEs13(xuu33000, xuu34000)
new_esEs22(xuu50001, xuu4001, ty_@0) → new_esEs14(xuu50001, xuu4001)
new_fsEs(xuu146) → new_not(new_esEs16(xuu146, GT))
new_esEs25(xuu50001, xuu4001, app(app(app(ty_@3, cea), ceb), cec)) → new_esEs5(xuu50001, xuu4001, cea, ceb, cec)
new_esEs26(xuu50000, xuu4000, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_esEs22(xuu50001, xuu4001, app(app(ty_Either, bdd), bde)) → new_esEs6(xuu50001, xuu4001, bdd, bde)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Char) → new_ltEs9(xuu33000, xuu34000)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Ordering, bbb) → new_ltEs16(xuu33000, xuu34000)
new_esEs21(xuu50002, xuu4002, ty_Double) → new_esEs12(xuu50002, xuu4002)
new_esEs18(False, True) → False
new_esEs18(True, False) → False
new_esEs4(Just(xuu50000), Just(xuu4000), app(app(ty_@2, cbf), cbg)) → new_esEs7(xuu50000, xuu4000, cbf, cbg)
new_esEs29(xuu5000, xuu400, ty_Bool) → new_esEs18(xuu5000, xuu400)
new_esEs8(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, ty_Float) → new_esEs11(xuu22, xuu17)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(ty_Ratio, dda)) → new_ltEs12(xuu33000, xuu34000, dda)
new_ltEs11(xuu3300, xuu3400) → new_fsEs(new_compare29(xuu3300, xuu3400))
new_esEs21(xuu50002, xuu4002, ty_Float) → new_esEs11(xuu50002, xuu4002)
new_ltEs6(xuu33001, xuu34001, ty_Int) → new_ltEs14(xuu33001, xuu34001)
new_ltEs19(xuu33002, xuu34002, ty_Integer) → new_ltEs7(xuu33002, xuu34002)
new_esEs8(xuu33000, xuu34000, app(ty_[], dg)) → new_esEs17(xuu33000, xuu34000, dg)
new_compare30(xuu33000, xuu34000, ty_Bool) → new_compare19(xuu33000, xuu34000)
new_esEs23(xuu50000, xuu4000, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_esEs20(xuu33000, xuu34000, app(app(ty_@2, bad), bae)) → new_esEs7(xuu33000, xuu34000, bad, bae)
new_ltEs18(False, True) → True
new_primPlusNat0(Succ(xuu28200), Succ(xuu9700)) → Succ(Succ(new_primPlusNat0(xuu28200, xuu9700)))
new_esEs26(xuu50000, xuu4000, app(app(ty_Either, ceh), cfa)) → new_esEs6(xuu50000, xuu4000, ceh, cfa)
new_ltEs7(xuu3300, xuu3400) → new_fsEs(new_compare6(xuu3300, xuu3400))
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(ty_Maybe, dch)) → new_ltEs8(xuu33000, xuu34000, dch)
new_compare0([], :(xuu34000, xuu34001), bd) → LT
new_asAs(True, xuu136) → xuu136
new_esEs26(xuu50000, xuu4000, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs5(xuu50000, xuu4000, cfc, cfd, cfe)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(app(ty_@2, dcf), dcg), bbb) → new_ltEs5(xuu33000, xuu34000, dcf, dcg)
new_esEs25(xuu50001, xuu4001, ty_Float) → new_esEs11(xuu50001, xuu4001)
new_lt20(xuu33000, xuu34000, app(ty_Ratio, hg)) → new_lt10(xuu33000, xuu34000, hg)
new_ltEs16(LT, LT) → True
new_primPlusNat1(xuu107, xuu400000) → new_primPlusNat0(xuu107, Succ(xuu400000))
new_compare27(xuu33000, xuu34000, True, hh, baa, bab) → EQ
new_esEs30(xuu22, xuu17, ty_Char) → new_esEs10(xuu22, xuu17)
new_esEs19(xuu33001, xuu34001, ty_Char) → new_esEs10(xuu33001, xuu34001)
new_esEs17([], [], bfd) → True
new_esEs17([], :(xuu4000, xuu4001), bfd) → False
new_esEs17(:(xuu50000, xuu50001), [], bfd) → False
new_esEs19(xuu33001, xuu34001, ty_Int) → new_esEs15(xuu33001, xuu34001)
new_lt20(xuu33000, xuu34000, ty_@0) → new_lt11(xuu33000, xuu34000)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(ty_Ratio, cfg)) → new_ltEs12(xuu33000, xuu34000, cfg)
new_esEs23(xuu50000, xuu4000, app(app(app(ty_@3, bfa), bfb), bfc)) → new_esEs5(xuu50000, xuu4000, bfa, bfb, bfc)
new_esEs8(xuu33000, xuu34000, ty_Integer) → new_esEs9(xuu33000, xuu34000)
new_compare30(xuu33000, xuu34000, ty_Char) → new_compare9(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs5(xuu22, xuu17, dbc, dbd, dbe)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs10(xuu50000, xuu4000)
new_esEs29(xuu5000, xuu400, app(ty_Maybe, cbe)) → new_esEs4(xuu5000, xuu400, cbe)
new_compare24(xuu33000, xuu34000, False) → new_compare11(xuu33000, xuu34000, new_ltEs16(xuu33000, xuu34000))
new_ltEs20(xuu3300, xuu3400, ty_@0) → new_ltEs13(xuu3300, xuu3400)
new_lt4(xuu33000, xuu34000, ty_Integer) → new_lt5(xuu33000, xuu34000)
new_esEs26(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_compare110(xuu33000, xuu34000, False, hh, baa, bab) → GT
new_compare30(xuu33000, xuu34000, ty_Integer) → new_compare6(xuu33000, xuu34000)
new_primCompAux00(xuu179, GT) → GT
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(ty_Ratio, cba)) → new_esEs13(xuu50000, xuu4000, cba)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs15(xuu33000, xuu34000, cfh, cga, cgb)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_compare30(xuu33000, xuu34000, ty_Double) → new_compare29(xuu33000, xuu34000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(app(app(ty_@3, cbb), cbc), cbd)) → new_esEs5(xuu50000, xuu4000, cbb, cbc, cbd)
new_ltEs6(xuu33001, xuu34001, ty_@0) → new_ltEs13(xuu33001, xuu34001)
new_lt7(xuu33000, xuu34000) → new_esEs16(new_compare9(xuu33000, xuu34000), LT)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs6(xuu33001, xuu34001, ty_Bool) → new_ltEs18(xuu33001, xuu34001)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_primCmpInt(Neg(Succ(xuu3300)), Pos(xuu340)) → LT
new_not(True) → False
new_esEs25(xuu50001, xuu4001, ty_Integer) → new_esEs9(xuu50001, xuu4001)
new_esEs18(False, False) → True

The set Q consists of the following terms:

new_primPlusNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare12(x0, x1, True, x2)
new_esEs28(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs12(Double(x0, x1), Double(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs4(Nothing, Just(x0), x1)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(x0, x1, ty_Double)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare10(x0, x1, True, x2, x3)
new_esEs26(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, True, x2)
new_esEs23(x0, x1, ty_Integer)
new_compare25(Just(x0), Nothing, False, x1)
new_ltEs19(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare24(x0, x1, False)
new_asAs(False, x0)
new_esEs21(x0, x1, ty_Integer)
new_esEs17(:(x0, x1), [], x2)
new_compare15(x0, x1, x2, x3, x4)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs10(Char(x0), Char(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs26(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs9(x0, x1)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_lt15(x0, x1, x2)
new_esEs23(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17([], [], x0)
new_lt5(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs18(True, True)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Ordering)
new_esEs16(LT, GT)
new_esEs16(GT, LT)
new_ltEs11(x0, x1)
new_ltEs6(x0, x1, ty_Bool)
new_compare17(@0, @0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_lt4(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_ltEs7(x0, x1)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_primPlusNat1(x0, x1)
new_esEs28(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Double)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Integer)
new_ltEs6(x0, x1, ty_Ordering)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs8(x0, x1, ty_Char)
new_compare10(x0, x1, False, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primEqNat0(Zero, Zero)
new_lt6(x0, x1, x2)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare12(x0, x1, False, x2)
new_esEs19(x0, x1, ty_Int)
new_compare26(x0, x1, True)
new_ltEs6(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs6(x0, x1, ty_Integer)
new_compare26(x0, x1, False)
new_ltEs20(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_primMulNat0(Zero, Zero)
new_ltEs12(x0, x1, x2)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs24(x0, x1, ty_Char)
new_lt17(x0, x1, x2, x3)
new_esEs19(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Int)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare6(Integer(x0), Integer(x1))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare8(x0, x1)
new_lt20(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs16(GT, GT)
new_compare23(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_sr(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs14(@0, @0)
new_compare19(x0, x1)
new_compare23(x0, x1, True, x2, x3)
new_compare18(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt4(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(x0, x1, x2)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, ty_Double)
new_esEs18(False, False)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_@0)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, GT)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Integer)
new_ltEs14(x0, x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare7(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare25(Just(x0), Just(x1), False, x2)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_@0)
new_ltEs18(True, True)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_primPlusNat0(Zero, Zero)
new_compare11(x0, x1, False)
new_ltEs16(EQ, EQ)
new_esEs19(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_lt4(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Ordering)
new_compare24(x0, x1, True)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(False, x0)
new_esEs15(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs30(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_compare9(Char(x0), Char(x1))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Double)
new_ltEs16(LT, GT)
new_ltEs16(GT, LT)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(x0, x1)
new_lt14(x0, x1)
new_lt20(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt13(x0, x1, x2, x3, x4)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_pePe(True, x0)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs8(Nothing, Nothing, x0)
new_primCompAux00(x0, LT)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare28(x0, x1, False, x2, x3)
new_ltEs18(False, False)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_lt11(x0, x1)
new_compare30(x0, x1, ty_Char)
new_primCompAux00(x0, EQ)
new_esEs24(x0, x1, ty_Double)
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs17([], :(x0, x1), x2)
new_compare30(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt12(x0, x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(Nothing, Nothing, False, x0)
new_esEs20(x0, x1, ty_Int)
new_esEs16(LT, LT)
new_esEs26(x0, x1, ty_Bool)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2, x3)
new_esEs22(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, ty_Double)
new_ltEs16(GT, GT)
new_esEs24(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Float)
new_compare30(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs6(x0, x1, ty_Char)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Zero, Succ(x0))
new_ltEs8(Nothing, Just(x0), x1)
new_compare13(x0, x1, True)
new_compare30(x0, x1, ty_Bool)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare27(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(Just(x0), Nothing, x1)
new_esEs20(x0, x1, ty_@0)
new_primCmpNat0(Zero, Zero)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt16(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_@0)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_fsEs(x0)
new_esEs8(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1)
new_esEs8(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs29(x0, x1, ty_Ordering)
new_compare110(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1, app(ty_[], x2))
new_esEs4(Nothing, Nothing, x0)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare18(x0, x1, False, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_compare33(x0, x1, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, ty_Double)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Bool)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_not(True)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Double)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_esEs16(EQ, LT)
new_esEs16(LT, EQ)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs16(EQ, EQ)
new_esEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_not(False)
new_compare31(x0, x1, x2)
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs18(False, True)
new_ltEs18(True, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_asAs(True, x0)
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Double)
new_lt4(x0, x1, ty_Char)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare25(Nothing, Just(x0), False, x1)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Char)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs11(Float(x0, x1), Float(x2, x3))
new_esEs25(x0, x1, ty_Char)
new_compare13(x0, x1, False)
new_ltEs20(x0, x1, ty_Float)
new_compare16(Float(x0, x1), Float(x2, x3))
new_lt4(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Int)
new_esEs16(EQ, GT)
new_esEs16(GT, EQ)
new_esEs9(Integer(x0), Integer(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs10(x0, x1)
new_esEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_compare29(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_primMulNat0(Zero, Succ(x0))
new_esEs23(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_compare27(x0, x1, False, x2, x3, x4)
new_compare30(x0, x1, ty_Double)
new_compare0([], [], x0)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare32(x0, x1, x2, x3)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Nothing, x1)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs19(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_compare0([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare30(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Bool)
new_esEs19(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_compare30(x0, x1, ty_@0)
new_esEs30(x0, x1, app(ty_Ratio, x2))

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_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, False, h, ba) → new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, new_esEs16(new_compare25(Nothing, Just(xuu400), False, h), GT), h, ba)
new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu44, Nothing, xuu501, h, ba)
new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu43, Nothing, xuu501, h, ba)
new_addToFM_C1(xuu3, xuu41, xuu42, xuu43, xuu44, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu44, Nothing, xuu501, h, ba)
new_addToFM_C(xuu3, Branch(Nothing, xuu41, xuu42, xuu43, xuu44), Nothing, xuu501, h, ba) → new_addToFM_C1(xuu3, xuu41, xuu42, xuu43, xuu44, xuu501, new_esEs16(new_compare25(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C(xuu3, Branch(Just(xuu400), xuu41, xuu42, xuu43, xuu44), Nothing, xuu501, h, ba) → new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, new_esEs16(new_compare25(Nothing, Just(xuu400), False, h), LT), h, ba)

The TRS R consists of the following rules:

new_esEs4(Just(xuu50000), Just(xuu4000), app(ty_Maybe, cbh)) → new_esEs4(xuu50000, xuu4000, cbh)
new_ltEs19(xuu33002, xuu34002, app(app(ty_@2, gb), gc)) → new_ltEs5(xuu33002, xuu34002, gb, gc)
new_lt19(xuu33001, xuu34001, ty_Char) → new_lt7(xuu33001, xuu34001)
new_esEs16(EQ, GT) → False
new_esEs16(GT, EQ) → False
new_ltEs19(xuu33002, xuu34002, ty_Ordering) → new_ltEs16(xuu33002, xuu34002)
new_lt19(xuu33001, xuu34001, app(ty_Ratio, ge)) → new_lt10(xuu33001, xuu34001, ge)
new_ltEs16(GT, GT) → True
new_esEs20(xuu33000, xuu34000, ty_Ordering) → new_esEs16(xuu33000, xuu34000)
new_lt5(xuu33000, xuu34000) → new_esEs16(new_compare6(xuu33000, xuu34000), LT)
new_compare9(Char(xuu33000), Char(xuu34000)) → new_primCmpNat0(xuu33000, xuu34000)
new_esEs26(xuu50000, xuu4000, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_esEs24(xuu50000, xuu4000, app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs5(xuu50000, xuu4000, bgd, bge, bgf)
new_ltEs10(xuu3300, xuu3400) → new_fsEs(new_compare16(xuu3300, xuu3400))
new_lt4(xuu33000, xuu34000, ty_Ordering) → new_lt14(xuu33000, xuu34000)
new_compare10(xuu33000, xuu34000, True, ed, ee) → LT
new_esEs4(Just(xuu50000), Nothing, cbe) → False
new_esEs4(Nothing, Just(xuu4000), cbe) → False
new_esEs24(xuu50000, xuu4000, app(ty_Maybe, bfg)) → new_esEs4(xuu50000, xuu4000, bfg)
new_lt19(xuu33001, xuu34001, ty_Integer) → new_lt5(xuu33001, xuu34001)
new_lt4(xuu33000, xuu34000, ty_Char) → new_lt7(xuu33000, xuu34000)
new_ltEs16(LT, GT) → True
new_lt14(xuu33000, xuu34000) → new_esEs16(new_compare8(xuu33000, xuu34000), LT)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs14(xuu50000, xuu4000)
new_lt4(xuu33000, xuu34000, app(app(ty_@2, eb), ec)) → new_lt18(xuu33000, xuu34000, eb, ec)
new_ltEs19(xuu33002, xuu34002, ty_Double) → new_ltEs11(xuu33002, xuu34002)
new_esEs20(xuu33000, xuu34000, ty_Double) → new_esEs12(xuu33000, xuu34000)
new_esEs29(xuu5000, xuu400, ty_Ordering) → new_esEs16(xuu5000, xuu400)
new_esEs23(xuu50000, xuu4000, app(ty_[], bee)) → new_esEs17(xuu50000, xuu4000, bee)
new_lt19(xuu33001, xuu34001, ty_Ordering) → new_lt14(xuu33001, xuu34001)
new_ltEs19(xuu33002, xuu34002, app(ty_Ratio, fb)) → new_ltEs12(xuu33002, xuu34002, fb)
new_primMulNat0(Zero, Zero) → Zero
new_esEs25(xuu50001, xuu4001, ty_Double) → new_esEs12(xuu50001, xuu4001)
new_compare16(Float(xuu33000, xuu33001), Float(xuu34000, xuu34001)) → new_compare7(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(app(ty_@2, cac), cad)) → new_esEs7(xuu50000, xuu4000, cac, cad)
new_esEs23(xuu50000, xuu4000, app(ty_Ratio, beh)) → new_esEs13(xuu50000, xuu4000, beh)
new_esEs25(xuu50001, xuu4001, app(app(ty_Either, cdf), cdg)) → new_esEs6(xuu50001, xuu4001, cdf, cdg)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs12(xuu50000, xuu4000)
new_esEs20(xuu33000, xuu34000, app(ty_Maybe, hf)) → new_esEs4(xuu33000, xuu34000, hf)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(app(ty_@2, cgf), cgg)) → new_ltEs5(xuu33000, xuu34000, cgf, cgg)
new_compare25(xuu330, xuu340, True, baf) → EQ
new_ltEs20(xuu3300, xuu3400, app(ty_Maybe, bag)) → new_ltEs8(xuu3300, xuu3400, bag)
new_esEs8(xuu33000, xuu34000, ty_Double) → new_esEs12(xuu33000, xuu34000)
new_esEs20(xuu33000, xuu34000, ty_Bool) → new_esEs18(xuu33000, xuu34000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Double) → new_ltEs11(xuu33000, xuu34000)
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_ltEs6(xuu33001, xuu34001, app(ty_Ratio, bh)) → new_ltEs12(xuu33001, xuu34001, bh)
new_esEs24(xuu50000, xuu4000, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Maybe, bed)) → new_esEs4(xuu50000, xuu4000, bed)
new_ltEs19(xuu33002, xuu34002, ty_Bool) → new_ltEs18(xuu33002, xuu34002)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_esEs20(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_lt4(xuu33000, xuu34000, app(ty_[], dg)) → new_lt15(xuu33000, xuu34000, dg)
new_compare30(xuu33000, xuu34000, app(ty_Ratio, cha)) → new_compare14(xuu33000, xuu34000, cha)
new_ltEs19(xuu33002, xuu34002, ty_@0) → new_ltEs13(xuu33002, xuu34002)
new_esEs20(xuu33000, xuu34000, app(ty_Ratio, hg)) → new_esEs13(xuu33000, xuu34000, hg)
new_esEs21(xuu50002, xuu4002, ty_Int) → new_esEs15(xuu50002, xuu4002)
new_compare0(:(xuu33000, xuu33001), :(xuu34000, xuu34001), bd) → new_primCompAux0(xuu33000, xuu34000, new_compare0(xuu33001, xuu34001, bd), bd)
new_lt19(xuu33001, xuu34001, ty_Int) → new_lt12(xuu33001, xuu34001)
new_esEs20(xuu33000, xuu34000, ty_Char) → new_esEs10(xuu33000, xuu34000)
new_esEs22(xuu50001, xuu4001, ty_Integer) → new_esEs9(xuu50001, xuu4001)
new_esEs21(xuu50002, xuu4002, app(app(ty_Either, bcb), bcc)) → new_esEs6(xuu50002, xuu4002, bcb, bcc)
new_compare30(xuu33000, xuu34000, app(app(app(ty_@3, chb), chc), chd)) → new_compare15(xuu33000, xuu34000, chb, chc, chd)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(ty_Maybe, dbf), bbb) → new_ltEs8(xuu33000, xuu34000, dbf)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Ordering) → new_ltEs16(xuu33000, xuu34000)
new_esEs8(xuu33000, xuu34000, app(app(ty_Either, dh), ea)) → new_esEs6(xuu33000, xuu34000, dh, ea)
new_esEs19(xuu33001, xuu34001, app(app(app(ty_@3, gf), gg), gh)) → new_esEs5(xuu33001, xuu34001, gf, gg, gh)
new_esEs19(xuu33001, xuu34001, ty_@0) → new_esEs14(xuu33001, xuu34001)
new_esEs26(xuu50000, xuu4000, app(ty_Maybe, cef)) → new_esEs4(xuu50000, xuu4000, cef)
new_esEs19(xuu33001, xuu34001, ty_Ordering) → new_esEs16(xuu33001, xuu34001)
new_lt4(xuu33000, xuu34000, app(ty_Maybe, db)) → new_lt6(xuu33000, xuu34000, db)
new_esEs20(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Float, bha) → new_esEs11(xuu50000, xuu4000)
new_ltEs19(xuu33002, xuu34002, app(app(ty_Either, fh), ga)) → new_ltEs4(xuu33002, xuu34002, fh, ga)
new_pePe(False, xuu162) → xuu162
new_esEs25(xuu50001, xuu4001, app(app(ty_@2, cdb), cdc)) → new_esEs7(xuu50001, xuu4001, cdb, cdc)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Double, bbb) → new_ltEs11(xuu33000, xuu34000)
new_ltEs14(xuu3300, xuu3400) → new_fsEs(new_compare7(xuu3300, xuu3400))
new_ltEs19(xuu33002, xuu34002, ty_Float) → new_ltEs10(xuu33002, xuu34002)
new_esEs15(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_ltEs20(xuu3300, xuu3400, app(app(ty_Either, bba), bbb)) → new_ltEs4(xuu3300, xuu3400, bba, bbb)
new_ltEs16(EQ, GT) → True
new_lt20(xuu33000, xuu34000, app(app(app(ty_@3, hh), baa), bab)) → new_lt13(xuu33000, xuu34000, hh, baa, bab)
new_esEs7(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), cch, cda) → new_asAs(new_esEs26(xuu50000, xuu4000, cch), new_esEs25(xuu50001, xuu4001, cda))
new_esEs8(xuu33000, xuu34000, ty_Char) → new_esEs10(xuu33000, xuu34000)
new_compare25(Just(xuu3300), Just(xuu3400), False, baf) → new_compare12(xuu3300, xuu3400, new_ltEs20(xuu3300, xuu3400, baf), baf)
new_ltEs20(xuu3300, xuu3400, app(app(app(ty_@3, ef), eg), eh)) → new_ltEs15(xuu3300, xuu3400, ef, eg, eh)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(app(ty_Either, ddf), ddg)) → new_ltEs4(xuu33000, xuu34000, ddf, ddg)
new_lt4(xuu33000, xuu34000, ty_Float) → new_lt8(xuu33000, xuu34000)
new_esEs29(xuu5000, xuu400, app(ty_Ratio, dac)) → new_esEs13(xuu5000, xuu400, dac)
new_ltEs4(Left(xuu33000), Right(xuu34000), bba, bbb) → True
new_primCmpNat0(Zero, Succ(xuu3400)) → LT
new_esEs26(xuu50000, xuu4000, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_ltEs8(Nothing, Just(xuu34000), bag) → True
new_esEs6(Right(xuu50000), Left(xuu4000), cab, bha) → False
new_esEs6(Left(xuu50000), Right(xuu4000), cab, bha) → False
new_lt6(xuu33000, xuu34000, hf) → new_esEs16(new_compare31(xuu33000, xuu34000, hf), LT)
new_esEs19(xuu33001, xuu34001, app(ty_[], ha)) → new_esEs17(xuu33001, xuu34001, ha)
new_esEs19(xuu33001, xuu34001, app(ty_Maybe, gd)) → new_esEs4(xuu33001, xuu34001, gd)
new_esEs21(xuu50002, xuu4002, app(ty_Ratio, bcd)) → new_esEs13(xuu50002, xuu4002, bcd)
new_compare27(xuu33000, xuu34000, False, hh, baa, bab) → new_compare110(xuu33000, xuu34000, new_ltEs15(xuu33000, xuu34000, hh, baa, bab), hh, baa, bab)
new_esEs29(xuu5000, xuu400, app(app(ty_@2, cch), cda)) → new_esEs7(xuu5000, xuu400, cch, cda)
new_esEs29(xuu5000, xuu400, ty_Char) → new_esEs10(xuu5000, xuu400)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs11(xuu50000, xuu4000)
new_esEs25(xuu50001, xuu4001, app(ty_Ratio, cdh)) → new_esEs13(xuu50001, xuu4001, cdh)
new_ltEs6(xuu33001, xuu34001, ty_Double) → new_ltEs11(xuu33001, xuu34001)
new_compare0([], [], bd) → EQ
new_pePe(True, xuu162) → True
new_primEqNat0(Zero, Zero) → True
new_lt20(xuu33000, xuu34000, app(ty_Maybe, hf)) → new_lt6(xuu33000, xuu34000, hf)
new_compare26(xuu33000, xuu34000, True) → EQ
new_esEs19(xuu33001, xuu34001, app(ty_Ratio, ge)) → new_esEs13(xuu33001, xuu34001, ge)
new_ltEs6(xuu33001, xuu34001, ty_Ordering) → new_ltEs16(xuu33001, xuu34001)
new_ltEs6(xuu33001, xuu34001, app(app(app(ty_@3, ca), cb), cc)) → new_ltEs15(xuu33001, xuu34001, ca, cb, cc)
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), bbc, bbd, bbe) → new_asAs(new_esEs23(xuu50000, xuu4000, bbc), new_asAs(new_esEs22(xuu50001, xuu4001, bbd), new_esEs21(xuu50002, xuu4002, bbe)))
new_compare17(@0, @0) → EQ
new_esEs23(xuu50000, xuu4000, app(app(ty_Either, bef), beg)) → new_esEs6(xuu50000, xuu4000, bef, beg)
new_esEs14(@0, @0) → True
new_primMulNat0(Succ(xuu5000000), Succ(xuu400000)) → new_primPlusNat1(new_primMulNat0(xuu5000000, Succ(xuu400000)), xuu400000)
new_esEs17(:(xuu50000, xuu50001), :(xuu4000, xuu4001), bfd) → new_asAs(new_esEs24(xuu50000, xuu4000, bfd), new_esEs17(xuu50001, xuu4001, bfd))
new_lt12(xuu330, xuu340) → new_esEs16(new_compare7(xuu330, xuu340), LT)
new_compare30(xuu33000, xuu34000, ty_Int) → new_compare7(xuu33000, xuu34000)
new_esEs25(xuu50001, xuu4001, ty_Bool) → new_esEs18(xuu50001, xuu4001)
new_esEs23(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_esEs16(LT, GT) → False
new_esEs16(GT, LT) → False
new_compare32(xuu33000, xuu34000, ed, ee) → new_compare23(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, ed, ee), ed, ee)
new_esEs26(xuu50000, xuu4000, app(ty_Ratio, cfb)) → new_esEs13(xuu50000, xuu4000, cfb)
new_compare30(xuu33000, xuu34000, ty_Ordering) → new_compare8(xuu33000, xuu34000)
new_esEs22(xuu50001, xuu4001, app(app(ty_@2, bch), bda)) → new_esEs7(xuu50001, xuu4001, bch, bda)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(app(ty_Either, cag), cah)) → new_esEs6(xuu50000, xuu4000, cag, cah)
new_esEs25(xuu50001, xuu4001, ty_Int) → new_esEs15(xuu50001, xuu4001)
new_esEs24(xuu50000, xuu4000, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_ltEs16(EQ, LT) → False
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Char, bbb) → new_ltEs9(xuu33000, xuu34000)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_compare12(xuu129, xuu130, False, dab) → GT
new_ltEs16(GT, EQ) → False
new_sr(xuu50000, xuu4000) → new_primMulInt(xuu50000, xuu4000)
new_compare7(xuu33, xuu34) → new_primCmpInt(xuu33, xuu34)
new_esEs24(xuu50000, xuu4000, app(app(ty_@2, bfe), bff)) → new_esEs7(xuu50000, xuu4000, bfe, bff)
new_esEs20(xuu33000, xuu34000, ty_Integer) → new_esEs9(xuu33000, xuu34000)
new_lt20(xuu33000, xuu34000, ty_Ordering) → new_lt14(xuu33000, xuu34000)
new_esEs23(xuu50000, xuu4000, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_esEs26(xuu50000, xuu4000, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_ltEs19(xuu33002, xuu34002, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs15(xuu33002, xuu34002, fc, fd, ff)
new_lt20(xuu33000, xuu34000, app(app(ty_Either, ed), ee)) → new_lt17(xuu33000, xuu34000, ed, ee)
new_ltEs20(xuu3300, xuu3400, ty_Int) → new_ltEs14(xuu3300, xuu3400)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Int, bha) → new_esEs15(xuu50000, xuu4000)
new_lt20(xuu33000, xuu34000, app(app(ty_@2, bad), bae)) → new_lt18(xuu33000, xuu34000, bad, bae)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_esEs24(xuu50000, xuu4000, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_ltEs12(xuu3300, xuu3400, bah) → new_fsEs(new_compare14(xuu3300, xuu3400, bah))
new_ltEs20(xuu3300, xuu3400, ty_Char) → new_ltEs9(xuu3300, xuu3400)
new_ltEs16(LT, EQ) → True
new_esEs23(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_esEs19(xuu33001, xuu34001, ty_Bool) → new_esEs18(xuu33001, xuu34001)
new_esEs30(xuu22, xuu17, app(ty_Maybe, daf)) → new_esEs4(xuu22, xuu17, daf)
new_compare25(Just(xuu3300), Nothing, False, baf) → GT
new_compare13(xuu33000, xuu34000, False) → GT
new_esEs22(xuu50001, xuu4001, ty_Int) → new_esEs15(xuu50001, xuu4001)
new_compare25(Nothing, Nothing, False, baf) → LT
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Float, bbb) → new_ltEs10(xuu33000, xuu34000)
new_esEs20(xuu33000, xuu34000, ty_Int) → new_esEs15(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, ty_Integer) → new_esEs9(xuu22, xuu17)
new_ltEs18(True, True) → True
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Integer, bha) → new_esEs9(xuu50000, xuu4000)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt8(xuu33000, xuu34000) → new_esEs16(new_compare16(xuu33000, xuu34000), LT)
new_esEs21(xuu50002, xuu4002, app(app(ty_@2, bbf), bbg)) → new_esEs7(xuu50002, xuu4002, bbf, bbg)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Integer) → new_ltEs7(xuu33000, xuu34000)
new_lt4(xuu33000, xuu34000, app(ty_Ratio, dc)) → new_lt10(xuu33000, xuu34000, dc)
new_esEs8(xuu33000, xuu34000, app(ty_Ratio, dc)) → new_esEs13(xuu33000, xuu34000, dc)
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_ltEs4(Left(xuu33000), Left(xuu34000), app(app(ty_Either, dcd), dce), bbb) → new_ltEs4(xuu33000, xuu34000, dcd, dce)
new_ltEs18(False, False) → True
new_lt4(xuu33000, xuu34000, app(app(app(ty_@3, dd), de), df)) → new_lt13(xuu33000, xuu34000, dd, de, df)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(ty_[], caf)) → new_esEs17(xuu50000, xuu4000, caf)
new_ltEs19(xuu33002, xuu34002, ty_Int) → new_ltEs14(xuu33002, xuu34002)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_esEs24(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_lt9(xuu33000, xuu34000) → new_esEs16(new_compare29(xuu33000, xuu34000), LT)
new_ltEs17(xuu3300, xuu3400, bd) → new_fsEs(new_compare0(xuu3300, xuu3400, bd))
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Char, bha) → new_esEs10(xuu50000, xuu4000)
new_compare14(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Int) → new_compare7(new_sr(xuu33000, xuu34001), new_sr(xuu34000, xuu33001))
new_esEs22(xuu50001, xuu4001, app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs5(xuu50001, xuu4001, bdg, bdh, bea)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Integer) → new_ltEs7(xuu33000, xuu34000)
new_esEs21(xuu50002, xuu4002, ty_Ordering) → new_esEs16(xuu50002, xuu4002)
new_ltEs13(xuu3300, xuu3400) → new_fsEs(new_compare17(xuu3300, xuu3400))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs8(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_ltEs20(xuu3300, xuu3400, ty_Bool) → new_ltEs18(xuu3300, xuu3400)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_ltEs16(GT, LT) → False
new_ltEs20(xuu3300, xuu3400, app(app(ty_@2, be), bf)) → new_ltEs5(xuu3300, xuu3400, be, bf)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Bool, bbb) → new_ltEs18(xuu33000, xuu34000)
new_primCmpNat0(Succ(xuu3300), Succ(xuu3400)) → new_primCmpNat0(xuu3300, xuu3400)
new_esEs9(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_esEs22(xuu50001, xuu4001, app(ty_Maybe, bdb)) → new_esEs4(xuu50001, xuu4001, bdb)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Int, bbb) → new_ltEs14(xuu33000, xuu34000)
new_esEs25(xuu50001, xuu4001, app(ty_Maybe, cdd)) → new_esEs4(xuu50001, xuu4001, cdd)
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_compare10(xuu33000, xuu34000, False, ed, ee) → GT
new_lt18(xuu33000, xuu34000, bad, bae) → new_esEs16(new_compare33(xuu33000, xuu34000, bad, bae), LT)
new_esEs4(Just(xuu50000), Just(xuu4000), app(app(ty_Either, ccb), ccc)) → new_esEs6(xuu50000, xuu4000, ccb, ccc)
new_esEs6(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, bhg), bhh), caa), bha) → new_esEs5(xuu50000, xuu4000, bhg, bhh, caa)
new_lt13(xuu33000, xuu34000, hh, baa, bab) → new_esEs16(new_compare15(xuu33000, xuu34000, hh, baa, bab), LT)
new_lt10(xuu33000, xuu34000, hg) → new_esEs16(new_compare14(xuu33000, xuu34000, hg), LT)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Float) → new_ltEs10(xuu33000, xuu34000)
new_esEs19(xuu33001, xuu34001, app(app(ty_Either, hb), hc)) → new_esEs6(xuu33001, xuu34001, hb, hc)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(ty_Maybe, cae)) → new_esEs4(xuu50000, xuu4000, cae)
new_esEs25(xuu50001, xuu4001, ty_Char) → new_esEs10(xuu50001, xuu4001)
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs20(xuu3300, xuu3400, app(ty_[], bd)) → new_ltEs17(xuu3300, xuu3400, bd)
new_esEs6(Left(xuu50000), Left(xuu4000), app(ty_[], bhc), bha) → new_esEs17(xuu50000, xuu4000, bhc)
new_ltEs9(xuu3300, xuu3400) → new_fsEs(new_compare9(xuu3300, xuu3400))
new_esEs4(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, cce), ccf), ccg)) → new_esEs5(xuu50000, xuu4000, cce, ccf, ccg)
new_compare30(xuu33000, xuu34000, ty_@0) → new_compare17(xuu33000, xuu34000)
new_esEs8(xuu33000, xuu34000, ty_Bool) → new_esEs18(xuu33000, xuu34000)
new_primCompAux00(xuu179, LT) → LT
new_primCmpInt(Neg(Succ(xuu3300)), Neg(xuu340)) → new_primCmpNat0(xuu340, Succ(xuu3300))
new_ltEs19(xuu33002, xuu34002, app(ty_[], fg)) → new_ltEs17(xuu33002, xuu34002, fg)
new_ltEs8(Just(xuu33000), Nothing, bag) → False
new_ltEs6(xuu33001, xuu34001, app(ty_[], cd)) → new_ltEs17(xuu33001, xuu34001, cd)
new_esEs8(xuu33000, xuu34000, app(app(ty_@2, eb), ec)) → new_esEs7(xuu33000, xuu34000, eb, ec)
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_ltEs5(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), be, bf) → new_pePe(new_lt4(xuu33000, xuu34000, be), new_asAs(new_esEs8(xuu33000, xuu34000, be), new_ltEs6(xuu33001, xuu34001, bf)))
new_primPlusNat0(Succ(xuu28200), Zero) → Succ(xuu28200)
new_primPlusNat0(Zero, Succ(xuu9700)) → Succ(xuu9700)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu3300), Zero) → GT
new_esEs19(xuu33001, xuu34001, ty_Integer) → new_esEs9(xuu33001, xuu34001)
new_esEs8(xuu33000, xuu34000, app(app(app(ty_@3, dd), de), df)) → new_esEs5(xuu33000, xuu34000, dd, de, df)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3400))) → LT
new_esEs6(Left(xuu50000), Left(xuu4000), ty_@0, bha) → new_esEs14(xuu50000, xuu4000)
new_esEs22(xuu50001, xuu4001, ty_Bool) → new_esEs18(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(ty_Ratio, bdf)) → new_esEs13(xuu50001, xuu4001, bdf)
new_compare31(xuu33000, xuu34000, hf) → new_compare25(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, hf), hf)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs9(xuu50001, xuu4001)
new_esEs30(xuu22, xuu17, ty_Bool) → new_esEs18(xuu22, xuu17)
new_sr0(Integer(xuu340000), Integer(xuu330010)) → Integer(new_primMulInt(xuu340000, xuu330010))
new_compare13(xuu33000, xuu34000, True) → LT
new_compare6(Integer(xuu33000), Integer(xuu34000)) → new_primCmpInt(xuu33000, xuu34000)
new_compare12(xuu129, xuu130, True, dab) → LT
new_compare28(xuu33000, xuu34000, True, bad, bae) → EQ
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_lt19(xuu33001, xuu34001, app(ty_Maybe, gd)) → new_lt6(xuu33001, xuu34001, gd)
new_esEs24(xuu50000, xuu4000, app(ty_Ratio, bgc)) → new_esEs13(xuu50000, xuu4000, bgc)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Bool, bha) → new_esEs18(xuu50000, xuu4000)
new_esEs6(Left(xuu50000), Left(xuu4000), app(ty_Maybe, bhb), bha) → new_esEs4(xuu50000, xuu4000, bhb)
new_ltEs6(xuu33001, xuu34001, app(ty_Maybe, bg)) → new_ltEs8(xuu33001, xuu34001, bg)
new_esEs29(xuu5000, xuu400, ty_@0) → new_esEs14(xuu5000, xuu400)
new_esEs12(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs15(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_compare30(xuu33000, xuu34000, app(app(ty_Either, chf), chg)) → new_compare32(xuu33000, xuu34000, chf, chg)
