YES 11.795 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
  ((listToFM :: Ord b => [(Maybe b,a)]  ->  FiniteMap (Maybe b) a) :: Ord b => [(Maybe b,a)]  ->  FiniteMap (Maybe b) a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

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

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

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

The following Lambda expression
\oldnewnew

is transformed to
addListToFM0 old new = new



↳ HASKELL
  ↳ LR
HASKELL
      ↳ CR

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
addListToFM0 old new new

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

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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

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

  findMin :: FiniteMap 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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
addListToFM0 old new new

  addListToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b
addListToFM_C combiner fm key_elt_pairs 
foldl 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 a b  ->  (a,b)
findMin (Branch key elt _ EmptyFM _) (key,elt)
findMin (Branch key elt _ fm_l _) findMin fm_l

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

  
fmToList0 key elt rest (key,elt: rest

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

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

  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



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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
addListToFM0 old new new

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Replaced joker patterns by fresh variables and removed binding patterns.

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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
addListToFM0 old new new

  addListToFM_C :: Ord 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 a b
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
addListToFM0 old new new

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

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

  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 vw vx vy vz
let 
biggest_left_key fst (findMax fm_l)
in biggest_left_key < key
left_size sizeFM fm_l
right_ok right_ok0 fm_r key fm_r
right_ok0 fm_r key EmptyFM True
right_ok0 fm_r key (Branch right_key wu wv ww wx
let 
smallest_right_key fst (findMin fm_r)
in key < smallest_right_key
right_size sizeFM fm_r
unbox :: Int  ->  Int
unbox x x

  sIZE_RATIO :: Int
sIZE_RATIO 5

  sizeFM :: FiniteMap 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



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

are unpacked to the following functions on top level
mkBranchRight_ok0 wxw wxx wxy fm_r key EmptyFM = True
mkBranchRight_ok0 wxw wxx wxy fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

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

mkBranchBalance_ok wxw wxx wxy = True

mkBranchLeft_size wxw wxx wxy = sizeFM wxy

mkBranchLeft_ok wxw wxx wxy = mkBranchLeft_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 vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

mkBranchRight_size wxw wxx wxy = sizeFM wxw

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

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

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

are unpacked to the following functions on top level
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

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)

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)

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)

mkBalBranch6Size_r wyx wyy wyz wzu = sizeFM wyx

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)

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 wyy wyz fm_l fm_rlfm_rr

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

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_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 wyy wyz fm_lr fm_r)

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

mkBalBranch6Size_l wyx wyy wyz wzu = sizeFM wzu

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 wyy wyz fm_lrr fm_r)

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

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

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

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
reduce2D wzy wzz = gcd wzy wzz

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

reduce2Reduce0 wzy wzz x y True = x `quot` reduce2D wzy wzz :% (y `quot` reduce2D 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' x wuy = gcd0Gcd'2 x wuy
gcd0Gcd' x y = gcd0Gcd'0 x y

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

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

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



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

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

  
addListToFM0 old new new

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

  
addListToFM_CAdd wzv fmap (key,eltaddToFM_C wzv fmap key elt

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

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

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

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

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

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

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

  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 fm_R key elt fm_L key elt fm_L fm_R (mkBalBranch6Size_l fm_R key elt fm_L + mkBalBranch6Size_r fm_R key elt 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 wyy wyz 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 wyy wyz 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 wyy wyz 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 wyy wyz fm_lr fm_r)

  
mkBalBranch6Size_l wyx wyy wyz wzu sizeFM wzu

  
mkBalBranch6Size_r wyx wyy wyz wzu sizeFM wyx

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

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxy wxx wxy

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

  
mkBranchLeft_ok0Biggest_left_key wzx fst (findMax wzx)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxy

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

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxw wxx wxw

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

  
mkBranchRight_ok0Smallest_right_key wzw fst (findMin wzw)

  
mkBranchRight_size wxw wxx wxy sizeFM wxw

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
addListToFM0 old new new

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

  
addListToFM_CAdd wzv fmap (key,eltaddToFM_C wzv fmap key elt

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

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

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

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

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

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

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

  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 fm_R key elt fm_L key elt fm_L fm_R (mkBalBranch6Size_l fm_R key elt fm_L + mkBalBranch6Size_r fm_R key elt 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))))))) wyy wyz 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))))))))))))) wyy wyz 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))))) wyy wyz 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)))))))))) wyy wyz fm_lr fm_r)

  
mkBalBranch6Size_l wyx wyy wyz wzu sizeFM wzu

  
mkBalBranch6Size_r wyx wyy wyz wzu sizeFM wyx

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

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxy wxx wxy

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

  
mkBranchLeft_ok0Biggest_left_key wzx fst (findMax wzx)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxy

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

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxw wxx wxw

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

  
mkBranchRight_ok0Smallest_right_key wzw fst (findMin wzw)

  
mkBranchRight_size wxw wxx wxy sizeFM wxw

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

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

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

  unitFM :: b  ->  a  ->  FiniteMap b a
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(xuu31100000), Succ(xuu60000)) → new_primEqNat(xuu31100000, xuu60000)

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(xuu311000100), Succ(xuu600100)) → new_primMulNat(xuu311000100, Succ(xuu600100))

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

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



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

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

new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), dd, app(app(ty_@2, fh), ga), eh) → new_esEs3(xuu3110001, xuu6001, fh, ga)
new_esEs2(Left(xuu3110000), Left(xuu6000), app(ty_[], hc), hd) → new_esEs(xuu3110000, xuu6000, hc)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), dd, app(app(app(ty_@3, fb), fc), fd), eh) → new_esEs1(xuu3110001, xuu6001, fb, fc, fd)
new_esEs2(Left(xuu3110000), Left(xuu6000), app(app(ty_@2, bac), bad), hd) → new_esEs3(xuu3110000, xuu6000, bac, bad)
new_esEs2(Right(xuu3110000), Right(xuu6000), bae, app(ty_[], baf)) → new_esEs(xuu3110000, xuu6000, baf)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), dd, de, app(app(ty_Either, ec), ed)) → new_esEs2(xuu3110002, xuu6002, ec, ed)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), app(app(ty_Either, gg), gh), de, eh) → new_esEs2(xuu3110000, xuu6000, gg, gh)
new_esEs3(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), app(ty_[], bda), bdb) → new_esEs(xuu3110000, xuu6000, bda)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), dd, app(ty_Maybe, fa), eh) → new_esEs0(xuu3110001, xuu6001, fa)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), dd, de, app(app(app(ty_@3, dh), ea), eb)) → new_esEs1(xuu3110002, xuu6002, dh, ea, eb)
new_esEs0(Just(xuu3110000), Just(xuu6000), app(ty_Maybe, cc)) → new_esEs0(xuu3110000, xuu6000, cc)
new_esEs0(Just(xuu3110000), Just(xuu6000), app(ty_[], cb)) → new_esEs(xuu3110000, xuu6000, cb)
new_esEs2(Left(xuu3110000), Left(xuu6000), app(app(ty_Either, baa), bab), hd) → new_esEs2(xuu3110000, xuu6000, baa, bab)
new_esEs2(Right(xuu3110000), Right(xuu6000), bae, app(app(ty_@2, bbe), bbf)) → new_esEs3(xuu3110000, xuu6000, bbe, bbf)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), dd, app(app(ty_Either, ff), fg), eh) → new_esEs2(xuu3110001, xuu6001, ff, fg)
new_esEs3(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), app(app(app(ty_@3, bdd), bde), bdf), bdb) → new_esEs1(xuu3110000, xuu6000, bdd, bde, bdf)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), dd, de, app(ty_Maybe, dg)) → new_esEs0(xuu3110002, xuu6002, dg)
new_esEs3(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), bbg, app(ty_[], bbh)) → new_esEs(xuu3110001, xuu6001, bbh)
new_esEs2(Right(xuu3110000), Right(xuu6000), bae, app(app(app(ty_@3, bah), bba), bbb)) → new_esEs1(xuu3110000, xuu6000, bah, bba, bbb)
new_esEs3(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), bbg, app(app(ty_@2, bcg), bch)) → new_esEs3(xuu3110001, xuu6001, bcg, bch)
new_esEs(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), app(ty_Maybe, bb)) → new_esEs0(xuu3110000, xuu6000, bb)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), app(app(app(ty_@3, gd), ge), gf), de, eh) → new_esEs1(xuu3110000, xuu6000, gd, ge, gf)
new_esEs(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), h) → new_esEs(xuu3110001, xuu6001, h)
new_esEs3(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), app(ty_Maybe, bdc), bdb) → new_esEs0(xuu3110000, xuu6000, bdc)
new_esEs2(Left(xuu3110000), Left(xuu6000), app(app(app(ty_@3, hf), hg), hh), hd) → new_esEs1(xuu3110000, xuu6000, hf, hg, hh)
new_esEs(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), app(app(app(ty_@3, bc), bd), be)) → new_esEs1(xuu3110000, xuu6000, bc, bd, be)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), app(app(ty_@2, ha), hb), de, eh) → new_esEs3(xuu3110000, xuu6000, ha, hb)
new_esEs(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), app(app(ty_Either, bf), bg)) → new_esEs2(xuu3110000, xuu6000, bf, bg)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), app(ty_[], gb), de, eh) → new_esEs(xuu3110000, xuu6000, gb)
new_esEs2(Right(xuu3110000), Right(xuu6000), bae, app(app(ty_Either, bbc), bbd)) → new_esEs2(xuu3110000, xuu6000, bbc, bbd)
new_esEs3(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), app(app(ty_@2, bea), beb), bdb) → new_esEs3(xuu3110000, xuu6000, bea, beb)
new_esEs3(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), bbg, app(ty_Maybe, bca)) → new_esEs0(xuu3110001, xuu6001, bca)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), app(ty_Maybe, gc), de, eh) → new_esEs0(xuu3110000, xuu6000, gc)
new_esEs(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), app(app(ty_@2, bh), ca)) → new_esEs3(xuu3110000, xuu6000, bh, ca)
new_esEs3(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), bbg, app(app(app(ty_@3, bcb), bcc), bcd)) → new_esEs1(xuu3110001, xuu6001, bcb, bcc, bcd)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), dd, de, app(app(ty_@2, ee), ef)) → new_esEs3(xuu3110002, xuu6002, ee, ef)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), dd, de, app(ty_[], df)) → new_esEs(xuu3110002, xuu6002, df)
new_esEs2(Left(xuu3110000), Left(xuu6000), app(ty_Maybe, he), hd) → new_esEs0(xuu3110000, xuu6000, he)
new_esEs3(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), bbg, app(app(ty_Either, bce), bcf)) → new_esEs2(xuu3110001, xuu6001, bce, bcf)
new_esEs3(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), app(app(ty_Either, bdg), bdh), bdb) → new_esEs2(xuu3110000, xuu6000, bdg, bdh)
new_esEs2(Right(xuu3110000), Right(xuu6000), bae, app(ty_Maybe, bag)) → new_esEs0(xuu3110000, xuu6000, bag)
new_esEs0(Just(xuu3110000), Just(xuu6000), app(app(ty_@2, db), dc)) → new_esEs3(xuu3110000, xuu6000, db, dc)
new_esEs1(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), dd, app(ty_[], eg), eh) → new_esEs(xuu3110001, xuu6001, eg)
new_esEs(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), app(ty_[], ba)) → new_esEs(xuu3110000, xuu6000, ba)
new_esEs0(Just(xuu3110000), Just(xuu6000), app(app(app(ty_@3, cd), ce), cf)) → new_esEs1(xuu3110000, xuu6000, cd, ce, cf)
new_esEs0(Just(xuu3110000), Just(xuu6000), app(app(ty_Either, cg), da)) → new_esEs2(xuu3110000, xuu6000, cg, da)