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_esEs10(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_esEs26(xuu50000, xuu4000, app(ty_[], ceg)) → new_esEs17(xuu50000, xuu4000, ceg)
new_primCompAux00(xuu179, EQ) → xuu179
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3400))) → new_primCmpNat0(Zero, Succ(xuu3400))
new_compare30(xuu33000, xuu34000, app(ty_Maybe, cgh)) → new_compare31(xuu33000, xuu34000, cgh)
new_compare15(xuu33000, xuu34000, hh, baa, bab) → new_compare27(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, hh, baa, bab), hh, baa, bab)
new_compare24(xuu33000, xuu34000, True) → EQ
new_esEs25(xuu50001, xuu4001, ty_@0) → new_esEs14(xuu50001, xuu4001)
new_esEs23(xuu50000, xuu4000, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(ty_[], dcc), bbb) → new_ltEs17(xuu33000, xuu34000, dcc)
new_ltEs16(EQ, EQ) → True
new_lt19(xuu33001, xuu34001, ty_@0) → new_lt11(xuu33001, xuu34001)
new_compare25(Nothing, Just(xuu3400), False, baf) → LT
new_esEs29(xuu5000, xuu400, ty_Double) → new_esEs12(xuu5000, xuu400)
new_esEs21(xuu50002, xuu4002, app(ty_[], bca)) → new_esEs17(xuu50002, xuu4002, bca)
new_esEs8(xuu33000, xuu34000, ty_Int) → new_esEs15(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, app(app(ty_Either, dah), dba)) → new_esEs6(xuu22, xuu17, dah, dba)
new_esEs6(Left(xuu50000), Left(xuu4000), app(app(ty_@2, bgg), bgh), bha) → new_esEs7(xuu50000, xuu4000, bgg, bgh)
new_esEs23(xuu50000, xuu4000, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_esEs30(xuu22, xuu17, ty_Int) → new_esEs15(xuu22, xuu17)
new_not(False) → True
new_ltEs4(Right(xuu33000), Left(xuu34000), bba, bbb) → False
new_esEs6(Left(xuu50000), Left(xuu4000), app(app(ty_Either, bhd), bhe), bha) → new_esEs6(xuu50000, xuu4000, bhd, bhe)
new_ltEs6(xuu33001, xuu34001, ty_Char) → new_ltEs9(xuu33001, xuu34001)
new_esEs30(xuu22, xuu17, ty_@0) → new_esEs14(xuu22, xuu17)
new_esEs23(xuu50000, xuu4000, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_esEs30(xuu22, xuu17, ty_Double) → new_esEs12(xuu22, xuu17)
new_primCmpInt(Pos(Succ(xuu3300)), Pos(xuu340)) → new_primCmpNat0(Succ(xuu3300), xuu340)
new_esEs19(xuu33001, xuu34001, app(app(ty_@2, hd), he)) → new_esEs7(xuu33001, xuu34001, hd, he)
new_esEs22(xuu50001, xuu4001, ty_Float) → new_esEs11(xuu50001, xuu4001)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Double) → new_ltEs11(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, app(app(ty_@2, dad), dae)) → new_esEs7(xuu22, xuu17, dad, dae)
new_esEs29(xuu5000, xuu400, app(ty_[], bfd)) → new_esEs17(xuu5000, xuu400, bfd)
new_esEs24(xuu50000, xuu4000, app(app(ty_Either, bga), bgb)) → new_esEs6(xuu50000, xuu4000, bga, bgb)
new_esEs16(LT, EQ) → False
new_esEs16(EQ, LT) → False
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Ordering) → new_ltEs16(xuu33000, xuu34000)
new_esEs19(xuu33001, xuu34001, ty_Double) → new_esEs12(xuu33001, xuu34001)
new_compare14(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Integer) → new_compare6(new_sr0(xuu33000, xuu34001), new_sr0(xuu34000, xuu33001))
new_lt4(xuu33000, xuu34000, ty_Double) → new_lt9(xuu33000, xuu34000)
new_compare0(:(xuu33000, xuu33001), [], bd) → GT
new_lt19(xuu33001, xuu34001, app(app(ty_@2, hd), he)) → new_lt18(xuu33001, xuu34001, hd, he)
new_esEs24(xuu50000, xuu4000, app(ty_[], bfh)) → new_esEs17(xuu50000, xuu4000, bfh)
new_esEs29(xuu5000, xuu400, ty_Int) → new_esEs15(xuu5000, xuu400)
new_lt4(xuu33000, xuu34000, app(app(ty_Either, dh), ea)) → new_lt17(xuu33000, xuu34000, dh, ea)
new_lt20(xuu33000, xuu34000, ty_Double) → new_lt9(xuu33000, xuu34000)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs15(xuu50000, xuu4000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Float) → new_ltEs10(xuu33000, xuu34000)
new_esEs24(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_esEs30(xuu22, xuu17, app(ty_[], dag)) → new_esEs17(xuu22, xuu17, dag)
new_esEs20(xuu33000, xuu34000, app(app(app(ty_@3, hh), baa), bab)) → new_esEs5(xuu33000, xuu34000, hh, baa, bab)
new_primCmpInt(Pos(Succ(xuu3300)), Neg(xuu340)) → GT
new_esEs21(xuu50002, xuu4002, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs5(xuu50002, xuu4002, bce, bcf, bcg)
new_esEs29(xuu5000, xuu400, ty_Integer) → new_esEs9(xuu5000, xuu400)
new_lt19(xuu33001, xuu34001, app(ty_[], ha)) → new_lt15(xuu33001, xuu34001, ha)
new_ltEs6(xuu33001, xuu34001, ty_Integer) → new_ltEs7(xuu33001, xuu34001)
new_primMulInt(Pos(xuu500000), Pos(xuu40000)) → Pos(new_primMulNat0(xuu500000, xuu40000))
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(ty_[], dde)) → new_ltEs17(xuu33000, xuu34000, dde)
new_ltEs6(xuu33001, xuu34001, app(app(ty_Either, ce), cf)) → new_ltEs4(xuu33001, xuu34001, ce, cf)
new_primMulInt(Neg(xuu500000), Neg(xuu40000)) → Pos(new_primMulNat0(xuu500000, xuu40000))
new_ltEs19(xuu33002, xuu34002, app(ty_Maybe, fa)) → new_ltEs8(xuu33002, xuu34002, fa)
new_esEs21(xuu50002, xuu4002, ty_Char) → new_esEs10(xuu50002, xuu4002)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Ordering, bha) → new_esEs16(xuu50000, xuu4000)
new_esEs16(EQ, EQ) → True
new_esEs26(xuu50000, xuu4000, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_primEqNat0(Succ(xuu500000), Zero) → False
new_compare8(xuu33000, xuu34000) → new_compare24(xuu33000, xuu34000, new_esEs16(xuu33000, xuu34000))
new_primPlusNat0(Zero, Zero) → Zero
new_esEs26(xuu50000, xuu4000, app(app(ty_@2, ced), cee)) → new_esEs7(xuu50000, xuu4000, ced, cee)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare23(xuu33000, xuu34000, False, ed, ee) → new_compare10(xuu33000, xuu34000, new_ltEs4(xuu33000, xuu34000, ed, ee), ed, ee)
new_esEs4(Nothing, Nothing, cbe) → True
new_esEs4(Just(xuu50000), Just(xuu4000), app(ty_Ratio, ccd)) → new_esEs13(xuu50000, xuu4000, ccd)
new_esEs20(xuu33000, xuu34000, app(ty_[], bac)) → new_esEs17(xuu33000, xuu34000, bac)
new_esEs20(xuu33000, xuu34000, app(app(ty_Either, ed), ee)) → new_esEs6(xuu33000, xuu34000, ed, ee)
new_ltEs6(xuu33001, xuu34001, ty_Float) → new_ltEs10(xuu33001, xuu34001)
new_esEs22(xuu50001, xuu4001, app(ty_[], bdc)) → new_esEs17(xuu50001, xuu4001, bdc)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(app(ty_Either, cgd), cge)) → new_ltEs4(xuu33000, xuu34000, cgd, cge)
new_esEs29(xuu5000, xuu400, app(app(ty_Either, cab), bha)) → new_esEs6(xuu5000, xuu400, cab, bha)
new_ltEs20(xuu3300, xuu3400, ty_Ordering) → new_ltEs16(xuu3300, xuu3400)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Int) → new_ltEs14(xuu33000, xuu34000)
new_ltEs19(xuu33002, xuu34002, ty_Char) → new_ltEs9(xuu33002, xuu34002)
new_ltEs15(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ef, eg, eh) → new_pePe(new_lt20(xuu33000, xuu34000, ef), new_asAs(new_esEs20(xuu33000, xuu34000, ef), new_pePe(new_lt19(xuu33001, xuu34001, eg), new_asAs(new_esEs19(xuu33001, xuu34001, eg), new_ltEs19(xuu33002, xuu34002, eh)))))
new_esEs8(xuu33000, xuu34000, ty_Ordering) → new_esEs16(xuu33000, xuu34000)
new_lt20(xuu33000, xuu34000, ty_Int) → new_lt12(xuu33000, xuu34000)
new_esEs29(xuu5000, xuu400, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs5(xuu5000, xuu400, bbc, bbd, bbe)
new_lt19(xuu33001, xuu34001, app(app(ty_Either, hb), hc)) → new_lt17(xuu33001, xuu34001, hb, hc)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3400))) → new_primCmpNat0(Succ(xuu3400), Zero)
new_compare23(xuu33000, xuu34000, True, ed, ee) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3400))) → GT
new_lt4(xuu33000, xuu34000, ty_@0) → new_lt11(xuu33000, xuu34000)
new_lt20(xuu33000, xuu34000, ty_Char) → new_lt7(xuu33000, xuu34000)
new_esEs6(Left(xuu50000), Left(xuu4000), app(ty_Ratio, bhf), bha) → new_esEs13(xuu50000, xuu4000, bhf)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(ty_Ratio, dbg), bbb) → new_ltEs12(xuu33000, xuu34000, dbg)
new_esEs26(xuu50000, xuu4000, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(app(app(ty_@3, ddb), ddc), ddd)) → new_ltEs15(xuu33000, xuu34000, ddb, ddc, ddd)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_esEs19(xuu33001, xuu34001, ty_Float) → new_esEs11(xuu33001, xuu34001)
new_compare30(xuu33000, xuu34000, ty_Float) → new_compare16(xuu33000, xuu34000)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Integer, bbb) → new_ltEs7(xuu33000, xuu34000)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(ty_[], cgc)) → new_ltEs17(xuu33000, xuu34000, cgc)
new_esEs21(xuu50002, xuu4002, app(ty_Maybe, bbh)) → new_esEs4(xuu50002, xuu4002, bbh)
new_compare18(xuu33000, xuu34000, True, bad, bae) → LT
new_ltEs6(xuu33001, xuu34001, app(app(ty_@2, cg), da)) → new_ltEs5(xuu33001, xuu34001, cg, da)
new_esEs25(xuu50001, xuu4001, ty_Ordering) → new_esEs16(xuu50001, xuu4001)
new_compare19(xuu33000, xuu34000) → new_compare26(xuu33000, xuu34000, new_esEs18(xuu33000, xuu34000))
new_lt19(xuu33001, xuu34001, ty_Double) → new_lt9(xuu33001, xuu34001)
new_compare26(xuu33000, xuu34000, False) → new_compare13(xuu33000, xuu34000, new_ltEs18(xuu33000, xuu34000))
new_lt17(xuu33000, xuu34000, ed, ee) → new_esEs16(new_compare32(xuu33000, xuu34000, ed, ee), LT)
new_esEs23(xuu50000, xuu4000, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_primCompAux0(xuu33000, xuu34000, xuu173, bd) → new_primCompAux00(xuu173, new_compare30(xuu33000, xuu34000, bd))
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt20(xuu33000, xuu34000, app(ty_[], bac)) → new_lt15(xuu33000, xuu34000, bac)
new_esEs21(xuu50002, xuu4002, ty_@0) → new_esEs14(xuu50002, xuu4002)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Double, bha) → new_esEs12(xuu50000, xuu4000)
new_compare29(Double(xuu33000, xuu33001), Double(xuu34000, xuu34001)) → new_compare7(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_lt4(xuu33000, xuu34000, ty_Bool) → new_lt16(xuu33000, xuu34000)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(ty_Maybe, cff)) → new_ltEs8(xuu33000, xuu34000, cff)
new_esEs21(xuu50002, xuu4002, ty_Bool) → new_esEs18(xuu50002, xuu4002)
new_compare30(xuu33000, xuu34000, app(ty_[], che)) → new_compare0(xuu33000, xuu34000, che)
new_esEs24(xuu50000, xuu4000, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_esEs30(xuu22, xuu17, ty_Ordering) → new_esEs16(xuu22, xuu17)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(app(ty_@2, ddh), dea)) → new_ltEs5(xuu33000, xuu34000, ddh, dea)
new_compare33(xuu33000, xuu34000, bad, bae) → new_compare28(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, bad, bae), bad, bae)
new_esEs16(LT, LT) → True
new_ltEs4(Left(xuu33000), Left(xuu34000), app(app(app(ty_@3, dbh), dca), dcb), bbb) → new_ltEs15(xuu33000, xuu34000, dbh, dca, dcb)
new_esEs13(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), dac) → new_asAs(new_esEs28(xuu50000, xuu4000, dac), new_esEs27(xuu50001, xuu4001, dac))
new_asAs(False, xuu136) → False
new_esEs22(xuu50001, xuu4001, ty_Double) → new_esEs12(xuu50001, xuu4001)
new_lt20(xuu33000, xuu34000, ty_Bool) → new_lt16(xuu33000, xuu34000)
new_esEs11(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs15(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_primMulInt(Neg(xuu500000), Pos(xuu40000)) → Neg(new_primMulNat0(xuu500000, xuu40000))
new_primMulInt(Pos(xuu500000), Neg(xuu40000)) → Neg(new_primMulNat0(xuu500000, xuu40000))
new_lt4(xuu33000, xuu34000, ty_Int) → new_lt12(xuu33000, xuu34000)
new_primMulNat0(Succ(xuu5000000), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu400000)) → Zero
new_esEs22(xuu50001, xuu4001, ty_Ordering) → new_esEs16(xuu50001, xuu4001)
new_ltEs20(xuu3300, xuu3400, ty_Integer) → new_ltEs7(xuu3300, xuu3400)
new_esEs16(GT, GT) → True
new_esEs29(xuu5000, xuu400, ty_Float) → new_esEs11(xuu5000, xuu400)
new_esEs4(Just(xuu50000), Just(xuu4000), app(ty_[], cca)) → new_esEs17(xuu50000, xuu4000, cca)
new_ltEs20(xuu3300, xuu3400, ty_Double) → new_ltEs11(xuu3300, xuu3400)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_@0, bbb) → new_ltEs13(xuu33000, xuu34000)
new_compare28(xuu33000, xuu34000, False, bad, bae) → new_compare18(xuu33000, xuu34000, new_ltEs5(xuu33000, xuu34000, bad, bae), bad, bae)
new_esEs18(True, True) → True
new_esEs23(xuu50000, xuu4000, app(app(ty_@2, beb), bec)) → new_esEs7(xuu50000, xuu4000, beb, bec)
new_esEs30(xuu22, xuu17, app(ty_Ratio, dbb)) → new_esEs13(xuu22, xuu17, dbb)
new_lt19(xuu33001, xuu34001, ty_Float) → new_lt8(xuu33001, xuu34001)
new_esEs24(xuu50000, xuu4000, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_lt20(xuu33000, xuu34000, ty_Float) → new_lt8(xuu33000, xuu34000)
new_compare110(xuu33000, xuu34000, True, hh, baa, bab) → LT
new_esEs22(xuu50001, xuu4001, ty_Char) → new_esEs10(xuu50001, xuu4001)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_@0) → new_ltEs13(xuu33000, xuu34000)
new_lt16(xuu33000, xuu34000) → new_esEs16(new_compare19(xuu33000, xuu34000), LT)
new_lt19(xuu33001, xuu34001, ty_Bool) → new_lt16(xuu33001, xuu34001)
new_esEs25(xuu50001, xuu4001, app(ty_[], cde)) → new_esEs17(xuu50001, xuu4001, cde)
new_esEs21(xuu50002, xuu4002, ty_Integer) → new_esEs9(xuu50002, xuu4002)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_ltEs20(xuu3300, xuu3400, app(ty_Ratio, bah)) → new_ltEs12(xuu3300, xuu3400, bah)
new_esEs26(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_compare18(xuu33000, xuu34000, False, bad, bae) → GT
new_lt11(xuu33000, xuu34000) → new_esEs16(new_compare17(xuu33000, xuu34000), LT)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Char) → new_ltEs9(xuu33000, xuu34000)
new_lt19(xuu33001, xuu34001, app(app(app(ty_@3, gf), gg), gh)) → new_lt13(xuu33001, xuu34001, gf, gg, gh)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Int) → new_ltEs14(xuu33000, xuu34000)
new_compare30(xuu33000, xuu34000, app(app(ty_@2, chh), daa)) → new_compare33(xuu33000, xuu34000, chh, daa)
new_lt15(xuu33000, xuu34000, bac) → new_esEs16(new_compare0(xuu33000, xuu34000, bac), LT)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_esEs24(xuu50000, xuu4000, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_ltEs18(True, False) → False
new_ltEs20(xuu3300, xuu3400, ty_Float) → new_ltEs10(xuu3300, xuu3400)
new_lt20(xuu33000, xuu34000, ty_Integer) → new_lt5(xuu33000, xuu34000)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs15(xuu50001, xuu4001)
new_compare11(xuu33000, xuu34000, False) → GT
new_esEs8(xuu33000, xuu34000, app(ty_Maybe, db)) → new_esEs4(xuu33000, xuu34000, db)
new_ltEs8(Nothing, Nothing, bag) → True
new_compare11(xuu33000, xuu34000, True) → LT
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_@0) → new_ltEs13(xuu33000, xuu34000)
new_esEs22(xuu50001, xuu4001, ty_@0) → new_esEs14(xuu50001, xuu4001)
new_fsEs(xuu146) → new_not(new_esEs16(xuu146, GT))
new_esEs25(xuu50001, xuu4001, app(app(app(ty_@3, cea), ceb), cec)) → new_esEs5(xuu50001, xuu4001, cea, ceb, cec)
new_esEs26(xuu50000, xuu4000, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_esEs22(xuu50001, xuu4001, app(app(ty_Either, bdd), bde)) → new_esEs6(xuu50001, xuu4001, bdd, bde)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Char) → new_ltEs9(xuu33000, xuu34000)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Ordering, bbb) → new_ltEs16(xuu33000, xuu34000)
new_esEs21(xuu50002, xuu4002, ty_Double) → new_esEs12(xuu50002, xuu4002)
new_esEs18(False, True) → False
new_esEs18(True, False) → False
new_esEs4(Just(xuu50000), Just(xuu4000), app(app(ty_@2, cbf), cbg)) → new_esEs7(xuu50000, xuu4000, cbf, cbg)
new_esEs29(xuu5000, xuu400, ty_Bool) → new_esEs18(xuu5000, xuu400)
new_esEs8(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, ty_Float) → new_esEs11(xuu22, xuu17)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(ty_Ratio, dda)) → new_ltEs12(xuu33000, xuu34000, dda)
new_ltEs11(xuu3300, xuu3400) → new_fsEs(new_compare29(xuu3300, xuu3400))
new_esEs21(xuu50002, xuu4002, ty_Float) → new_esEs11(xuu50002, xuu4002)
new_ltEs6(xuu33001, xuu34001, ty_Int) → new_ltEs14(xuu33001, xuu34001)
new_ltEs19(xuu33002, xuu34002, ty_Integer) → new_ltEs7(xuu33002, xuu34002)
new_esEs8(xuu33000, xuu34000, app(ty_[], dg)) → new_esEs17(xuu33000, xuu34000, dg)
new_compare30(xuu33000, xuu34000, ty_Bool) → new_compare19(xuu33000, xuu34000)
new_esEs23(xuu50000, xuu4000, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_esEs20(xuu33000, xuu34000, app(app(ty_@2, bad), bae)) → new_esEs7(xuu33000, xuu34000, bad, bae)
new_ltEs18(False, True) → True
new_primPlusNat0(Succ(xuu28200), Succ(xuu9700)) → Succ(Succ(new_primPlusNat0(xuu28200, xuu9700)))
new_esEs26(xuu50000, xuu4000, app(app(ty_Either, ceh), cfa)) → new_esEs6(xuu50000, xuu4000, ceh, cfa)
new_ltEs7(xuu3300, xuu3400) → new_fsEs(new_compare6(xuu3300, xuu3400))
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(ty_Maybe, dch)) → new_ltEs8(xuu33000, xuu34000, dch)
new_compare0([], :(xuu34000, xuu34001), bd) → LT
new_asAs(True, xuu136) → xuu136
new_esEs26(xuu50000, xuu4000, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs5(xuu50000, xuu4000, cfc, cfd, cfe)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(app(ty_@2, dcf), dcg), bbb) → new_ltEs5(xuu33000, xuu34000, dcf, dcg)
new_esEs25(xuu50001, xuu4001, ty_Float) → new_esEs11(xuu50001, xuu4001)
new_lt20(xuu33000, xuu34000, app(ty_Ratio, hg)) → new_lt10(xuu33000, xuu34000, hg)
new_ltEs16(LT, LT) → True
new_primPlusNat1(xuu107, xuu400000) → new_primPlusNat0(xuu107, Succ(xuu400000))
new_compare27(xuu33000, xuu34000, True, hh, baa, bab) → EQ
new_esEs30(xuu22, xuu17, ty_Char) → new_esEs10(xuu22, xuu17)
new_esEs19(xuu33001, xuu34001, ty_Char) → new_esEs10(xuu33001, xuu34001)
new_esEs17([], [], bfd) → True
new_esEs17([], :(xuu4000, xuu4001), bfd) → False
new_esEs17(:(xuu50000, xuu50001), [], bfd) → False
new_esEs19(xuu33001, xuu34001, ty_Int) → new_esEs15(xuu33001, xuu34001)
new_lt20(xuu33000, xuu34000, ty_@0) → new_lt11(xuu33000, xuu34000)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(ty_Ratio, cfg)) → new_ltEs12(xuu33000, xuu34000, cfg)
new_esEs23(xuu50000, xuu4000, app(app(app(ty_@3, bfa), bfb), bfc)) → new_esEs5(xuu50000, xuu4000, bfa, bfb, bfc)
new_esEs8(xuu33000, xuu34000, ty_Integer) → new_esEs9(xuu33000, xuu34000)
new_compare30(xuu33000, xuu34000, ty_Char) → new_compare9(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs5(xuu22, xuu17, dbc, dbd, dbe)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs10(xuu50000, xuu4000)
new_esEs29(xuu5000, xuu400, app(ty_Maybe, cbe)) → new_esEs4(xuu5000, xuu400, cbe)
new_compare24(xuu33000, xuu34000, False) → new_compare11(xuu33000, xuu34000, new_ltEs16(xuu33000, xuu34000))
new_ltEs20(xuu3300, xuu3400, ty_@0) → new_ltEs13(xuu3300, xuu3400)
new_lt4(xuu33000, xuu34000, ty_Integer) → new_lt5(xuu33000, xuu34000)
new_esEs26(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_compare110(xuu33000, xuu34000, False, hh, baa, bab) → GT
new_compare30(xuu33000, xuu34000, ty_Integer) → new_compare6(xuu33000, xuu34000)
new_primCompAux00(xuu179, GT) → GT
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(ty_Ratio, cba)) → new_esEs13(xuu50000, xuu4000, cba)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs15(xuu33000, xuu34000, cfh, cga, cgb)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_compare30(xuu33000, xuu34000, ty_Double) → new_compare29(xuu33000, xuu34000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(app(app(ty_@3, cbb), cbc), cbd)) → new_esEs5(xuu50000, xuu4000, cbb, cbc, cbd)
new_ltEs6(xuu33001, xuu34001, ty_@0) → new_ltEs13(xuu33001, xuu34001)
new_lt7(xuu33000, xuu34000) → new_esEs16(new_compare9(xuu33000, xuu34000), LT)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs6(xuu33001, xuu34001, ty_Bool) → new_ltEs18(xuu33001, xuu34001)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_primCmpInt(Neg(Succ(xuu3300)), Pos(xuu340)) → LT
new_not(True) → False
new_esEs25(xuu50001, xuu4001, ty_Integer) → new_esEs9(xuu50001, xuu4001)
new_esEs18(False, False) → True