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_compare20(Just(:(xuu33000, xuu33001)), Just(:(xuu34000, xuu34001)), False, app(ty_[], eh)) → new_compare0(xuu33001, xuu34001, eh)
new_ltEs(Right(xuu33000), Right(xuu34000), cd, app(ty_[], da)) → new_ltEs1(xuu33000, xuu34000, da)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, app(app(ty_Either, h), ba)), gd), ge)) → new_compare2(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, h, ba), h, ba)
new_compare20(Just(Just(xuu33000)), Just(Just(xuu34000)), False, app(ty_Maybe, app(ty_[], eb))) → new_ltEs1(xuu33000, xuu34000, eb)
new_ltEs(Right(xuu33000), Right(xuu34000), cd, app(app(ty_Either, ce), cf)) → new_ltEs(xuu33000, xuu34000, ce, cf)
new_compare3(xuu33000, xuu34000, gc) → new_compare20(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, gc), gc)
new_compare0(:(xuu33000, xuu33001), :(xuu34000, xuu34001), eh) → new_compare0(xuu33001, xuu34001, eh)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), hd, app(app(app(ty_@3, baa), bab), bac), ge) → new_lt2(xuu33001, xuu34001, baa, bab, bac)
new_compare20(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, bda), app(app(ty_@2, bea), beb))) → new_ltEs3(xuu33001, xuu34001, bea, beb)
new_ltEs0(Just(xuu33000), Just(xuu34000), app(ty_Maybe, ea)) → new_ltEs0(xuu33000, xuu34000, ea)
new_compare20(Just(Left(xuu33000)), Just(Left(xuu34000)), False, app(app(ty_Either, app(ty_Maybe, be)), bd)) → new_ltEs0(xuu33000, xuu34000, be)
new_compare20(Just(Right(xuu33000)), Just(Right(xuu34000)), False, app(app(ty_Either, cd), app(app(ty_@2, de), df))) → new_ltEs3(xuu33000, xuu34000, de, df)
new_lt3(xuu33000, xuu34000, hb, hc) → new_compare22(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, hb, hc), hb, hc)
new_compare20(Just(Just(xuu33000)), Just(Just(xuu34000)), False, app(ty_Maybe, app(app(ty_Either, dg), dh))) → new_ltEs(xuu33000, xuu34000, dg, dh)
new_ltEs(Left(xuu33000), Left(xuu34000), app(app(ty_@2, cb), cc), bd) → new_ltEs3(xuu33000, xuu34000, cb, cc)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bda, app(app(ty_@2, bea), beb)) → new_ltEs3(xuu33001, xuu34001, bea, beb)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, hd), gd), app(ty_Maybe, bah))) → new_ltEs0(xuu33002, xuu34002, bah)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), hd, gd, app(ty_[], bba)) → new_ltEs1(xuu33002, xuu34002, bba)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), app(ty_[], gf), gd, ge) → new_compare0(xuu33000, xuu34000, gf)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, hd), app(app(ty_Either, he), hf)), ge)) → new_lt(xuu33001, xuu34001, he, hf)
new_ltEs(Left(xuu33000), Left(xuu34000), app(app(app(ty_@3, bg), bh), ca), bd) → new_ltEs2(xuu33000, xuu34000, bg, bh, ca)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), app(app(ty_@2, hb), hc), gd, ge) → new_compare22(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, hb, hc), hb, hc)
new_ltEs(Right(xuu33000), Right(xuu34000), cd, app(app(ty_@2, de), df)) → new_ltEs3(xuu33000, xuu34000, de, df)
new_compare20(Just(Right(xuu33000)), Just(Right(xuu34000)), False, app(app(ty_Either, cd), app(app(app(ty_@3, db), dc), dd))) → new_ltEs2(xuu33000, xuu34000, db, dc, dd)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bda, app(app(ty_Either, bdb), bdc)) → new_ltEs(xuu33001, xuu34001, bdb, bdc)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), app(app(ty_@2, bcg), bch), bca) → new_lt3(xuu33000, xuu34000, bcg, bch)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, app(app(app(ty_@3, gg), gh), ha)), gd), ge)) → new_compare21(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, gg, gh, ha), gg, gh, ha)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, hd), app(ty_Maybe, hg)), ge)) → new_lt0(xuu33001, xuu34001, hg)
new_ltEs(Left(xuu33000), Left(xuu34000), app(ty_Maybe, be), bd) → new_ltEs0(xuu33000, xuu34000, be)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, hd), app(app(ty_@2, bad), bae)), ge)) → new_lt3(xuu33001, xuu34001, bad, bae)
new_ltEs1(:(xuu33000, xuu33001), :(xuu34000, xuu34001), eh) → new_compare0(xuu33001, xuu34001, eh)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), hd, app(ty_Maybe, hg), ge) → new_lt0(xuu33001, xuu34001, hg)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), app(app(app(ty_@3, gg), gh), ha), gd, ge) → new_compare21(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, gg, gh, ha), gg, gh, ha)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), app(app(ty_Either, bbg), bbh), bca) → new_lt(xuu33000, xuu34000, bbg, bbh)
new_ltEs(Left(xuu33000), Left(xuu34000), app(ty_[], bf), bd) → new_ltEs1(xuu33000, xuu34000, bf)
new_compare20(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, app(ty_Maybe, bcb)), bca)) → new_lt0(xuu33000, xuu34000, bcb)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, hd), gd), app(app(ty_@2, bbe), bbf))) → new_ltEs3(xuu33002, xuu34002, bbe, bbf)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, app(app(ty_@2, hb), hc)), gd), ge)) → new_compare22(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, hb, hc), hb, hc)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), hd, app(app(ty_Either, he), hf), ge) → new_lt(xuu33001, xuu34001, he, hf)
new_compare20(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, bda), app(ty_[], bde))) → new_ltEs1(xuu33001, xuu34001, bde)
new_ltEs(Right(xuu33000), Right(xuu34000), cd, app(ty_Maybe, cg)) → new_ltEs0(xuu33000, xuu34000, cg)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), hd, app(app(ty_@2, bad), bae), ge) → new_lt3(xuu33001, xuu34001, bad, bae)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), app(ty_Maybe, gc), gd, ge) → new_compare20(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, gc), gc)
new_compare21(xuu33000, xuu34000, False, gg, gh, ha) → new_ltEs2(xuu33000, xuu34000, gg, gh, ha)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), hd, app(ty_[], hh), ge) → new_lt1(xuu33001, xuu34001, hh)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), app(ty_[], bcc), bca) → new_lt1(xuu33000, xuu34000, bcc)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bda, app(ty_[], bde)) → new_ltEs1(xuu33001, xuu34001, bde)
new_lt(xuu33000, xuu34000, h, ba) → new_compare2(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, h, ba), h, ba)
new_primCompAux(xuu33000, xuu34000, xuu169, app(app(ty_@2, ga), gb)) → new_compare5(xuu33000, xuu34000, ga, gb)
new_compare20(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, bda), app(app(app(ty_@3, bdf), bdg), bdh))) → new_ltEs2(xuu33001, xuu34001, bdf, bdg, bdh)
new_compare22(xuu33000, xuu34000, False, hb, hc) → new_ltEs3(xuu33000, xuu34000, hb, hc)
new_compare2(xuu33000, xuu34000, False, h, ba) → new_ltEs(xuu33000, xuu34000, h, ba)
new_compare0(:(xuu33000, xuu33001), :(xuu34000, xuu34001), eh) → new_primCompAux(xuu33000, xuu34000, new_compare(xuu33001, xuu34001, eh), eh)
new_compare20(Just(Right(xuu33000)), Just(Right(xuu34000)), False, app(app(ty_Either, cd), app(ty_[], da))) → new_ltEs1(xuu33000, xuu34000, da)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), hd, gd, app(app(app(ty_@3, bbb), bbc), bbd)) → new_ltEs2(xuu33002, xuu34002, bbb, bbc, bbd)
new_ltEs(Left(xuu33000), Left(xuu34000), app(app(ty_Either, bb), bc), bd) → new_ltEs(xuu33000, xuu34000, bb, bc)
new_compare20(Just(Just(xuu33000)), Just(Just(xuu34000)), False, app(ty_Maybe, app(app(ty_@2, ef), eg))) → new_ltEs3(xuu33000, xuu34000, ef, eg)
new_ltEs0(Just(xuu33000), Just(xuu34000), app(app(ty_@2, ef), eg)) → new_ltEs3(xuu33000, xuu34000, ef, eg)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bda, app(ty_Maybe, bdd)) → new_ltEs0(xuu33001, xuu34001, bdd)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, app(ty_Maybe, gc)), gd), ge)) → new_compare20(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, gc), gc)
new_compare20(Just(Left(xuu33000)), Just(Left(xuu34000)), False, app(app(ty_Either, app(ty_[], bf)), bd)) → new_ltEs1(xuu33000, xuu34000, bf)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, hd), gd), app(ty_[], bba))) → new_ltEs1(xuu33002, xuu34002, bba)
new_compare20(Just(Left(xuu33000)), Just(Left(xuu34000)), False, app(app(ty_Either, app(app(ty_@2, cb), cc)), bd)) → new_ltEs3(xuu33000, xuu34000, cb, cc)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, hd), gd), app(app(app(ty_@3, bbb), bbc), bbd))) → new_ltEs2(xuu33002, xuu34002, bbb, bbc, bbd)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), app(app(ty_Either, h), ba), gd, ge) → new_compare2(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, h, ba), h, ba)
new_ltEs0(Just(xuu33000), Just(xuu34000), app(app(app(ty_@3, ec), ed), ee)) → new_ltEs2(xuu33000, xuu34000, ec, ed, ee)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, app(ty_[], gf)), gd), ge)) → new_compare0(xuu33000, xuu34000, gf)
new_compare20(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, app(ty_[], bcc)), bca)) → new_lt1(xuu33000, xuu34000, bcc)
new_compare20(Just(Just(xuu33000)), Just(Just(xuu34000)), False, app(ty_Maybe, app(ty_Maybe, ea))) → new_ltEs0(xuu33000, xuu34000, ea)
new_primCompAux(xuu33000, xuu34000, xuu169, app(ty_[], fd)) → new_compare0(xuu33000, xuu34000, fd)
new_compare4(xuu33000, xuu34000, gg, gh, ha) → new_compare21(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, gg, gh, ha), gg, gh, ha)
new_compare20(Just(Left(xuu33000)), Just(Left(xuu34000)), False, app(app(ty_Either, app(app(app(ty_@3, bg), bh), ca)), bd)) → new_ltEs2(xuu33000, xuu34000, bg, bh, ca)
new_ltEs1(:(xuu33000, xuu33001), :(xuu34000, xuu34001), eh) → new_primCompAux(xuu33000, xuu34000, new_compare(xuu33001, xuu34001, eh), eh)
new_compare20(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, bda), app(app(ty_Either, bdb), bdc))) → new_ltEs(xuu33001, xuu34001, bdb, bdc)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), hd, gd, app(app(ty_@2, bbe), bbf)) → new_ltEs3(xuu33002, xuu34002, bbe, bbf)
new_primCompAux(xuu33000, xuu34000, xuu169, app(app(ty_Either, fa), fb)) → new_compare1(xuu33000, xuu34000, fa, fb)
new_compare20(Just(Just(xuu33000)), Just(Just(xuu34000)), False, app(ty_Maybe, app(app(app(ty_@3, ec), ed), ee))) → new_ltEs2(xuu33000, xuu34000, ec, ed, ee)
new_lt2(xuu33000, xuu34000, gg, gh, ha) → new_compare21(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, gg, gh, ha), gg, gh, ha)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), app(ty_Maybe, bcb), bca) → new_lt0(xuu33000, xuu34000, bcb)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bda, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs2(xuu33001, xuu34001, bdf, bdg, bdh)
new_lt1(xuu33000, xuu34000, gf) → new_compare0(xuu33000, xuu34000, gf)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), hd, gd, app(app(ty_Either, baf), bag)) → new_ltEs(xuu33002, xuu34002, baf, bag)
new_compare20(Just(Left(xuu33000)), Just(Left(xuu34000)), False, app(app(ty_Either, app(app(ty_Either, bb), bc)), bd)) → new_ltEs(xuu33000, xuu34000, bb, bc)
new_ltEs2(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), hd, gd, app(ty_Maybe, bah)) → new_ltEs0(xuu33002, xuu34002, bah)
new_ltEs3(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), app(app(app(ty_@3, bcd), bce), bcf), bca) → new_lt2(xuu33000, xuu34000, bcd, bce, bcf)
new_compare20(Just(Right(xuu33000)), Just(Right(xuu34000)), False, app(app(ty_Either, cd), app(app(ty_Either, ce), cf))) → new_ltEs(xuu33000, xuu34000, ce, cf)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, hd), app(ty_[], hh)), ge)) → new_lt1(xuu33001, xuu34001, hh)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, hd), gd), app(app(ty_Either, baf), bag))) → new_ltEs(xuu33002, xuu34002, baf, bag)
new_compare20(Just(:(xuu33000, xuu33001)), Just(:(xuu34000, xuu34001)), False, app(ty_[], eh)) → new_primCompAux(xuu33000, xuu34000, new_compare(xuu33001, xuu34001, eh), eh)
new_compare20(Just(@3(xuu33000, xuu33001, xuu33002)), Just(@3(xuu34000, xuu34001, xuu34002)), False, app(app(app(ty_@3, hd), app(app(app(ty_@3, baa), bab), bac)), ge)) → new_lt2(xuu33001, xuu34001, baa, bab, bac)
new_compare5(xuu33000, xuu34000, hb, hc) → new_compare22(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, hb, hc), hb, hc)
new_compare20(Just(Right(xuu33000)), Just(Right(xuu34000)), False, app(app(ty_Either, cd), app(ty_Maybe, cg))) → new_ltEs0(xuu33000, xuu34000, cg)
new_ltEs(Right(xuu33000), Right(xuu34000), cd, app(app(app(ty_@3, db), dc), dd)) → new_ltEs2(xuu33000, xuu34000, db, dc, dd)
new_ltEs0(Just(xuu33000), Just(xuu34000), app(ty_[], eb)) → new_ltEs1(xuu33000, xuu34000, eb)
new_compare20(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, bda), app(ty_Maybe, bdd))) → new_ltEs0(xuu33001, xuu34001, bdd)
new_compare20(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, app(app(ty_Either, bbg), bbh)), bca)) → new_lt(xuu33000, xuu34000, bbg, bbh)
new_compare20(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, app(app(app(ty_@3, bcd), bce), bcf)), bca)) → new_lt2(xuu33000, xuu34000, bcd, bce, bcf)
new_compare20(Just(@2(xuu33000, xuu33001)), Just(@2(xuu34000, xuu34001)), False, app(app(ty_@2, app(app(ty_@2, bcg), bch)), bca)) → new_lt3(xuu33000, xuu34000, bcg, bch)
new_primCompAux(xuu33000, xuu34000, xuu169, app(ty_Maybe, fc)) → new_compare3(xuu33000, xuu34000, fc)
new_primCompAux(xuu33000, xuu34000, xuu169, app(app(app(ty_@3, ff), fg), fh)) → new_compare4(xuu33000, xuu34000, ff, fg, fh)
new_lt0(xuu33000, xuu34000, gc) → new_compare20(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, gc), gc)
new_ltEs0(Just(xuu33000), Just(xuu34000), app(app(ty_Either, dg), dh)) → new_ltEs(xuu33000, xuu34000, dg, dh)
new_compare1(xuu33000, xuu34000, h, ba) → new_compare2(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, h, ba), h, ba)