The set Q consists of the following terms:

new_primPlusNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare12(x0, x1, True, x2)
new_esEs28(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs12(Double(x0, x1), Double(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs4(Nothing, Just(x0), x1)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(x0, x1, ty_Double)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare10(x0, x1, True, x2, x3)
new_esEs26(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, True, x2)
new_esEs23(x0, x1, ty_Integer)
new_compare25(Just(x0), Nothing, False, x1)
new_ltEs19(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare24(x0, x1, False)
new_asAs(False, x0)
new_esEs21(x0, x1, ty_Integer)
new_esEs17(:(x0, x1), [], x2)
new_compare15(x0, x1, x2, x3, x4)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs10(Char(x0), Char(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs26(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs9(x0, x1)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_lt15(x0, x1, x2)
new_esEs23(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17([], [], x0)
new_lt5(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs18(True, True)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Ordering)
new_esEs16(LT, GT)
new_esEs16(GT, LT)
new_ltEs11(x0, x1)
new_ltEs6(x0, x1, ty_Bool)
new_compare17(@0, @0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_lt4(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_ltEs7(x0, x1)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_primPlusNat1(x0, x1)
new_esEs28(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Double)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Integer)
new_ltEs6(x0, x1, ty_Ordering)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs8(x0, x1, ty_Char)
new_compare10(x0, x1, False, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primEqNat0(Zero, Zero)
new_lt6(x0, x1, x2)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare12(x0, x1, False, x2)
new_esEs19(x0, x1, ty_Int)
new_compare26(x0, x1, True)
new_ltEs6(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs6(x0, x1, ty_Integer)
new_compare26(x0, x1, False)
new_ltEs20(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_primMulNat0(Zero, Zero)
new_ltEs12(x0, x1, x2)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs24(x0, x1, ty_Char)
new_lt17(x0, x1, x2, x3)
new_esEs19(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Int)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare6(Integer(x0), Integer(x1))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare8(x0, x1)
new_lt20(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs16(GT, GT)
new_compare23(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_sr(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs14(@0, @0)
new_compare19(x0, x1)
new_compare23(x0, x1, True, x2, x3)
new_compare18(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt4(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(x0, x1, x2)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, ty_Double)
new_esEs18(False, False)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_@0)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, GT)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Integer)
new_ltEs14(x0, x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare7(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare25(Just(x0), Just(x1), False, x2)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_@0)
new_ltEs18(True, True)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_primPlusNat0(Zero, Zero)
new_compare11(x0, x1, False)
new_ltEs16(EQ, EQ)
new_esEs19(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_lt4(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Ordering)
new_compare24(x0, x1, True)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(False, x0)
new_esEs15(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs30(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_compare9(Char(x0), Char(x1))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Double)
new_ltEs16(LT, GT)
new_ltEs16(GT, LT)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(x0, x1)
new_lt14(x0, x1)
new_lt20(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt13(x0, x1, x2, x3, x4)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_pePe(True, x0)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs8(Nothing, Nothing, x0)
new_primCompAux00(x0, LT)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare28(x0, x1, False, x2, x3)
new_ltEs18(False, False)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_lt11(x0, x1)
new_compare30(x0, x1, ty_Char)
new_primCompAux00(x0, EQ)
new_esEs24(x0, x1, ty_Double)
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs17([], :(x0, x1), x2)
new_compare30(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt12(x0, x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(Nothing, Nothing, False, x0)
new_esEs20(x0, x1, ty_Int)
new_esEs16(LT, LT)
new_esEs26(x0, x1, ty_Bool)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2, x3)
new_esEs22(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, ty_Double)
new_ltEs16(GT, GT)
new_esEs24(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Float)
new_compare30(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs6(x0, x1, ty_Char)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Zero, Succ(x0))
new_ltEs8(Nothing, Just(x0), x1)
new_compare13(x0, x1, True)
new_compare30(x0, x1, ty_Bool)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare27(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(Just(x0), Nothing, x1)
new_esEs20(x0, x1, ty_@0)
new_primCmpNat0(Zero, Zero)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt16(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_@0)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_fsEs(x0)
new_esEs8(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1)
new_esEs8(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs29(x0, x1, ty_Ordering)
new_compare110(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1, app(ty_[], x2))
new_esEs4(Nothing, Nothing, x0)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare18(x0, x1, False, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_compare33(x0, x1, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, ty_Double)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Bool)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_not(True)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Double)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_esEs16(EQ, LT)
new_esEs16(LT, EQ)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs16(EQ, EQ)
new_esEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_not(False)
new_compare31(x0, x1, x2)
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs18(False, True)
new_ltEs18(True, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_asAs(True, x0)
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Double)
new_lt4(x0, x1, ty_Char)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare25(Nothing, Just(x0), False, x1)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Char)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs11(Float(x0, x1), Float(x2, x3))
new_esEs25(x0, x1, ty_Char)
new_compare13(x0, x1, False)
new_ltEs20(x0, x1, ty_Float)
new_compare16(Float(x0, x1), Float(x2, x3))
new_lt4(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Int)
new_esEs16(EQ, GT)
new_esEs16(GT, EQ)
new_esEs9(Integer(x0), Integer(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs10(x0, x1)
new_esEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_compare29(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_primMulNat0(Zero, Succ(x0))
new_esEs23(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_compare27(x0, x1, False, x2, x3, x4)
new_compare30(x0, x1, ty_Double)
new_compare0([], [], x0)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare32(x0, x1, x2, x3)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Nothing, x1)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs19(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_compare0([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare30(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Bool)
new_esEs19(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_compare30(x0, x1, ty_@0)
new_esEs30(x0, x1, app(ty_Ratio, x2))

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_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, False, h, ba) → new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, new_esEs16(new_compare25(Nothing, Just(xuu400), False, h), GT), h, ba)
new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu44, Nothing, xuu501, h, ba)
new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu43, Nothing, xuu501, h, ba)
new_addToFM_C1(xuu3, xuu41, xuu42, xuu43, xuu44, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu44, Nothing, xuu501, h, ba)
new_addToFM_C(xuu3, Branch(Nothing, xuu41, xuu42, xuu43, xuu44), Nothing, xuu501, h, ba) → new_addToFM_C1(xuu3, xuu41, xuu42, xuu43, xuu44, xuu501, new_esEs16(new_compare25(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C(xuu3, Branch(Just(xuu400), xuu41, xuu42, xuu43, xuu44), Nothing, xuu501, h, ba) → new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, new_esEs16(new_compare25(Nothing, Just(xuu400), False, h), LT), h, ba)

The TRS R consists of the following rules:

new_compare25(Nothing, Just(xuu3400), False, baf) → LT
new_esEs16(GT, LT) → False
new_esEs16(EQ, LT) → False
new_esEs16(LT, LT) → True
new_esEs16(EQ, GT) → False
new_esEs16(LT, GT) → False
new_esEs16(GT, GT) → True
new_compare25(xuu330, xuu340, True, baf) → EQ