The TRS R consists of the following rules:

new_esEs4(Right(xuu3110000), Right(xuu6000), bff, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_ltEs19(xuu3300, xuu3400, app(ty_Ratio, bhc)) → new_ltEs11(xuu3300, xuu3400, bhc)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_@0, bd) → new_ltEs14(xuu33000, xuu34000)
new_lt20(xuu33001, xuu34001, app(app(app(ty_@3, baa), bab), bac)) → new_lt12(xuu33001, xuu34001, baa, bab, bac)
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, app(ty_Maybe, cg)) → new_ltEs9(xuu33000, xuu34000, cg)
new_esEs22(xuu3110002, xuu6002, app(ty_Ratio, cga)) → new_esEs9(xuu3110002, xuu6002, cga)
new_ltEs5(xuu33001, xuu34001, ty_@0) → new_ltEs14(xuu33001, xuu34001)
new_ltEs17(LT, LT) → True
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs17(Char(xuu3110000), Char(xuu6000)) → new_primEqNat0(xuu3110000, xuu6000)
new_esEs18(xuu33000, xuu34000, ty_Integer) → new_esEs16(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_ltEs20(xuu33002, xuu34002, app(ty_[], bba)) → new_ltEs10(xuu33002, xuu34002, bba)
new_esEs19(xuu3110001, xuu6001, ty_Bool) → new_esEs15(xuu3110001, xuu6001)
new_compare([], :(xuu34000, xuu34001), eh) → LT
new_esEs4(Right(xuu3110000), Right(xuu6000), bff, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs6(xuu3110000, xuu6000, bgb, bgc, bgd)
new_ltEs9(Nothing, Just(xuu34000), cdh) → True
new_ltEs4(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bda, bca) → new_pePe(new_lt5(xuu33000, xuu34000, bda), new_asAs(new_esEs18(xuu33000, xuu34000, bda), new_ltEs5(xuu33001, xuu34001, bca)))
new_ltEs8(xuu3300, xuu3400) → new_fsEs(new_compare30(xuu3300, xuu3400))
new_compare23(Just(xuu3300), Nothing, False, dbh) → GT
new_esEs4(Right(xuu3110000), Right(xuu6000), bff, app(ty_Maybe, bga)) → new_esEs5(xuu3110000, xuu6000, bga)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(xuu33000), Right(xuu34000), cd, bd) → True
new_compare(:(xuu33000, xuu33001), [], eh) → GT
new_lt5(xuu33000, xuu34000, ty_Ordering) → new_lt18(xuu33000, xuu34000)
new_compare28(xuu33000, xuu34000, False, hb, hc) → new_compare19(xuu33000, xuu34000, new_ltEs4(xuu33000, xuu34000, hb, hc), hb, hc)
new_compare13(xuu33000, xuu34000, False, gg, gh, ha) → GT
new_esEs18(xuu33000, xuu34000, ty_Double) → new_esEs13(xuu33000, xuu34000)
new_lt19(xuu33000, xuu34000, app(ty_Maybe, gc)) → new_lt9(xuu33000, xuu34000, gc)
new_esEs22(xuu3110002, xuu6002, ty_Char) → new_esEs17(xuu3110002, xuu6002)
new_ltEs5(xuu33001, xuu34001, ty_Float) → new_ltEs15(xuu33001, xuu34001)
new_esEs4(Right(xuu3110000), Right(xuu6000), bff, app(ty_[], bfh)) → new_esEs12(xuu3110000, xuu6000, bfh)
new_compare31(Float(xuu33000, xuu33001), Float(xuu34000, xuu34001)) → new_compare11(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_lt19(xuu33000, xuu34000, ty_Bool) → new_lt4(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(app(ty_@3, bg), bh), ca), bd) → new_ltEs12(xuu33000, xuu34000, bg, bh, ca)
new_lt5(xuu33000, xuu34000, app(app(ty_Either, bbg), bbh)) → new_lt7(xuu33000, xuu34000, bbg, bbh)
new_esEs24(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_compare16(@0, @0) → EQ
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_ltEs19(xuu3300, xuu3400, ty_Bool) → new_ltEs18(xuu3300, xuu3400)
new_esEs20(xuu3110000, xuu6000, app(app(ty_Either, cbf), cbg)) → new_esEs4(xuu3110000, xuu6000, cbf, cbg)
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, app(app(ty_@2, de), df)) → new_ltEs4(xuu33000, xuu34000, de, df)
new_esEs27(xuu33001, xuu34001, app(ty_Ratio, dcb)) → new_esEs9(xuu33001, xuu34001, dcb)
new_esEs9(:%(xuu3110000, xuu3110001), :%(xuu6000, xuu6001), dbg) → new_asAs(new_esEs26(xuu3110000, xuu6000, dbg), new_esEs25(xuu3110001, xuu6001, dbg))
new_esEs4(Right(xuu3110000), Right(xuu6000), bff, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_esEs12([], [], ceb) → True
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Maybe, cch)) → new_esEs5(xuu3110000, xuu6000, cch)
new_esEs23(xuu3110001, xuu6001, ty_Double) → new_esEs13(xuu3110001, xuu6001)
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_@0) → new_ltEs14(xuu33000, xuu34000)
new_esEs18(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, ty_@0) → new_esEs14(xuu3110001, xuu6001)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Integer, bd) → new_ltEs13(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, app(ty_Ratio, cfe)) → new_compare9(xuu33000, xuu34000, cfe)
new_esEs20(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_lt6(xuu330, xuu340) → new_esEs8(new_compare11(xuu330, xuu340), LT)
new_ltEs17(EQ, LT) → False
new_esEs24(xuu3110000, xuu6000, app(ty_[], daf)) → new_esEs12(xuu3110000, xuu6000, daf)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Ordering, bed) → new_esEs8(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Float) → new_lt15(xuu33000, xuu34000)
new_lt20(xuu33001, xuu34001, ty_Bool) → new_lt4(xuu33001, xuu34001)
new_pePe(False, xuu168) → xuu168
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Integer) → new_ltEs13(xuu33000, xuu34000)
new_esEs12([], :(xuu6000, xuu6001), ceb) → False
new_esEs12(:(xuu3110000, xuu3110001), [], ceb) → False
new_esEs27(xuu33001, xuu34001, ty_Float) → new_esEs11(xuu33001, xuu34001)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_esEs18(xuu33000, xuu34000, app(app(ty_@2, bcg), bch)) → new_esEs7(xuu33000, xuu34000, bcg, bch)
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, ty_Integer) → new_ltEs13(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, app(app(ty_Either, cgg), cgh)) → new_esEs4(xuu3110002, xuu6002, cgg, cgh)
new_ltEs19(xuu3300, xuu3400, app(app(ty_@2, bda), bca)) → new_ltEs4(xuu3300, xuu3400, bda, bca)
new_ltEs10(xuu3300, xuu3400, eh) → new_fsEs(new_compare(xuu3300, xuu3400, eh))
new_compare32(xuu33000, xuu34000, ty_Double) → new_compare15(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, app(app(ty_@2, bea), beb)) → new_ltEs4(xuu33001, xuu34001, bea, beb)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Char, bd) → new_ltEs8(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, ty_Ordering) → new_esEs8(xuu3110002, xuu6002)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_[], ccg)) → new_esEs12(xuu3110000, xuu6000, ccg)
new_lt20(xuu33001, xuu34001, app(app(ty_Either, he), hf)) → new_lt7(xuu33001, xuu34001, he, hf)
new_ltEs20(xuu33002, xuu34002, app(app(ty_@2, bbe), bbf)) → new_ltEs4(xuu33002, xuu34002, bbe, bbf)
new_primCmpNat0(Zero, Succ(xuu3400)) → LT
new_lt5(xuu33000, xuu34000, ty_Float) → new_lt15(xuu33000, xuu34000)
new_ltEs19(xuu3300, xuu3400, ty_Float) → new_ltEs15(xuu3300, xuu3400)
new_esEs4(Right(xuu3110000), Right(xuu6000), bff, app(app(ty_@2, bgg), bgh)) → new_esEs7(xuu3110000, xuu6000, bgg, bgh)
new_compare14(xuu33000, xuu34000, False) → GT
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_Ratio, ccc), bd) → new_ltEs11(xuu33000, xuu34000, ccc)
new_esEs8(LT, LT) → True
new_compare25(xuu33000, xuu34000, True, gg, gh, ha) → EQ
new_lt18(xuu33000, xuu34000) → new_esEs8(new_compare8(xuu33000, xuu34000), LT)
new_lt19(xuu33000, xuu34000, app(app(ty_@2, hb), hc)) → new_lt16(xuu33000, xuu34000, hb, hc)
new_esEs18(xuu33000, xuu34000, app(ty_Ratio, bha)) → new_esEs9(xuu33000, xuu34000, bha)
new_ltEs20(xuu33002, xuu34002, app(ty_Maybe, bah)) → new_ltEs9(xuu33002, xuu34002, bah)
new_esEs28(xuu33000, xuu34000, ty_Integer) → new_esEs16(xuu33000, xuu34000)
new_esEs20(xuu3110000, xuu6000, app(app(app(ty_@3, cbc), cbd), cbe)) → new_esEs6(xuu3110000, xuu6000, cbc, cbd, cbe)
new_pePe(True, xuu168) → True
new_primEqNat0(Zero, Zero) → True
new_compare26(xuu33000, xuu34000, True) → EQ
new_compare23(Nothing, Just(xuu3400), False, dbh) → LT
new_ltEs20(xuu33002, xuu34002, app(app(app(ty_@3, bbb), bbc), bbd)) → new_ltEs12(xuu33002, xuu34002, bbb, bbc, bbd)
new_lt16(xuu33000, xuu34000, hb, hc) → new_esEs8(new_compare27(xuu33000, xuu34000, hb, hc), LT)
new_compare29(xuu33000, xuu34000, True, h, ba) → EQ
new_esEs14(@0, @0) → True
new_compare111(xuu33000, xuu34000, False, h, ba) → GT
new_esEs18(xuu33000, xuu34000, ty_Bool) → new_esEs15(xuu33000, xuu34000)
new_compare14(xuu33000, xuu34000, True) → LT
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Bool, bd) → new_ltEs18(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, app(app(ty_@2, cha), chb)) → new_esEs7(xuu3110002, xuu6002, cha, chb)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Integer, bed) → new_esEs16(xuu3110000, xuu6000)
new_esEs19(xuu3110001, xuu6001, app(ty_[], bhg)) → new_esEs12(xuu3110001, xuu6001, bhg)
new_compare26(xuu33000, xuu34000, False) → new_compare14(xuu33000, xuu34000, new_ltEs17(xuu33000, xuu34000))
new_ltEs17(GT, LT) → False
new_compare(:(xuu33000, xuu33001), :(xuu34000, xuu34001), eh) → new_primCompAux1(xuu33000, xuu34000, new_compare(xuu33001, xuu34001, eh), eh)
new_lt5(xuu33000, xuu34000, ty_Char) → new_lt8(xuu33000, xuu34000)
new_sr(xuu3110001, xuu6001) → new_primMulInt(xuu3110001, xuu6001)
new_ltEs19(xuu3300, xuu3400, app(app(app(ty_@3, hd), gd), ge)) → new_ltEs12(xuu3300, xuu3400, hd, gd, ge)
new_esEs24(xuu3110000, xuu6000, app(app(ty_@2, dbe), dbf)) → new_esEs7(xuu3110000, xuu6000, dbe, dbf)
new_compare32(xuu33000, xuu34000, ty_Int) → new_compare11(xuu33000, xuu34000)
new_esEs8(GT, GT) → True
new_esEs18(xuu33000, xuu34000, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs6(xuu33000, xuu34000, bcd, bce, bcf)
new_ltEs20(xuu33002, xuu34002, app(ty_Ratio, dcc)) → new_ltEs11(xuu33002, xuu34002, dcc)
new_compare32(xuu33000, xuu34000, ty_Bool) → new_compare6(xuu33000, xuu34000)
new_lt19(xuu33000, xuu34000, app(ty_Ratio, dca)) → new_lt11(xuu33000, xuu34000, dca)
new_lt20(xuu33001, xuu34001, ty_Double) → new_lt17(xuu33001, xuu34001)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs19(xuu3300, xuu3400, app(ty_Maybe, cdh)) → new_ltEs9(xuu3300, xuu3400, cdh)
new_esEs28(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_esEs4(Right(xuu3110000), Right(xuu6000), bff, app(app(ty_Either, bge), bgf)) → new_esEs4(xuu3110000, xuu6000, bge, bgf)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Int, bd) → new_ltEs6(xuu33000, xuu34000)
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_lt20(xuu33001, xuu34001, app(ty_Ratio, dcb)) → new_lt11(xuu33001, xuu34001, dcb)
new_esEs15(True, True) → True
new_esEs20(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_compare18(xuu33000, xuu34000, gg, gh, ha) → new_compare25(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, gg, gh, ha), gg, gh, ha)
new_esEs22(xuu3110002, xuu6002, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs6(xuu3110002, xuu6002, cgd, cge, cgf)
new_esEs23(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs4(Right(xuu3110000), Right(xuu6000), bff, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(ty_Either, bfb), bfc), bed) → new_esEs4(xuu3110000, xuu6000, bfb, bfc)
new_ltEs17(LT, GT) → True
new_primPlusNat1(Zero, Succ(xuu9700)) → Succ(xuu9700)
new_primPlusNat1(Succ(xuu28200), Zero) → Succ(xuu28200)
new_esEs13(Double(xuu3110000, xuu3110001), Double(xuu6000, xuu6001)) → new_esEs10(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Float) → new_ltEs15(xuu33000, xuu34000)
new_esEs21(xuu3110000, xuu6000, app(ty_Ratio, cec)) → new_esEs9(xuu3110000, xuu6000, cec)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(ty_@2, ef), eg)) → new_ltEs4(xuu33000, xuu34000, ef, eg)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_Ratio, cea)) → new_ltEs11(xuu33000, xuu34000, cea)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Double, bed) → new_esEs13(xuu3110000, xuu6000)
new_ltEs18(True, True) → True
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Int, bed) → new_esEs10(xuu3110000, xuu6000)
new_compare32(xuu33000, xuu34000, app(app(ty_@2, ga), gb)) → new_compare27(xuu33000, xuu34000, ga, gb)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs5(xuu33001, xuu34001, ty_Double) → new_ltEs16(xuu33001, xuu34001)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_ltEs7(Right(xuu33000), Left(xuu34000), cd, bd) → False
new_esEs24(xuu3110000, xuu6000, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs6(xuu3110000, xuu6000, dah, dba, dbb)
new_lt12(xuu33000, xuu34000, gg, gh, ha) → new_esEs8(new_compare18(xuu33000, xuu34000, gg, gh, ha), LT)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(ty_Either, dg), dh)) → new_ltEs7(xuu33000, xuu34000, dg, dh)
new_compare6(xuu33000, xuu34000) → new_compare24(xuu33000, xuu34000, new_esEs15(xuu33000, xuu34000))
new_esEs21(xuu3110000, xuu6000, app(app(ty_@2, cfc), cfd)) → new_esEs7(xuu3110000, xuu6000, cfc, cfd)
new_esEs28(xuu33000, xuu34000, ty_Double) → new_esEs13(xuu33000, xuu34000)
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu60000))) → False
new_ltEs18(False, False) → True
new_primCompAux0(xuu183, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs20(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_ltEs5(xuu33001, xuu34001, ty_Integer) → new_ltEs13(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_compare32(xuu33000, xuu34000, app(app(app(ty_@3, ff), fg), fh)) → new_compare18(xuu33000, xuu34000, ff, fg, fh)
new_compare32(xuu33000, xuu34000, app(app(ty_Either, fa), fb)) → new_compare17(xuu33000, xuu34000, fa, fb)
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, app(ty_Ratio, ccd)) → new_ltEs11(xuu33000, xuu34000, ccd)
new_esEs20(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs21(xuu3110000, xuu6000, app(app(ty_Either, cfa), cfb)) → new_esEs4(xuu3110000, xuu6000, cfa, cfb)
new_compare23(Nothing, Nothing, False, dbh) → LT
new_esEs4(Right(xuu3110000), Right(xuu6000), bff, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_compare([], [], eh) → EQ
new_ltEs17(EQ, EQ) → True
new_ltEs19(xuu3300, xuu3400, ty_Ordering) → new_ltEs17(xuu3300, xuu3400)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Char, bed) → new_esEs17(xuu3110000, xuu6000)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(ty_@2, cb), cc), bd) → new_ltEs4(xuu33000, xuu34000, cb, cc)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_compare25(xuu33000, xuu34000, False, gg, gh, ha) → new_compare13(xuu33000, xuu34000, new_ltEs12(xuu33000, xuu34000, gg, gh, ha), gg, gh, ha)
new_ltEs20(xuu33002, xuu34002, ty_Bool) → new_ltEs18(xuu33002, xuu34002)
new_lt20(xuu33001, xuu34001, ty_Char) → new_lt8(xuu33001, xuu34001)
new_esEs28(xuu33000, xuu34000, app(app(ty_@2, hb), hc)) → new_esEs7(xuu33000, xuu34000, hb, hc)
new_esEs4(Right(xuu3110000), Right(xuu6000), bff, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Int) → new_lt6(xuu33000, xuu34000)
new_primCmpNat0(Succ(xuu3300), Succ(xuu3400)) → new_primCmpNat0(xuu3300, xuu3400)
new_lt20(xuu33001, xuu34001, ty_Integer) → new_lt13(xuu33001, xuu34001)
new_lt8(xuu33000, xuu34000) → new_esEs8(new_compare30(xuu33000, xuu34000), LT)
new_esEs18(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_esEs26(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Double) → new_ltEs16(xuu33000, xuu34000)