The set Q consists of the following terms:

new_primPlusNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare12(x0, x1, True, x2)
new_esEs28(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs12(Double(x0, x1), Double(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs4(Nothing, Just(x0), x1)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(x0, x1, ty_Double)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare10(x0, x1, True, x2, x3)
new_esEs26(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, True, x2)
new_esEs23(x0, x1, ty_Integer)
new_compare25(Just(x0), Nothing, False, x1)
new_ltEs19(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare24(x0, x1, False)
new_asAs(False, x0)
new_esEs21(x0, x1, ty_Integer)
new_esEs17(:(x0, x1), [], x2)
new_compare15(x0, x1, x2, x3, x4)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs10(Char(x0), Char(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs26(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs9(x0, x1)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_lt15(x0, x1, x2)
new_esEs23(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17([], [], x0)
new_lt5(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs18(True, True)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Ordering)
new_esEs16(LT, GT)
new_esEs16(GT, LT)
new_ltEs11(x0, x1)
new_ltEs6(x0, x1, ty_Bool)
new_compare17(@0, @0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_lt4(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_ltEs7(x0, x1)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_primPlusNat1(x0, x1)
new_esEs28(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Double)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Integer)
new_ltEs6(x0, x1, ty_Ordering)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs8(x0, x1, ty_Char)
new_compare10(x0, x1, False, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primEqNat0(Zero, Zero)
new_lt6(x0, x1, x2)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare12(x0, x1, False, x2)
new_esEs19(x0, x1, ty_Int)
new_compare26(x0, x1, True)
new_ltEs6(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs6(x0, x1, ty_Integer)
new_compare26(x0, x1, False)
new_ltEs20(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_primMulNat0(Zero, Zero)
new_ltEs12(x0, x1, x2)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs24(x0, x1, ty_Char)
new_lt17(x0, x1, x2, x3)
new_esEs19(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Int)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare6(Integer(x0), Integer(x1))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare8(x0, x1)
new_lt20(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs16(GT, GT)
new_compare23(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_sr(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs14(@0, @0)
new_compare19(x0, x1)
new_compare23(x0, x1, True, x2, x3)
new_compare18(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt4(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(x0, x1, x2)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, ty_Double)
new_esEs18(False, False)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_@0)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, GT)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Integer)
new_ltEs14(x0, x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare7(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare25(Just(x0), Just(x1), False, x2)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_@0)
new_ltEs18(True, True)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_primPlusNat0(Zero, Zero)
new_compare11(x0, x1, False)
new_ltEs16(EQ, EQ)
new_esEs19(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_lt4(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Ordering)
new_compare24(x0, x1, True)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(False, x0)
new_esEs15(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs30(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_compare9(Char(x0), Char(x1))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Double)
new_ltEs16(LT, GT)
new_ltEs16(GT, LT)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(x0, x1)
new_lt14(x0, x1)
new_lt20(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt13(x0, x1, x2, x3, x4)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_pePe(True, x0)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs8(Nothing, Nothing, x0)
new_primCompAux00(x0, LT)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare28(x0, x1, False, x2, x3)
new_ltEs18(False, False)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_lt11(x0, x1)
new_compare30(x0, x1, ty_Char)
new_primCompAux00(x0, EQ)
new_esEs24(x0, x1, ty_Double)
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs17([], :(x0, x1), x2)
new_compare30(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt12(x0, x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(Nothing, Nothing, False, x0)
new_esEs20(x0, x1, ty_Int)
new_esEs16(LT, LT)
new_esEs26(x0, x1, ty_Bool)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2, x3)
new_esEs22(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, ty_Double)
new_ltEs16(GT, GT)
new_esEs24(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Float)
new_compare30(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs6(x0, x1, ty_Char)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Zero, Succ(x0))
new_ltEs8(Nothing, Just(x0), x1)
new_compare13(x0, x1, True)
new_compare30(x0, x1, ty_Bool)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare27(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(Just(x0), Nothing, x1)
new_esEs20(x0, x1, ty_@0)
new_primCmpNat0(Zero, Zero)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt16(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_@0)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_fsEs(x0)
new_esEs8(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1)
new_esEs8(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs29(x0, x1, ty_Ordering)
new_compare110(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1, app(ty_[], x2))
new_esEs4(Nothing, Nothing, x0)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare18(x0, x1, False, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_compare33(x0, x1, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, ty_Double)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Bool)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_not(True)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Double)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_esEs16(EQ, LT)
new_esEs16(LT, EQ)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs16(EQ, EQ)
new_esEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_not(False)
new_compare31(x0, x1, x2)
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs18(False, True)
new_ltEs18(True, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_asAs(True, x0)
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Double)
new_lt4(x0, x1, ty_Char)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare25(Nothing, Just(x0), False, x1)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Char)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs11(Float(x0, x1), Float(x2, x3))
new_esEs25(x0, x1, ty_Char)
new_compare13(x0, x1, False)
new_ltEs20(x0, x1, ty_Float)
new_compare16(Float(x0, x1), Float(x2, x3))
new_lt4(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Int)
new_esEs16(EQ, GT)
new_esEs16(GT, EQ)
new_esEs9(Integer(x0), Integer(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs10(x0, x1)
new_esEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_compare29(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_primMulNat0(Zero, Succ(x0))
new_esEs23(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_compare27(x0, x1, False, x2, x3, x4)
new_compare30(x0, x1, ty_Double)
new_compare0([], [], x0)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare32(x0, x1, x2, x3)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Nothing, x1)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs19(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_compare0([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare30(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Bool)
new_esEs19(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_compare30(x0, x1, ty_@0)
new_esEs30(x0, x1, app(ty_Ratio, x2))

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_primPlusNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare12(x0, x1, True, x2)
new_esEs28(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs12(Double(x0, x1), Double(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs4(Nothing, Just(x0), x1)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(x0, x1, ty_Double)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare10(x0, x1, True, x2, x3)
new_esEs26(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare24(x0, x1, False)
new_asAs(False, x0)
new_esEs21(x0, x1, ty_Integer)
new_esEs17(:(x0, x1), [], x2)
new_compare15(x0, x1, x2, x3, x4)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs10(Char(x0), Char(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs26(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs9(x0, x1)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_lt15(x0, x1, x2)
new_esEs23(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17([], [], x0)
new_lt5(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs18(True, True)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_ltEs6(x0, x1, ty_Bool)
new_compare17(@0, @0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_lt4(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_ltEs7(x0, x1)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_primPlusNat1(x0, x1)
new_esEs28(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Double)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Integer)
new_ltEs6(x0, x1, ty_Ordering)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs8(x0, x1, ty_Char)
new_compare10(x0, x1, False, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primEqNat0(Zero, Zero)
new_lt6(x0, x1, x2)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare12(x0, x1, False, x2)
new_esEs19(x0, x1, ty_Int)
new_compare26(x0, x1, True)
new_ltEs6(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs6(x0, x1, ty_Integer)
new_compare26(x0, x1, False)
new_ltEs20(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_primMulNat0(Zero, Zero)
new_ltEs12(x0, x1, x2)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs24(x0, x1, ty_Char)
new_lt17(x0, x1, x2, x3)
new_esEs19(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Int)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare6(Integer(x0), Integer(x1))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare8(x0, x1)
new_lt20(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare23(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_sr(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs14(@0, @0)
new_compare19(x0, x1)
new_compare23(x0, x1, True, x2, x3)
new_compare18(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt4(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(x0, x1, x2)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, ty_Double)
new_esEs18(False, False)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_@0)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, GT)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Integer)
new_ltEs14(x0, x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare7(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_@0)
new_ltEs18(True, True)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_primPlusNat0(Zero, Zero)
new_compare11(x0, x1, False)
new_ltEs16(EQ, EQ)
new_esEs19(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_lt4(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Ordering)
new_compare24(x0, x1, True)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(False, x0)
new_esEs15(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs30(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_compare9(Char(x0), Char(x1))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Double)
new_ltEs16(LT, GT)
new_ltEs16(GT, LT)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(x0, x1)
new_lt14(x0, x1)
new_lt20(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt13(x0, x1, x2, x3, x4)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_pePe(True, x0)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs8(Nothing, Nothing, x0)
new_primCompAux00(x0, LT)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare28(x0, x1, False, x2, x3)
new_ltEs18(False, False)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_lt11(x0, x1)
new_compare30(x0, x1, ty_Char)
new_primCompAux00(x0, EQ)
new_esEs24(x0, x1, ty_Double)
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs17([], :(x0, x1), x2)
new_compare30(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt12(x0, x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Bool)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2, x3)
new_esEs22(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, ty_Double)
new_ltEs16(GT, GT)
new_esEs24(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Float)
new_compare30(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs6(x0, x1, ty_Char)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Zero, Succ(x0))
new_ltEs8(Nothing, Just(x0), x1)
new_compare13(x0, x1, True)
new_compare30(x0, x1, ty_Bool)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare27(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(Just(x0), Nothing, x1)
new_esEs20(x0, x1, ty_@0)
new_primCmpNat0(Zero, Zero)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt16(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_@0)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_fsEs(x0)
new_esEs8(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1)
new_esEs8(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs29(x0, x1, ty_Ordering)
new_compare110(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1, app(ty_[], x2))
new_esEs4(Nothing, Nothing, x0)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare18(x0, x1, False, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_compare33(x0, x1, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, ty_Double)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Bool)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_not(True)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Double)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_not(False)
new_compare31(x0, x1, x2)
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs18(False, True)
new_ltEs18(True, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_asAs(True, x0)
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Double)
new_lt4(x0, x1, ty_Char)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Char)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs11(Float(x0, x1), Float(x2, x3))
new_esEs25(x0, x1, ty_Char)
new_compare13(x0, x1, False)
new_ltEs20(x0, x1, ty_Float)
new_compare16(Float(x0, x1), Float(x2, x3))
new_lt4(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Int)
new_esEs9(Integer(x0), Integer(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs10(x0, x1)
new_esEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_compare29(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_primMulNat0(Zero, Succ(x0))
new_esEs23(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_compare27(x0, x1, False, x2, x3, x4)
new_compare30(x0, x1, ty_Double)
new_compare0([], [], x0)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare32(x0, x1, x2, x3)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Nothing, x1)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs19(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_compare0([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare30(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Bool)
new_esEs19(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_compare30(x0, x1, ty_@0)
new_esEs30(x0, x1, app(ty_Ratio, x2))



↳ 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_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu44, Nothing, xuu501, h, ba)
new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, False, h, ba) → new_addToFM_C10(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, new_esEs16(new_compare25(Nothing, Just(xuu400), False, h), GT), h, ba)
new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu43, Nothing, xuu501, h, ba)
new_addToFM_C(xuu3, Branch(Nothing, xuu41, xuu42, xuu43, xuu44), Nothing, xuu501, h, ba) → new_addToFM_C1(xuu3, xuu41, xuu42, xuu43, xuu44, xuu501, new_esEs16(new_compare25(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C1(xuu3, xuu41, xuu42, xuu43, xuu44, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu44, Nothing, xuu501, h, ba)
new_addToFM_C(xuu3, Branch(Just(xuu400), xuu41, xuu42, xuu43, xuu44), Nothing, xuu501, h, ba) → new_addToFM_C2(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu501, new_esEs16(new_compare25(Nothing, Just(xuu400), False, h), LT), h, ba)

The TRS R consists of the following rules:

new_compare25(Nothing, Just(xuu3400), False, baf) → LT
new_esEs16(GT, LT) → False
new_esEs16(EQ, LT) → False
new_esEs16(LT, LT) → True
new_esEs16(EQ, GT) → False
new_esEs16(LT, GT) → False
new_esEs16(GT, GT) → True
new_compare25(xuu330, xuu340, True, baf) → EQ

The set Q consists of the following terms:

new_compare25(x0, x1, True, x2)
new_compare25(Just(x0), Nothing, False, x1)
new_esEs16(LT, GT)
new_esEs16(GT, LT)
new_esEs16(GT, GT)
new_compare25(Just(x0), Just(x1), False, x2)
new_compare25(Nothing, Nothing, False, x0)
new_esEs16(LT, LT)
new_esEs16(EQ, LT)
new_esEs16(LT, EQ)
new_esEs16(EQ, EQ)
new_compare25(Nothing, Just(x0), False, x1)
new_esEs16(EQ, GT)
new_esEs16(GT, EQ)

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

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



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

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

new_addToFM_C11(xuu3, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu44, Just(xuu5000), xuu501, h, ba)
new_addToFM_C(xuu3, Branch(Just(xuu400), xuu41, xuu42, xuu43, xuu44), Just(xuu5000), xuu501, h, ba) → new_addToFM_C21(xuu3, xuu400, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs16(new_compare25(Just(xuu5000), Just(xuu400), new_esEs29(xuu5000, xuu400, h), h), LT), h, ba)
new_addToFM_C21(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, False, bb, bc) → new_addToFM_C12(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, new_esEs16(new_compare25(Just(xuu22), Just(xuu17), new_esEs30(xuu22, xuu17, bb), bb), GT), bb, bc)
new_addToFM_C21(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, bb, bc) → new_addToFM_C(xuu16, xuu20, Just(xuu22), xuu23, bb, bc)
new_addToFM_C20(xuu3, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, False, h, ba) → new_addToFM_C11(xuu3, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs16(new_compare25(Just(xuu5000), Nothing, False, h), GT), h, ba)
new_addToFM_C(xuu3, Branch(Nothing, xuu41, xuu42, xuu43, xuu44), Just(xuu5000), xuu501, h, ba) → new_addToFM_C20(xuu3, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, new_esEs16(new_compare25(Just(xuu5000), Nothing, False, h), LT), h, ba)
new_addToFM_C20(xuu3, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu501, True, h, ba) → new_addToFM_C(xuu3, xuu43, Just(xuu5000), xuu501, h, ba)
new_addToFM_C12(xuu16, xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, bb, bc) → new_addToFM_C(xuu16, xuu21, Just(xuu22), xuu23, bb, bc)

The TRS R consists of the following rules:

new_esEs4(Just(xuu50000), Just(xuu4000), app(ty_Maybe, cbh)) → new_esEs4(xuu50000, xuu4000, cbh)
new_ltEs19(xuu33002, xuu34002, app(app(ty_@2, gb), gc)) → new_ltEs5(xuu33002, xuu34002, gb, gc)
new_lt19(xuu33001, xuu34001, ty_Char) → new_lt7(xuu33001, xuu34001)
new_esEs16(EQ, GT) → False
new_esEs16(GT, EQ) → False
new_ltEs19(xuu33002, xuu34002, ty_Ordering) → new_ltEs16(xuu33002, xuu34002)
new_lt19(xuu33001, xuu34001, app(ty_Ratio, ge)) → new_lt10(xuu33001, xuu34001, ge)
new_ltEs16(GT, GT) → True
new_esEs20(xuu33000, xuu34000, ty_Ordering) → new_esEs16(xuu33000, xuu34000)
new_lt5(xuu33000, xuu34000) → new_esEs16(new_compare6(xuu33000, xuu34000), LT)
new_compare9(Char(xuu33000), Char(xuu34000)) → new_primCmpNat0(xuu33000, xuu34000)
new_esEs26(xuu50000, xuu4000, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_esEs24(xuu50000, xuu4000, app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs5(xuu50000, xuu4000, bgd, bge, bgf)
new_ltEs10(xuu3300, xuu3400) → new_fsEs(new_compare16(xuu3300, xuu3400))
new_lt4(xuu33000, xuu34000, ty_Ordering) → new_lt14(xuu33000, xuu34000)
new_compare10(xuu33000, xuu34000, True, ed, ee) → LT
new_esEs4(Just(xuu50000), Nothing, cbe) → False
new_esEs4(Nothing, Just(xuu4000), cbe) → False
new_esEs24(xuu50000, xuu4000, app(ty_Maybe, bfg)) → new_esEs4(xuu50000, xuu4000, bfg)
new_lt19(xuu33001, xuu34001, ty_Integer) → new_lt5(xuu33001, xuu34001)
new_lt4(xuu33000, xuu34000, ty_Char) → new_lt7(xuu33000, xuu34000)
new_ltEs16(LT, GT) → True
new_lt14(xuu33000, xuu34000) → new_esEs16(new_compare8(xuu33000, xuu34000), LT)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs14(xuu50000, xuu4000)
new_lt4(xuu33000, xuu34000, app(app(ty_@2, eb), ec)) → new_lt18(xuu33000, xuu34000, eb, ec)
new_ltEs19(xuu33002, xuu34002, ty_Double) → new_ltEs11(xuu33002, xuu34002)
new_esEs20(xuu33000, xuu34000, ty_Double) → new_esEs12(xuu33000, xuu34000)
new_esEs29(xuu5000, xuu400, ty_Ordering) → new_esEs16(xuu5000, xuu400)
new_esEs23(xuu50000, xuu4000, app(ty_[], bee)) → new_esEs17(xuu50000, xuu4000, bee)
new_lt19(xuu33001, xuu34001, ty_Ordering) → new_lt14(xuu33001, xuu34001)
new_ltEs19(xuu33002, xuu34002, app(ty_Ratio, fb)) → new_ltEs12(xuu33002, xuu34002, fb)
new_primMulNat0(Zero, Zero) → Zero
new_esEs25(xuu50001, xuu4001, ty_Double) → new_esEs12(xuu50001, xuu4001)
new_compare16(Float(xuu33000, xuu33001), Float(xuu34000, xuu34001)) → new_compare7(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(app(ty_@2, cac), cad)) → new_esEs7(xuu50000, xuu4000, cac, cad)
new_esEs23(xuu50000, xuu4000, app(ty_Ratio, beh)) → new_esEs13(xuu50000, xuu4000, beh)
new_esEs25(xuu50001, xuu4001, app(app(ty_Either, cdf), cdg)) → new_esEs6(xuu50001, xuu4001, cdf, cdg)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs12(xuu50000, xuu4000)
new_esEs20(xuu33000, xuu34000, app(ty_Maybe, hf)) → new_esEs4(xuu33000, xuu34000, hf)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(app(ty_@2, cgf), cgg)) → new_ltEs5(xuu33000, xuu34000, cgf, cgg)
new_compare25(xuu330, xuu340, True, baf) → EQ
new_ltEs20(xuu3300, xuu3400, app(ty_Maybe, bag)) → new_ltEs8(xuu3300, xuu3400, bag)
new_esEs8(xuu33000, xuu34000, ty_Double) → new_esEs12(xuu33000, xuu34000)
new_esEs20(xuu33000, xuu34000, ty_Bool) → new_esEs18(xuu33000, xuu34000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Double) → new_ltEs11(xuu33000, xuu34000)
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_ltEs6(xuu33001, xuu34001, app(ty_Ratio, bh)) → new_ltEs12(xuu33001, xuu34001, bh)
new_esEs24(xuu50000, xuu4000, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_esEs23(xuu50000, xuu4000, app(ty_Maybe, bed)) → new_esEs4(xuu50000, xuu4000, bed)
new_ltEs19(xuu33002, xuu34002, ty_Bool) → new_ltEs18(xuu33002, xuu34002)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_esEs20(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_lt4(xuu33000, xuu34000, app(ty_[], dg)) → new_lt15(xuu33000, xuu34000, dg)
new_compare30(xuu33000, xuu34000, app(ty_Ratio, cha)) → new_compare14(xuu33000, xuu34000, cha)
new_ltEs19(xuu33002, xuu34002, ty_@0) → new_ltEs13(xuu33002, xuu34002)
new_esEs20(xuu33000, xuu34000, app(ty_Ratio, hg)) → new_esEs13(xuu33000, xuu34000, hg)
new_esEs21(xuu50002, xuu4002, ty_Int) → new_esEs15(xuu50002, xuu4002)
new_compare0(:(xuu33000, xuu33001), :(xuu34000, xuu34001), bd) → new_primCompAux0(xuu33000, xuu34000, new_compare0(xuu33001, xuu34001, bd), bd)
new_lt19(xuu33001, xuu34001, ty_Int) → new_lt12(xuu33001, xuu34001)
new_esEs20(xuu33000, xuu34000, ty_Char) → new_esEs10(xuu33000, xuu34000)
new_esEs22(xuu50001, xuu4001, ty_Integer) → new_esEs9(xuu50001, xuu4001)
new_esEs21(xuu50002, xuu4002, app(app(ty_Either, bcb), bcc)) → new_esEs6(xuu50002, xuu4002, bcb, bcc)
new_compare30(xuu33000, xuu34000, app(app(app(ty_@3, chb), chc), chd)) → new_compare15(xuu33000, xuu34000, chb, chc, chd)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(ty_Maybe, dbf), bbb) → new_ltEs8(xuu33000, xuu34000, dbf)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Ordering) → new_ltEs16(xuu33000, xuu34000)
new_esEs8(xuu33000, xuu34000, app(app(ty_Either, dh), ea)) → new_esEs6(xuu33000, xuu34000, dh, ea)
new_esEs19(xuu33001, xuu34001, app(app(app(ty_@3, gf), gg), gh)) → new_esEs5(xuu33001, xuu34001, gf, gg, gh)
new_esEs19(xuu33001, xuu34001, ty_@0) → new_esEs14(xuu33001, xuu34001)
new_esEs26(xuu50000, xuu4000, app(ty_Maybe, cef)) → new_esEs4(xuu50000, xuu4000, cef)
new_esEs19(xuu33001, xuu34001, ty_Ordering) → new_esEs16(xuu33001, xuu34001)
new_lt4(xuu33000, xuu34000, app(ty_Maybe, db)) → new_lt6(xuu33000, xuu34000, db)
new_esEs20(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Float, bha) → new_esEs11(xuu50000, xuu4000)
new_ltEs19(xuu33002, xuu34002, app(app(ty_Either, fh), ga)) → new_ltEs4(xuu33002, xuu34002, fh, ga)
new_pePe(False, xuu162) → xuu162
new_esEs25(xuu50001, xuu4001, app(app(ty_@2, cdb), cdc)) → new_esEs7(xuu50001, xuu4001, cdb, cdc)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Double, bbb) → new_ltEs11(xuu33000, xuu34000)
new_ltEs14(xuu3300, xuu3400) → new_fsEs(new_compare7(xuu3300, xuu3400))
new_ltEs19(xuu33002, xuu34002, ty_Float) → new_ltEs10(xuu33002, xuu34002)
new_esEs15(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_ltEs20(xuu3300, xuu3400, app(app(ty_Either, bba), bbb)) → new_ltEs4(xuu3300, xuu3400, bba, bbb)
new_ltEs16(EQ, GT) → True
new_lt20(xuu33000, xuu34000, app(app(app(ty_@3, hh), baa), bab)) → new_lt13(xuu33000, xuu34000, hh, baa, bab)
new_esEs7(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), cch, cda) → new_asAs(new_esEs26(xuu50000, xuu4000, cch), new_esEs25(xuu50001, xuu4001, cda))
new_esEs8(xuu33000, xuu34000, ty_Char) → new_esEs10(xuu33000, xuu34000)
new_compare25(Just(xuu3300), Just(xuu3400), False, baf) → new_compare12(xuu3300, xuu3400, new_ltEs20(xuu3300, xuu3400, baf), baf)
new_ltEs20(xuu3300, xuu3400, app(app(app(ty_@3, ef), eg), eh)) → new_ltEs15(xuu3300, xuu3400, ef, eg, eh)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(app(ty_Either, ddf), ddg)) → new_ltEs4(xuu33000, xuu34000, ddf, ddg)
new_lt4(xuu33000, xuu34000, ty_Float) → new_lt8(xuu33000, xuu34000)
new_esEs29(xuu5000, xuu400, app(ty_Ratio, dac)) → new_esEs13(xuu5000, xuu400, dac)
new_ltEs4(Left(xuu33000), Right(xuu34000), bba, bbb) → True
new_primCmpNat0(Zero, Succ(xuu3400)) → LT
new_esEs26(xuu50000, xuu4000, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_ltEs8(Nothing, Just(xuu34000), bag) → True
new_esEs6(Right(xuu50000), Left(xuu4000), cab, bha) → False
new_esEs6(Left(xuu50000), Right(xuu4000), cab, bha) → False
new_lt6(xuu33000, xuu34000, hf) → new_esEs16(new_compare31(xuu33000, xuu34000, hf), LT)
new_esEs19(xuu33001, xuu34001, app(ty_[], ha)) → new_esEs17(xuu33001, xuu34001, ha)
new_esEs19(xuu33001, xuu34001, app(ty_Maybe, gd)) → new_esEs4(xuu33001, xuu34001, gd)
new_esEs21(xuu50002, xuu4002, app(ty_Ratio, bcd)) → new_esEs13(xuu50002, xuu4002, bcd)
new_compare27(xuu33000, xuu34000, False, hh, baa, bab) → new_compare110(xuu33000, xuu34000, new_ltEs15(xuu33000, xuu34000, hh, baa, bab), hh, baa, bab)
new_esEs29(xuu5000, xuu400, app(app(ty_@2, cch), cda)) → new_esEs7(xuu5000, xuu400, cch, cda)
new_esEs29(xuu5000, xuu400, ty_Char) → new_esEs10(xuu5000, xuu400)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs11(xuu50000, xuu4000)
new_esEs25(xuu50001, xuu4001, app(ty_Ratio, cdh)) → new_esEs13(xuu50001, xuu4001, cdh)
new_ltEs6(xuu33001, xuu34001, ty_Double) → new_ltEs11(xuu33001, xuu34001)
new_compare0([], [], bd) → EQ
new_pePe(True, xuu162) → True
new_primEqNat0(Zero, Zero) → True
new_lt20(xuu33000, xuu34000, app(ty_Maybe, hf)) → new_lt6(xuu33000, xuu34000, hf)
new_compare26(xuu33000, xuu34000, True) → EQ
new_esEs19(xuu33001, xuu34001, app(ty_Ratio, ge)) → new_esEs13(xuu33001, xuu34001, ge)
new_ltEs6(xuu33001, xuu34001, ty_Ordering) → new_ltEs16(xuu33001, xuu34001)
new_ltEs6(xuu33001, xuu34001, app(app(app(ty_@3, ca), cb), cc)) → new_ltEs15(xuu33001, xuu34001, ca, cb, cc)
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), bbc, bbd, bbe) → new_asAs(new_esEs23(xuu50000, xuu4000, bbc), new_asAs(new_esEs22(xuu50001, xuu4001, bbd), new_esEs21(xuu50002, xuu4002, bbe)))
new_compare17(@0, @0) → EQ
new_esEs23(xuu50000, xuu4000, app(app(ty_Either, bef), beg)) → new_esEs6(xuu50000, xuu4000, bef, beg)
new_esEs14(@0, @0) → True
new_primMulNat0(Succ(xuu5000000), Succ(xuu400000)) → new_primPlusNat1(new_primMulNat0(xuu5000000, Succ(xuu400000)), xuu400000)
new_esEs17(:(xuu50000, xuu50001), :(xuu4000, xuu4001), bfd) → new_asAs(new_esEs24(xuu50000, xuu4000, bfd), new_esEs17(xuu50001, xuu4001, bfd))
new_lt12(xuu330, xuu340) → new_esEs16(new_compare7(xuu330, xuu340), LT)
new_compare30(xuu33000, xuu34000, ty_Int) → new_compare7(xuu33000, xuu34000)
new_esEs25(xuu50001, xuu4001, ty_Bool) → new_esEs18(xuu50001, xuu4001)
new_esEs23(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_esEs16(LT, GT) → False
new_esEs16(GT, LT) → False
new_compare32(xuu33000, xuu34000, ed, ee) → new_compare23(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, ed, ee), ed, ee)
new_esEs26(xuu50000, xuu4000, app(ty_Ratio, cfb)) → new_esEs13(xuu50000, xuu4000, cfb)
new_compare30(xuu33000, xuu34000, ty_Ordering) → new_compare8(xuu33000, xuu34000)
new_esEs22(xuu50001, xuu4001, app(app(ty_@2, bch), bda)) → new_esEs7(xuu50001, xuu4001, bch, bda)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(app(ty_Either, cag), cah)) → new_esEs6(xuu50000, xuu4000, cag, cah)
new_esEs25(xuu50001, xuu4001, ty_Int) → new_esEs15(xuu50001, xuu4001)
new_esEs24(xuu50000, xuu4000, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_ltEs16(EQ, LT) → False
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Char, bbb) → new_ltEs9(xuu33000, xuu34000)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_compare12(xuu129, xuu130, False, dab) → GT
new_ltEs16(GT, EQ) → False
new_sr(xuu50000, xuu4000) → new_primMulInt(xuu50000, xuu4000)
new_compare7(xuu33, xuu34) → new_primCmpInt(xuu33, xuu34)
new_esEs24(xuu50000, xuu4000, app(app(ty_@2, bfe), bff)) → new_esEs7(xuu50000, xuu4000, bfe, bff)
new_esEs20(xuu33000, xuu34000, ty_Integer) → new_esEs9(xuu33000, xuu34000)
new_lt20(xuu33000, xuu34000, ty_Ordering) → new_lt14(xuu33000, xuu34000)
new_esEs23(xuu50000, xuu4000, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_esEs26(xuu50000, xuu4000, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_ltEs19(xuu33002, xuu34002, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs15(xuu33002, xuu34002, fc, fd, ff)
new_lt20(xuu33000, xuu34000, app(app(ty_Either, ed), ee)) → new_lt17(xuu33000, xuu34000, ed, ee)
new_ltEs20(xuu3300, xuu3400, ty_Int) → new_ltEs14(xuu3300, xuu3400)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Int, bha) → new_esEs15(xuu50000, xuu4000)
new_lt20(xuu33000, xuu34000, app(app(ty_@2, bad), bae)) → new_lt18(xuu33000, xuu34000, bad, bae)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_esEs24(xuu50000, xuu4000, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_ltEs12(xuu3300, xuu3400, bah) → new_fsEs(new_compare14(xuu3300, xuu3400, bah))
new_ltEs20(xuu3300, xuu3400, ty_Char) → new_ltEs9(xuu3300, xuu3400)
new_ltEs16(LT, EQ) → True
new_esEs23(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_esEs19(xuu33001, xuu34001, ty_Bool) → new_esEs18(xuu33001, xuu34001)
new_esEs30(xuu22, xuu17, app(ty_Maybe, daf)) → new_esEs4(xuu22, xuu17, daf)
new_compare25(Just(xuu3300), Nothing, False, baf) → GT
new_compare13(xuu33000, xuu34000, False) → GT
new_esEs22(xuu50001, xuu4001, ty_Int) → new_esEs15(xuu50001, xuu4001)
new_compare25(Nothing, Nothing, False, baf) → LT
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Float, bbb) → new_ltEs10(xuu33000, xuu34000)
new_esEs20(xuu33000, xuu34000, ty_Int) → new_esEs15(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, ty_Integer) → new_esEs9(xuu22, xuu17)
new_ltEs18(True, True) → True
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Integer, bha) → new_esEs9(xuu50000, xuu4000)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt8(xuu33000, xuu34000) → new_esEs16(new_compare16(xuu33000, xuu34000), LT)
new_esEs21(xuu50002, xuu4002, app(app(ty_@2, bbf), bbg)) → new_esEs7(xuu50002, xuu4002, bbf, bbg)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Integer) → new_ltEs7(xuu33000, xuu34000)
new_lt4(xuu33000, xuu34000, app(ty_Ratio, dc)) → new_lt10(xuu33000, xuu34000, dc)
new_esEs8(xuu33000, xuu34000, app(ty_Ratio, dc)) → new_esEs13(xuu33000, xuu34000, dc)
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_ltEs4(Left(xuu33000), Left(xuu34000), app(app(ty_Either, dcd), dce), bbb) → new_ltEs4(xuu33000, xuu34000, dcd, dce)
new_ltEs18(False, False) → True
new_lt4(xuu33000, xuu34000, app(app(app(ty_@3, dd), de), df)) → new_lt13(xuu33000, xuu34000, dd, de, df)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(ty_[], caf)) → new_esEs17(xuu50000, xuu4000, caf)
new_ltEs19(xuu33002, xuu34002, ty_Int) → new_ltEs14(xuu33002, xuu34002)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_esEs24(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_lt9(xuu33000, xuu34000) → new_esEs16(new_compare29(xuu33000, xuu34000), LT)
new_ltEs17(xuu3300, xuu3400, bd) → new_fsEs(new_compare0(xuu3300, xuu3400, bd))
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Char, bha) → new_esEs10(xuu50000, xuu4000)
new_compare14(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Int) → new_compare7(new_sr(xuu33000, xuu34001), new_sr(xuu34000, xuu33001))
new_esEs22(xuu50001, xuu4001, app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs5(xuu50001, xuu4001, bdg, bdh, bea)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Integer) → new_ltEs7(xuu33000, xuu34000)
new_esEs21(xuu50002, xuu4002, ty_Ordering) → new_esEs16(xuu50002, xuu4002)
new_ltEs13(xuu3300, xuu3400) → new_fsEs(new_compare17(xuu3300, xuu3400))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs8(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_ltEs20(xuu3300, xuu3400, ty_Bool) → new_ltEs18(xuu3300, xuu3400)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_ltEs16(GT, LT) → False
new_ltEs20(xuu3300, xuu3400, app(app(ty_@2, be), bf)) → new_ltEs5(xuu3300, xuu3400, be, bf)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Bool, bbb) → new_ltEs18(xuu33000, xuu34000)
new_primCmpNat0(Succ(xuu3300), Succ(xuu3400)) → new_primCmpNat0(xuu3300, xuu3400)
new_esEs9(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_esEs22(xuu50001, xuu4001, app(ty_Maybe, bdb)) → new_esEs4(xuu50001, xuu4001, bdb)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Int, bbb) → new_ltEs14(xuu33000, xuu34000)
new_esEs25(xuu50001, xuu4001, app(ty_Maybe, cdd)) → new_esEs4(xuu50001, xuu4001, cdd)
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_compare10(xuu33000, xuu34000, False, ed, ee) → GT
new_lt18(xuu33000, xuu34000, bad, bae) → new_esEs16(new_compare33(xuu33000, xuu34000, bad, bae), LT)
new_esEs4(Just(xuu50000), Just(xuu4000), app(app(ty_Either, ccb), ccc)) → new_esEs6(xuu50000, xuu4000, ccb, ccc)
new_esEs6(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, bhg), bhh), caa), bha) → new_esEs5(xuu50000, xuu4000, bhg, bhh, caa)
new_lt13(xuu33000, xuu34000, hh, baa, bab) → new_esEs16(new_compare15(xuu33000, xuu34000, hh, baa, bab), LT)
new_lt10(xuu33000, xuu34000, hg) → new_esEs16(new_compare14(xuu33000, xuu34000, hg), LT)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Float) → new_ltEs10(xuu33000, xuu34000)
new_esEs19(xuu33001, xuu34001, app(app(ty_Either, hb), hc)) → new_esEs6(xuu33001, xuu34001, hb, hc)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(ty_Maybe, cae)) → new_esEs4(xuu50000, xuu4000, cae)
new_esEs25(xuu50001, xuu4001, ty_Char) → new_esEs10(xuu50001, xuu4001)
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs20(xuu3300, xuu3400, app(ty_[], bd)) → new_ltEs17(xuu3300, xuu3400, bd)
new_esEs6(Left(xuu50000), Left(xuu4000), app(ty_[], bhc), bha) → new_esEs17(xuu50000, xuu4000, bhc)
new_ltEs9(xuu3300, xuu3400) → new_fsEs(new_compare9(xuu3300, xuu3400))
new_esEs4(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, cce), ccf), ccg)) → new_esEs5(xuu50000, xuu4000, cce, ccf, ccg)
new_compare30(xuu33000, xuu34000, ty_@0) → new_compare17(xuu33000, xuu34000)
new_esEs8(xuu33000, xuu34000, ty_Bool) → new_esEs18(xuu33000, xuu34000)
new_primCompAux00(xuu179, LT) → LT
new_primCmpInt(Neg(Succ(xuu3300)), Neg(xuu340)) → new_primCmpNat0(xuu340, Succ(xuu3300))
new_ltEs19(xuu33002, xuu34002, app(ty_[], fg)) → new_ltEs17(xuu33002, xuu34002, fg)
new_ltEs8(Just(xuu33000), Nothing, bag) → False
new_ltEs6(xuu33001, xuu34001, app(ty_[], cd)) → new_ltEs17(xuu33001, xuu34001, cd)
new_esEs8(xuu33000, xuu34000, app(app(ty_@2, eb), ec)) → new_esEs7(xuu33000, xuu34000, eb, ec)
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_ltEs5(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), be, bf) → new_pePe(new_lt4(xuu33000, xuu34000, be), new_asAs(new_esEs8(xuu33000, xuu34000, be), new_ltEs6(xuu33001, xuu34001, bf)))
new_primPlusNat0(Succ(xuu28200), Zero) → Succ(xuu28200)
new_primPlusNat0(Zero, Succ(xuu9700)) → Succ(xuu9700)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu3300), Zero) → GT
new_esEs19(xuu33001, xuu34001, ty_Integer) → new_esEs9(xuu33001, xuu34001)
new_esEs8(xuu33000, xuu34000, app(app(app(ty_@3, dd), de), df)) → new_esEs5(xuu33000, xuu34000, dd, de, df)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3400))) → LT
new_esEs6(Left(xuu50000), Left(xuu4000), ty_@0, bha) → new_esEs14(xuu50000, xuu4000)
new_esEs22(xuu50001, xuu4001, ty_Bool) → new_esEs18(xuu50001, xuu4001)
new_esEs22(xuu50001, xuu4001, app(ty_Ratio, bdf)) → new_esEs13(xuu50001, xuu4001, bdf)
new_compare31(xuu33000, xuu34000, hf) → new_compare25(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, hf), hf)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs9(xuu50001, xuu4001)
new_esEs30(xuu22, xuu17, ty_Bool) → new_esEs18(xuu22, xuu17)
new_sr0(Integer(xuu340000), Integer(xuu330010)) → Integer(new_primMulInt(xuu340000, xuu330010))
new_compare13(xuu33000, xuu34000, True) → LT
new_compare6(Integer(xuu33000), Integer(xuu34000)) → new_primCmpInt(xuu33000, xuu34000)
new_compare12(xuu129, xuu130, True, dab) → LT
new_compare28(xuu33000, xuu34000, True, bad, bae) → EQ
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_lt19(xuu33001, xuu34001, app(ty_Maybe, gd)) → new_lt6(xuu33001, xuu34001, gd)
new_esEs24(xuu50000, xuu4000, app(ty_Ratio, bgc)) → new_esEs13(xuu50000, xuu4000, bgc)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Bool, bha) → new_esEs18(xuu50000, xuu4000)
new_esEs6(Left(xuu50000), Left(xuu4000), app(ty_Maybe, bhb), bha) → new_esEs4(xuu50000, xuu4000, bhb)
new_ltEs6(xuu33001, xuu34001, app(ty_Maybe, bg)) → new_ltEs8(xuu33001, xuu34001, bg)
new_esEs29(xuu5000, xuu400, ty_@0) → new_esEs14(xuu5000, xuu400)
new_esEs12(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs15(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_compare30(xuu33000, xuu34000, app(app(ty_Either, chf), chg)) → new_compare32(xuu33000, xuu34000, chf, chg)