new_esEs18(xuu33000, xuu34000, ty_Int) → new_esEs10(xuu33000, xuu34000)
new_esEs28(xuu33000, xuu34000, ty_Char) → new_esEs17(xuu33000, xuu34000)
new_esEs4(Right(xuu3110000), Right(xuu6000), bff, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs23(xuu3110001, xuu6001, ty_Char) → new_esEs17(xuu3110001, xuu6001)
new_esEs23(xuu3110001, xuu6001, app(ty_[], chd)) → new_esEs12(xuu3110001, xuu6001, chd)
new_primEqNat0(Succ(xuu31100000), Succ(xuu60000)) → new_primEqNat0(xuu31100000, xuu60000)
new_esEs27(xuu33001, xuu34001, ty_Ordering) → new_esEs8(xuu33001, xuu34001)
new_esEs19(xuu3110001, xuu6001, app(app(app(ty_@3, caa), cab), cac)) → new_esEs6(xuu3110001, xuu6001, caa, cab, cac)
new_primCompAux1(xuu33000, xuu34000, xuu169, eh) → new_primCompAux0(xuu169, new_compare32(xuu33000, xuu34000, eh))
new_compare15(Double(xuu33000, xuu33001), Double(xuu34000, xuu34001)) → new_compare11(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_primCmpInt(Neg(Succ(xuu3300)), Neg(xuu340)) → new_primCmpNat0(xuu340, Succ(xuu3300))
new_ltEs19(xuu3300, xuu3400, app(app(ty_Either, cd), bd)) → new_ltEs7(xuu3300, xuu3400, cd, bd)
new_esEs24(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs18(xuu33000, xuu34000, ty_Char) → new_esEs17(xuu33000, xuu34000)
new_esEs23(xuu3110001, xuu6001, ty_Bool) → new_esEs15(xuu3110001, xuu6001)
new_lt19(xuu33000, xuu34000, app(app(ty_Either, h), ba)) → new_lt7(xuu33000, xuu34000, h, ba)
new_esEs28(xuu33000, xuu34000, ty_Ordering) → new_esEs8(xuu33000, xuu34000)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu60000))) → False
new_esEs21(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_lt4(xuu33000, xuu34000) → new_esEs8(new_compare6(xuu33000, xuu34000), LT)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(app(ty_@3, ec), ed), ee)) → new_ltEs12(xuu33000, xuu34000, ec, ed, ee)
new_ltEs20(xuu33002, xuu34002, ty_Integer) → new_ltEs13(xuu33002, xuu34002)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Float, bd) → new_ltEs15(xuu33000, xuu34000)
new_compare17(xuu33000, xuu34000, h, ba) → new_compare29(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, h, ba), h, ba)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu3300), Zero) → GT
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_Maybe, ea)) → new_ltEs9(xuu33000, xuu34000, ea)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3400))) → LT
new_ltEs20(xuu33002, xuu34002, ty_@0) → new_ltEs14(xuu33002, xuu34002)
new_esEs7(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), bhd, bhe) → new_asAs(new_esEs20(xuu3110000, xuu6000, bhd), new_esEs19(xuu3110001, xuu6001, bhe))
new_esEs21(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_sr0(Integer(xuu340000), Integer(xuu330010)) → Integer(new_primMulInt(xuu340000, xuu330010))
new_primPlusNat1(Succ(xuu28200), Succ(xuu9700)) → Succ(Succ(new_primPlusNat1(xuu28200, xuu9700)))
new_compare28(xuu33000, xuu34000, True, hb, hc) → EQ
new_primEqInt(Pos(Succ(xuu31100000)), Neg(xuu6000)) → False
new_primEqInt(Neg(Succ(xuu31100000)), Pos(xuu6000)) → False
new_ltEs19(xuu3300, xuu3400, ty_Double) → new_ltEs16(xuu3300, xuu3400)
new_esEs25(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_compare9(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Int) → new_compare11(new_sr(xuu33000, xuu34001), new_sr(xuu34000, xuu33001))
new_esEs27(xuu33001, xuu34001, app(ty_Maybe, hg)) → new_esEs5(xuu33001, xuu34001, hg)
new_compare32(xuu33000, xuu34000, app(ty_[], fd)) → new_compare(xuu33000, xuu34000, fd)
new_esEs18(xuu33000, xuu34000, app(ty_[], bcc)) → new_esEs12(xuu33000, xuu34000, bcc)
new_compare23(Just(xuu3300), Just(xuu3400), False, dbh) → new_compare110(xuu3300, xuu3400, new_ltEs19(xuu3300, xuu3400, dbh), dbh)
new_lt11(xuu33000, xuu34000, dca) → new_esEs8(new_compare9(xuu33000, xuu34000, dca), LT)
new_lt19(xuu33000, xuu34000, ty_@0) → new_lt14(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, ty_Float) → new_ltEs15(xuu33002, xuu34002)
new_lt7(xuu33000, xuu34000, h, ba) → new_esEs8(new_compare17(xuu33000, xuu34000, h, ba), LT)
new_esEs26(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_lt5(xuu33000, xuu34000, app(ty_Maybe, bcb)) → new_lt9(xuu33000, xuu34000, bcb)
new_primEqInt(Pos(Zero), Neg(Succ(xuu60000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu60000))) → False
new_esEs20(xuu3110000, xuu6000, app(ty_[], cba)) → new_esEs12(xuu3110000, xuu6000, cba)
new_ltEs9(Just(xuu33000), Nothing, cdh) → False
new_esEs4(Right(xuu3110000), Right(xuu6000), bff, app(ty_Ratio, bfg)) → new_esEs9(xuu3110000, xuu6000, bfg)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3400))) → new_primCmpNat0(Zero, Succ(xuu3400))
new_compare24(xuu33000, xuu34000, True) → EQ
new_esEs27(xuu33001, xuu34001, app(app(ty_@2, bad), bae)) → new_esEs7(xuu33001, xuu34001, bad, bae)
new_lt13(xuu33000, xuu34000) → new_esEs8(new_compare12(xuu33000, xuu34000), LT)
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, app(app(app(ty_@3, db), dc), dd)) → new_ltEs12(xuu33000, xuu34000, db, dc, dd)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, ty_Char) → new_compare30(xuu33000, xuu34000)
new_lt15(xuu33000, xuu34000) → new_esEs8(new_compare31(xuu33000, xuu34000), LT)
new_primCompAux0(xuu183, LT) → LT
new_ltEs19(xuu3300, xuu3400, ty_Char) → new_ltEs8(xuu3300, xuu3400)
new_esEs23(xuu3110001, xuu6001, ty_Float) → new_esEs11(xuu3110001, xuu6001)
new_esEs20(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_not(False) → True
new_primCmpInt(Pos(Succ(xuu3300)), Pos(xuu340)) → new_primCmpNat0(Succ(xuu3300), xuu340)
new_compare110(xuu135, xuu136, True, ccb) → LT
new_esEs22(xuu3110002, xuu6002, ty_Float) → new_esEs11(xuu3110002, xuu6002)
new_esEs19(xuu3110001, xuu6001, app(app(ty_@2, caf), cag)) → new_esEs7(xuu3110001, xuu6001, caf, cag)
new_ltEs19(xuu3300, xuu3400, app(ty_[], eh)) → new_ltEs10(xuu3300, xuu3400, eh)
new_ltEs5(xuu33001, xuu34001, app(ty_Ratio, bhb)) → new_ltEs11(xuu33001, xuu34001, bhb)
new_ltEs9(Nothing, Nothing, cdh) → True
new_esEs19(xuu3110001, xuu6001, ty_Char) → new_esEs17(xuu3110001, xuu6001)
new_lt20(xuu33001, xuu34001, app(ty_[], hh)) → new_lt10(xuu33001, xuu34001, hh)
new_ltEs19(xuu3300, xuu3400, ty_Int) → new_ltEs6(xuu3300, xuu3400)
new_esEs27(xuu33001, xuu34001, ty_@0) → new_esEs14(xuu33001, xuu34001)
new_ltEs16(xuu3300, xuu3400) → new_fsEs(new_compare15(xuu3300, xuu3400))
new_lt19(xuu33000, xuu34000, app(app(app(ty_@3, gg), gh), ha)) → new_lt12(xuu33000, xuu34000, gg, gh, ha)
new_lt20(xuu33001, xuu34001, ty_Int) → new_lt6(xuu33001, xuu34001)
new_lt20(xuu33001, xuu34001, ty_Ordering) → new_lt18(xuu33001, xuu34001)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_compare12(Integer(xuu33000), Integer(xuu34000)) → new_primCmpInt(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, app(ty_Maybe, dag)) → new_esEs5(xuu3110000, xuu6000, dag)
new_esEs18(xuu33000, xuu34000, app(app(ty_Either, bbg), bbh)) → new_esEs4(xuu33000, xuu34000, bbg, bbh)
new_lt5(xuu33000, xuu34000, app(app(ty_@2, bcg), bch)) → new_lt16(xuu33000, xuu34000, bcg, bch)
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, app(ty_[], da)) → new_ltEs10(xuu33000, xuu34000, da)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_primCmpInt(Pos(Succ(xuu3300)), Neg(xuu340)) → GT
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Double, bd) → new_ltEs16(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, ty_Bool) → new_ltEs18(xuu33001, xuu34001)
new_esEs21(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_compare32(xuu33000, xuu34000, ty_Ordering) → new_compare8(xuu33000, xuu34000)
new_lt5(xuu33000, xuu34000, app(ty_Ratio, bha)) → new_lt11(xuu33000, xuu34000, bha)
new_primMulInt(Pos(xuu31100010), Pos(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Bool, bed) → new_esEs15(xuu3110000, xuu6000)
new_esEs24(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs27(xuu33001, xuu34001, ty_Char) → new_esEs17(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, app(app(ty_Either, daa), dab)) → new_esEs4(xuu3110001, xuu6001, daa, dab)
new_esEs22(xuu3110002, xuu6002, ty_Double) → new_esEs13(xuu3110002, xuu6002)
new_esEs22(xuu3110002, xuu6002, ty_Int) → new_esEs10(xuu3110002, xuu6002)
new_compare32(xuu33000, xuu34000, ty_@0) → new_compare16(xuu33000, xuu34000)
new_primMulInt(Neg(xuu31100010), Neg(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_esEs24(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_esEs28(xuu33000, xuu34000, app(ty_Ratio, dca)) → new_esEs9(xuu33000, xuu34000, dca)
new_lt20(xuu33001, xuu34001, ty_@0) → new_lt14(xuu33001, xuu34001)
new_primEqNat0(Succ(xuu31100000), Zero) → False
new_primEqNat0(Zero, Succ(xuu60000)) → False
new_esEs21(xuu3110000, xuu6000, app(ty_[], ced)) → new_esEs12(xuu3110000, xuu6000, ced)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(ty_Either, bb), bc), bd) → new_ltEs7(xuu33000, xuu34000, bb, bc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(xuu3110000, xuu6000, app(app(ty_Either, dbc), dbd)) → new_esEs4(xuu3110000, xuu6000, dbc, dbd)
new_esEs28(xuu33000, xuu34000, app(app(app(ty_@3, gg), gh), ha)) → new_esEs6(xuu33000, xuu34000, gg, gh, ha)
new_primPlusNat0(xuu107, xuu600100) → new_primPlusNat1(xuu107, Succ(xuu600100))
new_lt19(xuu33000, xuu34000, ty_Double) → new_lt17(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, ty_Integer) → new_compare12(xuu33000, xuu34000)
new_esEs27(xuu33001, xuu34001, app(app(ty_Either, he), hf)) → new_esEs4(xuu33001, xuu34001, he, hf)
new_esEs27(xuu33001, xuu34001, app(app(app(ty_@3, baa), bab), bac)) → new_esEs6(xuu33001, xuu34001, baa, bab, bac)
new_esEs4(Right(xuu3110000), Right(xuu6000), bff, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_lt5(xuu33000, xuu34000, ty_Integer) → new_lt13(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, app(ty_Maybe, bhh)) → new_esEs5(xuu3110001, xuu6001, bhh)
new_esEs27(xuu33001, xuu34001, ty_Integer) → new_esEs16(xuu33001, xuu34001)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Float, bed) → new_esEs11(xuu3110000, xuu6000)
new_ltEs5(xuu33001, xuu34001, ty_Int) → new_ltEs6(xuu33001, xuu34001)
new_ltEs14(xuu3300, xuu3400) → new_fsEs(new_compare16(xuu3300, xuu3400))
new_ltEs5(xuu33001, xuu34001, app(ty_Maybe, bdd)) → new_ltEs9(xuu33001, xuu34001, bdd)
new_esEs25(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_esEs21(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3400))) → new_primCmpNat0(Succ(xuu3400), Zero)
new_ltEs5(xuu33001, xuu34001, ty_Ordering) → new_ltEs17(xuu33001, xuu34001)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3400))) → GT
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Ordering) → new_ltEs17(xuu33000, xuu34000)
new_compare110(xuu135, xuu136, False, ccb) → GT
new_ltEs20(xuu33002, xuu34002, ty_Char) → new_ltEs8(xuu33002, xuu34002)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(app(ty_@3, cda), cdb), cdc)) → new_esEs6(xuu3110000, xuu6000, cda, cdb, cdc)
new_compare19(xuu33000, xuu34000, True, hb, hc) → LT
new_lt20(xuu33001, xuu34001, app(ty_Maybe, hg)) → new_lt9(xuu33001, xuu34001, hg)
new_lt19(xuu33000, xuu34000, app(ty_[], gf)) → new_lt10(xuu33000, xuu34000, gf)
new_compare23(xuu330, xuu340, True, dbh) → EQ
new_esEs19(xuu3110001, xuu6001, ty_Float) → new_esEs11(xuu3110001, xuu6001)
new_esEs16(Integer(xuu3110000), Integer(xuu6000)) → new_primEqInt(xuu3110000, xuu6000)
new_ltEs20(xuu33002, xuu34002, ty_Ordering) → new_ltEs17(xuu33002, xuu34002)
new_lt5(xuu33000, xuu34000, ty_Bool) → new_lt4(xuu33000, xuu34000)
new_esEs23(xuu3110001, xuu6001, ty_@0) → new_esEs14(xuu3110001, xuu6001)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs21(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Ordering, bd) → new_ltEs17(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, app(ty_Maybe, cbb)) → new_esEs5(xuu3110000, xuu6000, cbb)
new_esEs4(Right(xuu3110000), Right(xuu6000), bff, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, app(app(ty_Either, ce), cf)) → new_ltEs7(xuu33000, xuu34000, ce, cf)
new_asAs(False, xuu142) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Int) → new_ltEs6(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, ty_Double) → new_ltEs16(xuu33002, xuu34002)
new_lt17(xuu33000, xuu34000) → new_esEs8(new_compare15(xuu33000, xuu34000), LT)
new_primMulInt(Pos(xuu31100010), Neg(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_primMulInt(Neg(xuu31100010), Pos(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_ltEs11(xuu3300, xuu3400, bhc) → new_fsEs(new_compare9(xuu3300, xuu3400, bhc))
new_primMulNat0(Zero, Succ(xuu600100)) → Zero
new_primMulNat0(Succ(xuu311000100), Zero) → Zero
new_esEs27(xuu33001, xuu34001, ty_Double) → new_esEs13(xuu33001, xuu34001)
new_esEs24(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_lt5(xuu33000, xuu34000, ty_Int) → new_lt6(xuu33000, xuu34000)
new_esEs23(xuu3110001, xuu6001, app(app(app(ty_@3, chf), chg), chh)) → new_esEs6(xuu3110001, xuu6001, chf, chg, chh)
new_lt19(xuu33000, xuu34000, ty_Ordering) → new_lt18(xuu33000, xuu34000)
new_esEs21(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Char) → new_lt8(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, app(ty_Maybe, fc)) → new_compare7(xuu33000, xuu34000, fc)
new_esEs23(xuu3110001, xuu6001, app(app(ty_@2, dac), dad)) → new_esEs7(xuu3110001, xuu6001, dac, dad)
new_lt5(xuu33000, xuu34000, app(app(app(ty_@3, bcd), bce), bcf)) → new_lt12(xuu33000, xuu34000, bcd, bce, bcf)
new_esEs18(xuu33000, xuu34000, app(ty_Maybe, bcb)) → new_esEs5(xuu33000, xuu34000, bcb)
new_esEs24(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_compare27(xuu33000, xuu34000, hb, hc) → new_compare28(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, hb, hc), hb, hc)
new_esEs18(xuu33000, xuu34000, ty_Ordering) → new_esEs8(xuu33000, xuu34000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_Maybe, bef), bed) → new_esEs5(xuu3110000, xuu6000, bef)
new_lt9(xuu33000, xuu34000, gc) → new_esEs8(new_compare7(xuu33000, xuu34000, gc), LT)
new_lt20(xuu33001, xuu34001, app(app(ty_@2, bad), bae)) → new_lt16(xuu33001, xuu34001, bad, bae)
new_esEs28(xuu33000, xuu34000, app(app(ty_Either, h), ba)) → new_esEs4(xuu33000, xuu34000, h, ba)
new_compare8(xuu33000, xuu34000) → new_compare26(xuu33000, xuu34000, new_esEs8(xuu33000, xuu34000))
new_esEs23(xuu3110001, xuu6001, app(ty_Maybe, che)) → new_esEs5(xuu3110001, xuu6001, che)
new_lt5(xuu33000, xuu34000, ty_Double) → new_lt17(xuu33000, xuu34000)
new_esEs6(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), cff, cfg, cfh) → new_asAs(new_esEs24(xuu3110000, xuu6000, cff), new_asAs(new_esEs23(xuu3110001, xuu6001, cfg), new_esEs22(xuu3110002, xuu6002, cfh)))
new_lt5(xuu33000, xuu34000, app(ty_[], bcc)) → new_lt10(xuu33000, xuu34000, bcc)
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, ty_Char) → new_ltEs8(xuu33000, xuu34000)
new_ltEs17(GT, GT) → True