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_esEs10(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_esEs26(xuu50000, xuu4000, app(ty_[], ceg)) → new_esEs17(xuu50000, xuu4000, ceg)
new_primCompAux00(xuu179, EQ) → xuu179
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3400))) → new_primCmpNat0(Zero, Succ(xuu3400))
new_compare30(xuu33000, xuu34000, app(ty_Maybe, cgh)) → new_compare31(xuu33000, xuu34000, cgh)
new_compare15(xuu33000, xuu34000, hh, baa, bab) → new_compare27(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, hh, baa, bab), hh, baa, bab)
new_compare24(xuu33000, xuu34000, True) → EQ
new_esEs25(xuu50001, xuu4001, ty_@0) → new_esEs14(xuu50001, xuu4001)
new_esEs23(xuu50000, xuu4000, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(ty_[], dcc), bbb) → new_ltEs17(xuu33000, xuu34000, dcc)
new_ltEs16(EQ, EQ) → True
new_lt19(xuu33001, xuu34001, ty_@0) → new_lt11(xuu33001, xuu34001)
new_compare25(Nothing, Just(xuu3400), False, baf) → LT
new_esEs29(xuu5000, xuu400, ty_Double) → new_esEs12(xuu5000, xuu400)
new_esEs21(xuu50002, xuu4002, app(ty_[], bca)) → new_esEs17(xuu50002, xuu4002, bca)
new_esEs8(xuu33000, xuu34000, ty_Int) → new_esEs15(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, app(app(ty_Either, dah), dba)) → new_esEs6(xuu22, xuu17, dah, dba)
new_esEs6(Left(xuu50000), Left(xuu4000), app(app(ty_@2, bgg), bgh), bha) → new_esEs7(xuu50000, xuu4000, bgg, bgh)
new_esEs23(xuu50000, xuu4000, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_esEs30(xuu22, xuu17, ty_Int) → new_esEs15(xuu22, xuu17)
new_not(False) → True
new_ltEs4(Right(xuu33000), Left(xuu34000), bba, bbb) → False
new_esEs6(Left(xuu50000), Left(xuu4000), app(app(ty_Either, bhd), bhe), bha) → new_esEs6(xuu50000, xuu4000, bhd, bhe)
new_ltEs6(xuu33001, xuu34001, ty_Char) → new_ltEs9(xuu33001, xuu34001)
new_esEs30(xuu22, xuu17, ty_@0) → new_esEs14(xuu22, xuu17)
new_esEs23(xuu50000, xuu4000, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_esEs30(xuu22, xuu17, ty_Double) → new_esEs12(xuu22, xuu17)
new_primCmpInt(Pos(Succ(xuu3300)), Pos(xuu340)) → new_primCmpNat0(Succ(xuu3300), xuu340)
new_esEs19(xuu33001, xuu34001, app(app(ty_@2, hd), he)) → new_esEs7(xuu33001, xuu34001, hd, he)
new_esEs22(xuu50001, xuu4001, ty_Float) → new_esEs11(xuu50001, xuu4001)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Double) → new_ltEs11(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, app(app(ty_@2, dad), dae)) → new_esEs7(xuu22, xuu17, dad, dae)
new_esEs29(xuu5000, xuu400, app(ty_[], bfd)) → new_esEs17(xuu5000, xuu400, bfd)
new_esEs24(xuu50000, xuu4000, app(app(ty_Either, bga), bgb)) → new_esEs6(xuu50000, xuu4000, bga, bgb)
new_esEs16(LT, EQ) → False
new_esEs16(EQ, LT) → False
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Ordering) → new_ltEs16(xuu33000, xuu34000)
new_esEs19(xuu33001, xuu34001, ty_Double) → new_esEs12(xuu33001, xuu34001)
new_compare14(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Integer) → new_compare6(new_sr0(xuu33000, xuu34001), new_sr0(xuu34000, xuu33001))
new_lt4(xuu33000, xuu34000, ty_Double) → new_lt9(xuu33000, xuu34000)
new_compare0(:(xuu33000, xuu33001), [], bd) → GT
new_lt19(xuu33001, xuu34001, app(app(ty_@2, hd), he)) → new_lt18(xuu33001, xuu34001, hd, he)
new_esEs24(xuu50000, xuu4000, app(ty_[], bfh)) → new_esEs17(xuu50000, xuu4000, bfh)
new_esEs29(xuu5000, xuu400, ty_Int) → new_esEs15(xuu5000, xuu400)
new_lt4(xuu33000, xuu34000, app(app(ty_Either, dh), ea)) → new_lt17(xuu33000, xuu34000, dh, ea)
new_lt20(xuu33000, xuu34000, ty_Double) → new_lt9(xuu33000, xuu34000)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs15(xuu50000, xuu4000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Float) → new_ltEs10(xuu33000, xuu34000)
new_esEs24(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_esEs30(xuu22, xuu17, app(ty_[], dag)) → new_esEs17(xuu22, xuu17, dag)
new_esEs20(xuu33000, xuu34000, app(app(app(ty_@3, hh), baa), bab)) → new_esEs5(xuu33000, xuu34000, hh, baa, bab)
new_primCmpInt(Pos(Succ(xuu3300)), Neg(xuu340)) → GT
new_esEs21(xuu50002, xuu4002, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs5(xuu50002, xuu4002, bce, bcf, bcg)
new_esEs29(xuu5000, xuu400, ty_Integer) → new_esEs9(xuu5000, xuu400)
new_lt19(xuu33001, xuu34001, app(ty_[], ha)) → new_lt15(xuu33001, xuu34001, ha)
new_ltEs6(xuu33001, xuu34001, ty_Integer) → new_ltEs7(xuu33001, xuu34001)
new_primMulInt(Pos(xuu500000), Pos(xuu40000)) → Pos(new_primMulNat0(xuu500000, xuu40000))
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(ty_[], dde)) → new_ltEs17(xuu33000, xuu34000, dde)
new_ltEs6(xuu33001, xuu34001, app(app(ty_Either, ce), cf)) → new_ltEs4(xuu33001, xuu34001, ce, cf)
new_primMulInt(Neg(xuu500000), Neg(xuu40000)) → Pos(new_primMulNat0(xuu500000, xuu40000))
new_ltEs19(xuu33002, xuu34002, app(ty_Maybe, fa)) → new_ltEs8(xuu33002, xuu34002, fa)
new_esEs21(xuu50002, xuu4002, ty_Char) → new_esEs10(xuu50002, xuu4002)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Ordering, bha) → new_esEs16(xuu50000, xuu4000)
new_esEs16(EQ, EQ) → True
new_esEs26(xuu50000, xuu4000, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_primEqNat0(Succ(xuu500000), Zero) → False
new_compare8(xuu33000, xuu34000) → new_compare24(xuu33000, xuu34000, new_esEs16(xuu33000, xuu34000))
new_primPlusNat0(Zero, Zero) → Zero
new_esEs26(xuu50000, xuu4000, app(app(ty_@2, ced), cee)) → new_esEs7(xuu50000, xuu4000, ced, cee)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare23(xuu33000, xuu34000, False, ed, ee) → new_compare10(xuu33000, xuu34000, new_ltEs4(xuu33000, xuu34000, ed, ee), ed, ee)
new_esEs4(Nothing, Nothing, cbe) → True
new_esEs4(Just(xuu50000), Just(xuu4000), app(ty_Ratio, ccd)) → new_esEs13(xuu50000, xuu4000, ccd)
new_esEs20(xuu33000, xuu34000, app(ty_[], bac)) → new_esEs17(xuu33000, xuu34000, bac)
new_esEs20(xuu33000, xuu34000, app(app(ty_Either, ed), ee)) → new_esEs6(xuu33000, xuu34000, ed, ee)
new_ltEs6(xuu33001, xuu34001, ty_Float) → new_ltEs10(xuu33001, xuu34001)
new_esEs22(xuu50001, xuu4001, app(ty_[], bdc)) → new_esEs17(xuu50001, xuu4001, bdc)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(app(ty_Either, cgd), cge)) → new_ltEs4(xuu33000, xuu34000, cgd, cge)
new_esEs29(xuu5000, xuu400, app(app(ty_Either, cab), bha)) → new_esEs6(xuu5000, xuu400, cab, bha)
new_ltEs20(xuu3300, xuu3400, ty_Ordering) → new_ltEs16(xuu3300, xuu3400)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Int) → new_ltEs14(xuu33000, xuu34000)
new_ltEs19(xuu33002, xuu34002, ty_Char) → new_ltEs9(xuu33002, xuu34002)
new_ltEs15(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), ef, eg, eh) → new_pePe(new_lt20(xuu33000, xuu34000, ef), new_asAs(new_esEs20(xuu33000, xuu34000, ef), new_pePe(new_lt19(xuu33001, xuu34001, eg), new_asAs(new_esEs19(xuu33001, xuu34001, eg), new_ltEs19(xuu33002, xuu34002, eh)))))
new_esEs8(xuu33000, xuu34000, ty_Ordering) → new_esEs16(xuu33000, xuu34000)
new_lt20(xuu33000, xuu34000, ty_Int) → new_lt12(xuu33000, xuu34000)
new_esEs29(xuu5000, xuu400, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs5(xuu5000, xuu400, bbc, bbd, bbe)
new_lt19(xuu33001, xuu34001, app(app(ty_Either, hb), hc)) → new_lt17(xuu33001, xuu34001, hb, hc)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3400))) → new_primCmpNat0(Succ(xuu3400), Zero)
new_compare23(xuu33000, xuu34000, True, ed, ee) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3400))) → GT
new_lt4(xuu33000, xuu34000, ty_@0) → new_lt11(xuu33000, xuu34000)
new_lt20(xuu33000, xuu34000, ty_Char) → new_lt7(xuu33000, xuu34000)
new_esEs6(Left(xuu50000), Left(xuu4000), app(ty_Ratio, bhf), bha) → new_esEs13(xuu50000, xuu4000, bhf)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(ty_Ratio, dbg), bbb) → new_ltEs12(xuu33000, xuu34000, dbg)
new_esEs26(xuu50000, xuu4000, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(app(app(ty_@3, ddb), ddc), ddd)) → new_ltEs15(xuu33000, xuu34000, ddb, ddc, ddd)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_esEs19(xuu33001, xuu34001, ty_Float) → new_esEs11(xuu33001, xuu34001)
new_compare30(xuu33000, xuu34000, ty_Float) → new_compare16(xuu33000, xuu34000)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Integer, bbb) → new_ltEs7(xuu33000, xuu34000)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(ty_[], cgc)) → new_ltEs17(xuu33000, xuu34000, cgc)
new_esEs21(xuu50002, xuu4002, app(ty_Maybe, bbh)) → new_esEs4(xuu50002, xuu4002, bbh)
new_compare18(xuu33000, xuu34000, True, bad, bae) → LT
new_ltEs6(xuu33001, xuu34001, app(app(ty_@2, cg), da)) → new_ltEs5(xuu33001, xuu34001, cg, da)
new_esEs25(xuu50001, xuu4001, ty_Ordering) → new_esEs16(xuu50001, xuu4001)
new_compare19(xuu33000, xuu34000) → new_compare26(xuu33000, xuu34000, new_esEs18(xuu33000, xuu34000))
new_lt19(xuu33001, xuu34001, ty_Double) → new_lt9(xuu33001, xuu34001)
new_compare26(xuu33000, xuu34000, False) → new_compare13(xuu33000, xuu34000, new_ltEs18(xuu33000, xuu34000))
new_lt17(xuu33000, xuu34000, ed, ee) → new_esEs16(new_compare32(xuu33000, xuu34000, ed, ee), LT)
new_esEs23(xuu50000, xuu4000, ty_@0) → new_esEs14(xuu50000, xuu4000)
new_primCompAux0(xuu33000, xuu34000, xuu173, bd) → new_primCompAux00(xuu173, new_compare30(xuu33000, xuu34000, bd))
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt20(xuu33000, xuu34000, app(ty_[], bac)) → new_lt15(xuu33000, xuu34000, bac)
new_esEs21(xuu50002, xuu4002, ty_@0) → new_esEs14(xuu50002, xuu4002)
new_esEs6(Left(xuu50000), Left(xuu4000), ty_Double, bha) → new_esEs12(xuu50000, xuu4000)
new_compare29(Double(xuu33000, xuu33001), Double(xuu34000, xuu34001)) → new_compare7(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_lt4(xuu33000, xuu34000, ty_Bool) → new_lt16(xuu33000, xuu34000)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(ty_Maybe, cff)) → new_ltEs8(xuu33000, xuu34000, cff)
new_esEs21(xuu50002, xuu4002, ty_Bool) → new_esEs18(xuu50002, xuu4002)
new_compare30(xuu33000, xuu34000, app(ty_[], che)) → new_compare0(xuu33000, xuu34000, che)
new_esEs24(xuu50000, xuu4000, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_esEs30(xuu22, xuu17, ty_Ordering) → new_esEs16(xuu22, xuu17)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(app(ty_@2, ddh), dea)) → new_ltEs5(xuu33000, xuu34000, ddh, dea)
new_compare33(xuu33000, xuu34000, bad, bae) → new_compare28(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, bad, bae), bad, bae)
new_esEs16(LT, LT) → True
new_ltEs4(Left(xuu33000), Left(xuu34000), app(app(app(ty_@3, dbh), dca), dcb), bbb) → new_ltEs15(xuu33000, xuu34000, dbh, dca, dcb)
new_esEs13(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), dac) → new_asAs(new_esEs28(xuu50000, xuu4000, dac), new_esEs27(xuu50001, xuu4001, dac))
new_asAs(False, xuu136) → False
new_esEs22(xuu50001, xuu4001, ty_Double) → new_esEs12(xuu50001, xuu4001)
new_lt20(xuu33000, xuu34000, ty_Bool) → new_lt16(xuu33000, xuu34000)
new_esEs11(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs15(new_sr(xuu50000, xuu4000), new_sr(xuu50001, xuu4001))
new_primMulInt(Neg(xuu500000), Pos(xuu40000)) → Neg(new_primMulNat0(xuu500000, xuu40000))
new_primMulInt(Pos(xuu500000), Neg(xuu40000)) → Neg(new_primMulNat0(xuu500000, xuu40000))
new_lt4(xuu33000, xuu34000, ty_Int) → new_lt12(xuu33000, xuu34000)
new_primMulNat0(Succ(xuu5000000), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu400000)) → Zero
new_esEs22(xuu50001, xuu4001, ty_Ordering) → new_esEs16(xuu50001, xuu4001)
new_ltEs20(xuu3300, xuu3400, ty_Integer) → new_ltEs7(xuu3300, xuu3400)
new_esEs16(GT, GT) → True
new_esEs29(xuu5000, xuu400, ty_Float) → new_esEs11(xuu5000, xuu400)
new_esEs4(Just(xuu50000), Just(xuu4000), app(ty_[], cca)) → new_esEs17(xuu50000, xuu4000, cca)
new_ltEs20(xuu3300, xuu3400, ty_Double) → new_ltEs11(xuu3300, xuu3400)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_@0, bbb) → new_ltEs13(xuu33000, xuu34000)
new_compare28(xuu33000, xuu34000, False, bad, bae) → new_compare18(xuu33000, xuu34000, new_ltEs5(xuu33000, xuu34000, bad, bae), bad, bae)
new_esEs18(True, True) → True
new_esEs23(xuu50000, xuu4000, app(app(ty_@2, beb), bec)) → new_esEs7(xuu50000, xuu4000, beb, bec)
new_esEs30(xuu22, xuu17, app(ty_Ratio, dbb)) → new_esEs13(xuu22, xuu17, dbb)
new_lt19(xuu33001, xuu34001, ty_Float) → new_lt8(xuu33001, xuu34001)
new_esEs24(xuu50000, xuu4000, ty_Float) → new_esEs11(xuu50000, xuu4000)
new_lt20(xuu33000, xuu34000, ty_Float) → new_lt8(xuu33000, xuu34000)
new_compare110(xuu33000, xuu34000, True, hh, baa, bab) → LT
new_esEs22(xuu50001, xuu4001, ty_Char) → new_esEs10(xuu50001, xuu4001)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_@0) → new_ltEs13(xuu33000, xuu34000)
new_lt16(xuu33000, xuu34000) → new_esEs16(new_compare19(xuu33000, xuu34000), LT)
new_lt19(xuu33001, xuu34001, ty_Bool) → new_lt16(xuu33001, xuu34001)
new_esEs25(xuu50001, xuu4001, app(ty_[], cde)) → new_esEs17(xuu50001, xuu4001, cde)
new_esEs21(xuu50002, xuu4002, ty_Integer) → new_esEs9(xuu50002, xuu4002)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_ltEs20(xuu3300, xuu3400, app(ty_Ratio, bah)) → new_ltEs12(xuu3300, xuu3400, bah)
new_esEs26(xuu50000, xuu4000, ty_Integer) → new_esEs9(xuu50000, xuu4000)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_compare18(xuu33000, xuu34000, False, bad, bae) → GT
new_lt11(xuu33000, xuu34000) → new_esEs16(new_compare17(xuu33000, xuu34000), LT)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Char) → new_ltEs9(xuu33000, xuu34000)
new_lt19(xuu33001, xuu34001, app(app(app(ty_@3, gf), gg), gh)) → new_lt13(xuu33001, xuu34001, gf, gg, gh)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Int) → new_ltEs14(xuu33000, xuu34000)
new_compare30(xuu33000, xuu34000, app(app(ty_@2, chh), daa)) → new_compare33(xuu33000, xuu34000, chh, daa)
new_lt15(xuu33000, xuu34000, bac) → new_esEs16(new_compare0(xuu33000, xuu34000, bac), LT)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs18(xuu50000, xuu4000)
new_esEs24(xuu50000, xuu4000, ty_Ordering) → new_esEs16(xuu50000, xuu4000)
new_ltEs18(True, False) → False
new_ltEs20(xuu3300, xuu3400, ty_Float) → new_ltEs10(xuu3300, xuu3400)
new_lt20(xuu33000, xuu34000, ty_Integer) → new_lt5(xuu33000, xuu34000)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs15(xuu50001, xuu4001)
new_compare11(xuu33000, xuu34000, False) → GT
new_esEs8(xuu33000, xuu34000, app(ty_Maybe, db)) → new_esEs4(xuu33000, xuu34000, db)
new_ltEs8(Nothing, Nothing, bag) → True
new_compare11(xuu33000, xuu34000, True) → LT
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_@0) → new_ltEs13(xuu33000, xuu34000)
new_esEs22(xuu50001, xuu4001, ty_@0) → new_esEs14(xuu50001, xuu4001)
new_fsEs(xuu146) → new_not(new_esEs16(xuu146, GT))
new_esEs25(xuu50001, xuu4001, app(app(app(ty_@3, cea), ceb), cec)) → new_esEs5(xuu50001, xuu4001, cea, ceb, cec)
new_esEs26(xuu50000, xuu4000, ty_Char) → new_esEs10(xuu50000, xuu4000)
new_esEs22(xuu50001, xuu4001, app(app(ty_Either, bdd), bde)) → new_esEs6(xuu50001, xuu4001, bdd, bde)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, ty_Char) → new_ltEs9(xuu33000, xuu34000)
new_ltEs4(Left(xuu33000), Left(xuu34000), ty_Ordering, bbb) → new_ltEs16(xuu33000, xuu34000)
new_esEs21(xuu50002, xuu4002, ty_Double) → new_esEs12(xuu50002, xuu4002)
new_esEs18(False, True) → False
new_esEs18(True, False) → False
new_esEs4(Just(xuu50000), Just(xuu4000), app(app(ty_@2, cbf), cbg)) → new_esEs7(xuu50000, xuu4000, cbf, cbg)
new_esEs29(xuu5000, xuu400, ty_Bool) → new_esEs18(xuu5000, xuu400)
new_esEs8(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, ty_Float) → new_esEs11(xuu22, xuu17)
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(ty_Ratio, dda)) → new_ltEs12(xuu33000, xuu34000, dda)
new_ltEs11(xuu3300, xuu3400) → new_fsEs(new_compare29(xuu3300, xuu3400))
new_esEs21(xuu50002, xuu4002, ty_Float) → new_esEs11(xuu50002, xuu4002)
new_ltEs6(xuu33001, xuu34001, ty_Int) → new_ltEs14(xuu33001, xuu34001)
new_ltEs19(xuu33002, xuu34002, ty_Integer) → new_ltEs7(xuu33002, xuu34002)
new_esEs8(xuu33000, xuu34000, app(ty_[], dg)) → new_esEs17(xuu33000, xuu34000, dg)
new_compare30(xuu33000, xuu34000, ty_Bool) → new_compare19(xuu33000, xuu34000)
new_esEs23(xuu50000, xuu4000, ty_Double) → new_esEs12(xuu50000, xuu4000)
new_esEs20(xuu33000, xuu34000, app(app(ty_@2, bad), bae)) → new_esEs7(xuu33000, xuu34000, bad, bae)
new_ltEs18(False, True) → True
new_primPlusNat0(Succ(xuu28200), Succ(xuu9700)) → Succ(Succ(new_primPlusNat0(xuu28200, xuu9700)))
new_esEs26(xuu50000, xuu4000, app(app(ty_Either, ceh), cfa)) → new_esEs6(xuu50000, xuu4000, ceh, cfa)
new_ltEs7(xuu3300, xuu3400) → new_fsEs(new_compare6(xuu3300, xuu3400))
new_ltEs4(Right(xuu33000), Right(xuu34000), bba, app(ty_Maybe, dch)) → new_ltEs8(xuu33000, xuu34000, dch)
new_compare0([], :(xuu34000, xuu34001), bd) → LT
new_asAs(True, xuu136) → xuu136
new_esEs26(xuu50000, xuu4000, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs5(xuu50000, xuu4000, cfc, cfd, cfe)
new_ltEs4(Left(xuu33000), Left(xuu34000), app(app(ty_@2, dcf), dcg), bbb) → new_ltEs5(xuu33000, xuu34000, dcf, dcg)
new_esEs25(xuu50001, xuu4001, ty_Float) → new_esEs11(xuu50001, xuu4001)
new_lt20(xuu33000, xuu34000, app(ty_Ratio, hg)) → new_lt10(xuu33000, xuu34000, hg)
new_ltEs16(LT, LT) → True
new_primPlusNat1(xuu107, xuu400000) → new_primPlusNat0(xuu107, Succ(xuu400000))
new_compare27(xuu33000, xuu34000, True, hh, baa, bab) → EQ
new_esEs30(xuu22, xuu17, ty_Char) → new_esEs10(xuu22, xuu17)
new_esEs19(xuu33001, xuu34001, ty_Char) → new_esEs10(xuu33001, xuu34001)
new_esEs17([], [], bfd) → True
new_esEs17([], :(xuu4000, xuu4001), bfd) → False
new_esEs17(:(xuu50000, xuu50001), [], bfd) → False
new_esEs19(xuu33001, xuu34001, ty_Int) → new_esEs15(xuu33001, xuu34001)
new_lt20(xuu33000, xuu34000, ty_@0) → new_lt11(xuu33000, xuu34000)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(ty_Ratio, cfg)) → new_ltEs12(xuu33000, xuu34000, cfg)
new_esEs23(xuu50000, xuu4000, app(app(app(ty_@3, bfa), bfb), bfc)) → new_esEs5(xuu50000, xuu4000, bfa, bfb, bfc)
new_esEs8(xuu33000, xuu34000, ty_Integer) → new_esEs9(xuu33000, xuu34000)
new_compare30(xuu33000, xuu34000, ty_Char) → new_compare9(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs5(xuu22, xuu17, dbc, dbd, dbe)
new_esEs4(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs10(xuu50000, xuu4000)
new_esEs29(xuu5000, xuu400, app(ty_Maybe, cbe)) → new_esEs4(xuu5000, xuu400, cbe)
new_compare24(xuu33000, xuu34000, False) → new_compare11(xuu33000, xuu34000, new_ltEs16(xuu33000, xuu34000))
new_ltEs20(xuu3300, xuu3400, ty_@0) → new_ltEs13(xuu3300, xuu3400)
new_lt4(xuu33000, xuu34000, ty_Integer) → new_lt5(xuu33000, xuu34000)
new_esEs26(xuu50000, xuu4000, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_compare110(xuu33000, xuu34000, False, hh, baa, bab) → GT
new_compare30(xuu33000, xuu34000, ty_Integer) → new_compare6(xuu33000, xuu34000)
new_primCompAux00(xuu179, GT) → GT
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(ty_Ratio, cba)) → new_esEs13(xuu50000, xuu4000, cba)
new_ltEs8(Just(xuu33000), Just(xuu34000), app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs15(xuu33000, xuu34000, cfh, cga, cgb)
new_ltEs8(Just(xuu33000), Just(xuu34000), ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_compare30(xuu33000, xuu34000, ty_Double) → new_compare29(xuu33000, xuu34000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(xuu50000), Right(xuu4000), cab, app(app(app(ty_@3, cbb), cbc), cbd)) → new_esEs5(xuu50000, xuu4000, cbb, cbc, cbd)
new_ltEs6(xuu33001, xuu34001, ty_@0) → new_ltEs13(xuu33001, xuu34001)
new_lt7(xuu33000, xuu34000) → new_esEs16(new_compare9(xuu33000, xuu34000), LT)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs6(xuu33001, xuu34001, ty_Bool) → new_ltEs18(xuu33001, xuu34001)
new_esEs6(Right(xuu50000), Right(xuu4000), cab, ty_Int) → new_esEs15(xuu50000, xuu4000)
new_primCmpInt(Neg(Succ(xuu3300)), Pos(xuu340)) → LT
new_not(True) → False
new_esEs25(xuu50001, xuu4001, ty_Integer) → new_esEs9(xuu50001, xuu4001)
new_esEs18(False, False) → True