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, ty_Ordering) → new_ltEs17(xuu33000, xuu34000)
new_ltEs19(xuu3300, xuu3400, ty_@0) → new_ltEs14(xuu3300, xuu3400)
new_ltEs17(GT, EQ) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Char) → new_ltEs8(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, app(ty_[], cgb)) → new_esEs12(xuu3110002, xuu6002, cgb)
new_esEs5(Just(xuu3110000), Nothing, cce) → False
new_esEs5(Nothing, Just(xuu6000), cce) → False
new_ltEs15(xuu3300, xuu3400) → new_fsEs(new_compare31(xuu3300, xuu3400))
new_esEs22(xuu3110002, xuu6002, ty_Bool) → new_esEs15(xuu3110002, xuu6002)
new_esEs19(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_compare11(xuu33, xuu34) → new_primCmpInt(xuu33, xuu34)
new_esEs28(xuu33000, xuu34000, ty_Bool) → new_esEs15(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, app(ty_[], bde)) → new_ltEs10(xuu33001, xuu34001, bde)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(ty_@2, bfd), bfe), bed) → new_esEs7(xuu3110000, xuu6000, bfd, bfe)
new_lt19(xuu33000, xuu34000, ty_Integer) → new_lt13(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, app(app(ty_Either, baf), bag)) → new_ltEs7(xuu33002, xuu34002, baf, bag)
new_ltEs18(True, False) → False
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_Maybe, be), bd) → new_ltEs9(xuu33000, xuu34000, be)
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, ty_Double) → new_ltEs16(xuu33000, xuu34000)
new_lt10(xuu33000, xuu34000, gf) → new_esEs8(new_compare(xuu33000, xuu34000, gf), LT)
new_esEs20(xuu3110000, xuu6000, app(ty_Ratio, cah)) → new_esEs9(xuu3110000, xuu6000, cah)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_[], eb)) → new_ltEs10(xuu33000, xuu34000, eb)
new_ltEs12(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), hd, gd, ge) → new_pePe(new_lt19(xuu33000, xuu34000, hd), new_asAs(new_esEs28(xuu33000, xuu34000, hd), new_pePe(new_lt20(xuu33001, xuu34001, gd), new_asAs(new_esEs27(xuu33001, xuu34001, gd), new_ltEs20(xuu33002, xuu34002, ge)))))
new_esEs22(xuu3110002, xuu6002, ty_@0) → new_esEs14(xuu3110002, xuu6002)
new_esEs5(Nothing, Nothing, cce) → True
new_esEs23(xuu3110001, xuu6001, app(ty_Ratio, chc)) → new_esEs9(xuu3110001, xuu6001, chc)
new_esEs28(xuu33000, xuu34000, app(ty_Maybe, gc)) → new_esEs5(xuu33000, xuu34000, gc)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs28(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, ty_Integer) → new_esEs16(xuu3110002, xuu6002)
new_esEs28(xuu33000, xuu34000, ty_Int) → new_esEs10(xuu33000, xuu34000)
new_ltEs13(xuu3300, xuu3400) → new_fsEs(new_compare12(xuu3300, xuu3400))
new_esEs19(xuu3110001, xuu6001, app(ty_Ratio, bhf)) → new_esEs9(xuu3110001, xuu6001, bhf)
new_esEs21(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_compare24(xuu33000, xuu34000, False) → new_compare10(xuu33000, xuu34000, new_ltEs18(xuu33000, xuu34000))
new_esEs20(xuu3110000, xuu6000, app(app(ty_@2, cbh), cca)) → new_esEs7(xuu3110000, xuu6000, cbh, cca)
new_ltEs18(False, True) → True
new_esEs20(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_esEs22(xuu3110002, xuu6002, app(ty_Maybe, cgc)) → new_esEs5(xuu3110002, xuu6002, cgc)
new_esEs21(xuu3110000, xuu6000, app(ty_Maybe, cee)) → new_esEs5(xuu3110000, xuu6000, cee)
new_primPlusNat1(Zero, Zero) → Zero
new_compare111(xuu33000, xuu34000, True, h, ba) → LT
new_esEs21(xuu3110000, xuu6000, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs6(xuu3110000, xuu6000, cef, ceg, ceh)
new_lt14(xuu33000, xuu34000) → new_esEs8(new_compare16(xuu33000, xuu34000), LT)
new_lt20(xuu33001, xuu34001, ty_Float) → new_lt15(xuu33001, xuu34001)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_[], bee), bed) → new_esEs12(xuu3110000, xuu6000, bee)
new_ltEs5(xuu33001, xuu34001, app(app(ty_Either, bdb), bdc)) → new_ltEs7(xuu33001, xuu34001, bdb, bdc)
new_esEs12(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), ceb) → new_asAs(new_esEs21(xuu3110000, xuu6000, ceb), new_esEs12(xuu3110001, xuu6001, ceb))
new_asAs(True, xuu142) → xuu142
new_esEs28(xuu33000, xuu34000, app(ty_[], gf)) → new_esEs12(xuu33000, xuu34000, gf)
new_esEs27(xuu33001, xuu34001, app(ty_[], hh)) → new_esEs12(xuu33001, xuu34001, hh)
new_esEs19(xuu3110001, xuu6001, app(app(ty_Either, cad), cae)) → new_esEs4(xuu3110001, xuu6001, cad, cae)
new_primMulNat0(Succ(xuu311000100), Succ(xuu600100)) → new_primPlusNat0(new_primMulNat0(xuu311000100, Succ(xuu600100)), xuu600100)
new_ltEs17(LT, EQ) → True
new_compare30(Char(xuu33000), Char(xuu34000)) → new_primCmpNat0(xuu33000, xuu34000)
new_esEs4(Right(xuu3110000), Left(xuu6000), bff, bed) → False
new_esEs4(Left(xuu3110000), Right(xuu6000), bff, bed) → False
new_compare29(xuu33000, xuu34000, False, h, ba) → new_compare111(xuu33000, xuu34000, new_ltEs7(xuu33000, xuu34000, h, ba), h, ba)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_@2, cdf), cdg)) → new_esEs7(xuu3110000, xuu6000, cdf, cdg)
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_esEs27(xuu33001, xuu34001, ty_Int) → new_esEs10(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_esEs27(xuu33001, xuu34001, ty_Bool) → new_esEs15(xuu33001, xuu34001)
new_esEs21(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(app(ty_@3, beg), beh), bfa), bed) → new_esEs6(xuu3110000, xuu6000, beg, beh, bfa)
new_ltEs6(xuu3300, xuu3400) → new_fsEs(new_compare11(xuu3300, xuu3400))
new_fsEs(xuu152) → new_not(new_esEs8(xuu152, GT))
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, ty_Float) → new_ltEs15(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, ty_Char) → new_ltEs8(xuu33001, xuu34001)
new_ltEs19(xuu3300, xuu3400, ty_Integer) → new_ltEs13(xuu3300, xuu3400)
new_esEs19(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_Ratio, bec), bed) → new_esEs9(xuu3110000, xuu6000, bec)
new_compare7(xuu33000, xuu34000, gc) → new_compare23(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, gc), gc)
new_compare10(xuu33000, xuu34000, True) → LT
new_ltEs5(xuu33001, xuu34001, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs12(xuu33001, xuu34001, bdf, bdg, bdh)
new_compare19(xuu33000, xuu34000, False, hb, hc) → GT
new_ltEs20(xuu33002, xuu34002, ty_Int) → new_ltEs6(xuu33002, xuu34002)
new_ltEs17(EQ, GT) → True
new_compare13(xuu33000, xuu34000, True, gg, gh, ha) → LT
new_compare10(xuu33000, xuu34000, False) → GT
new_esEs10(xuu311000, xuu600) → new_primEqInt(xuu311000, xuu600)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Ratio, ccf)) → new_esEs9(xuu3110000, xuu6000, ccf)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_@0, bed) → new_esEs14(xuu3110000, xuu6000)
new_lt5(xuu33000, xuu34000, ty_@0) → new_lt14(xuu33000, xuu34000)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_Either, cdd), cde)) → new_esEs4(xuu3110000, xuu6000, cdd, cde)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(xuu3110000, xuu6000, app(ty_Ratio, dae)) → new_esEs9(xuu3110000, xuu6000, dae)
new_primCompAux0(xuu183, EQ) → xuu183
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_[], bf), bd) → new_ltEs10(xuu33000, xuu34000, bf)
new_compare32(xuu33000, xuu34000, ty_Float) → new_compare31(xuu33000, xuu34000)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare9(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Integer) → new_compare12(new_sr0(xuu33000, xuu34001), new_sr0(xuu34000, xuu33001))
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, ty_@0) → new_ltEs14(xuu33000, xuu34000)
new_esEs11(Float(xuu3110000, xuu3110001