The set Q consists of the following terms:

new_primPlusNat0(Succ(x0), Zero)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_ltEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare12(x0, x1, True, x2)
new_esEs28(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs12(Double(x0, x1), Double(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs4(Nothing, Just(x0), x1)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(x0, x1, ty_Double)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare10(x0, x1, True, x2, x3)
new_esEs26(x0, x1, ty_Int)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, True, x2)
new_esEs23(x0, x1, ty_Integer)
new_compare25(Just(x0), Nothing, False, x1)
new_ltEs19(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare24(x0, x1, False)
new_asAs(False, x0)
new_esEs21(x0, x1, ty_Integer)
new_esEs17(:(x0, x1), [], x2)
new_compare15(x0, x1, x2, x3, x4)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs10(Char(x0), Char(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs26(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs9(x0, x1)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_lt15(x0, x1, x2)
new_esEs23(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs17([], [], x0)
new_lt5(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs18(True, True)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Ordering)
new_esEs16(LT, GT)
new_esEs16(GT, LT)
new_ltEs11(x0, x1)
new_ltEs6(x0, x1, ty_Bool)
new_compare17(@0, @0)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_lt4(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_ltEs7(x0, x1)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_primPlusNat1(x0, x1)
new_esEs28(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Double)
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Integer)
new_ltEs6(x0, x1, ty_Ordering)
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs8(x0, x1, ty_Char)
new_compare10(x0, x1, False, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primEqNat0(Zero, Zero)
new_lt6(x0, x1, x2)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare12(x0, x1, False, x2)
new_esEs19(x0, x1, ty_Int)
new_compare26(x0, x1, True)
new_ltEs6(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs6(x0, x1, ty_Integer)
new_compare26(x0, x1, False)
new_ltEs20(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_primMulNat0(Zero, Zero)
new_ltEs12(x0, x1, x2)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_@0)
new_ltEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs24(x0, x1, ty_Char)
new_lt17(x0, x1, x2, x3)
new_esEs19(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Int)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare6(Integer(x0), Integer(x1))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs27(x0, x1, ty_Integer)
new_ltEs4(Left(x0), Left(x1), ty_Float, x2)
new_compare8(x0, x1)
new_lt20(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs16(GT, GT)
new_compare23(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_sr(x0, x1)
new_ltEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs14(@0, @0)
new_compare19(x0, x1)
new_compare23(x0, x1, True, x2, x3)
new_compare18(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt4(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs17(x0, x1, x2)
new_ltEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, ty_Double)
new_esEs18(False, False)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_@0)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, GT)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Integer)
new_ltEs14(x0, x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare7(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare25(Just(x0), Just(x1), False, x2)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_@0)
new_ltEs18(True, True)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_primPlusNat0(Zero, Zero)
new_compare11(x0, x1, False)
new_ltEs16(EQ, EQ)
new_esEs19(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_lt4(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Ordering)
new_compare24(x0, x1, True)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Zero)
new_ltEs16(LT, LT)
new_ltEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(False, x0)
new_esEs15(x0, x1)
new_ltEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs30(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_compare9(Char(x0), Char(x1))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs6(x0, x1, ty_Double)
new_ltEs16(LT, GT)
new_ltEs16(GT, LT)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(x0, x1)
new_lt14(x0, x1)
new_lt20(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt13(x0, x1, x2, x3, x4)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_pePe(True, x0)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs8(Nothing, Nothing, x0)
new_primCompAux00(x0, LT)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare28(x0, x1, False, x2, x3)
new_ltEs18(False, False)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_lt11(x0, x1)
new_compare30(x0, x1, ty_Char)
new_primCompAux00(x0, EQ)
new_esEs24(x0, x1, ty_Double)
new_sr0(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs17([], :(x0, x1), x2)
new_compare30(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt12(x0, x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(Nothing, Nothing, False, x0)
new_esEs20(x0, x1, ty_Int)
new_esEs16(LT, LT)
new_esEs26(x0, x1, ty_Bool)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2, x3)
new_esEs22(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, ty_Double)
new_ltEs16(GT, GT)
new_esEs24(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Float)
new_compare30(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs6(x0, x1, ty_Char)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Zero, Succ(x0))
new_ltEs8(Nothing, Just(x0), x1)
new_compare13(x0, x1, True)
new_compare30(x0, x1, ty_Bool)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare27(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs8(Just(x0), Nothing, x1)
new_esEs20(x0, x1, ty_@0)
new_primCmpNat0(Zero, Zero)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt16(x0, x1)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_@0)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs4(Right(x0), Right(x1), x2, ty_Char)
new_fsEs(x0)
new_esEs8(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1)
new_esEs8(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs29(x0, x1, ty_Ordering)
new_compare110(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1, app(ty_[], x2))
new_esEs4(Nothing, Nothing, x0)
new_ltEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs25(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare18(x0, x1, False, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_compare33(x0, x1, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, ty_Double)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Bool)
new_esEs13(:%(x0, x1), :%(x2, x3), x4)
new_not(True)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Double)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(GT, EQ)
new_ltEs16(EQ, GT)
new_esEs16(EQ, LT)
new_esEs16(LT, EQ)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs16(EQ, EQ)
new_esEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_not(False)
new_compare31(x0, x1, x2)
new_ltEs16(LT, EQ)
new_ltEs16(EQ, LT)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs18(False, True)
new_ltEs18(True, False)
new_ltEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_asAs(True, x0)
new_esEs24(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Double)
new_lt4(x0, x1, ty_Char)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare25(Nothing, Just(x0), False, x1)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Char)
new_ltEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs11(Float(x0, x1), Float(x2, x3))
new_esEs25(x0, x1, ty_Char)
new_compare13(x0, x1, False)
new_ltEs20(x0, x1, ty_Float)
new_compare16(Float(x0, x1), Float(x2, x3))
new_lt4(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Int)
new_esEs16(EQ, GT)
new_esEs16(GT, EQ)
new_esEs9(Integer(x0), Integer(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs20(x0, x1, ty_@0)
new_ltEs4(Left(x0), Right(x1), x2, x3)
new_ltEs4(Right(x0), Left(x1), x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs10(x0, x1)
new_esEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_compare29(Double(x0, x1), Double(x2, x3))
new_ltEs19(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_primMulNat0(Zero, Succ(x0))
new_esEs23(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_ltEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_compare27(x0, x1, False, x2, x3, x4)
new_compare30(x0, x1, ty_Double)
new_compare0([], [], x0)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Float)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_compare32(x0, x1, x2, x3)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Nothing, x1)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_esEs19(x0, x1, ty_@0)
new_ltEs4(Left(x0), Left(x1), ty_Bool, x2)
new_compare0([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare30(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Bool)
new_esEs19(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt8(x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_compare30(x0, x1, ty_@0)
new_esEs30(x0, x1, app(ty_Ratio, x2))

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

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



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

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

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

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: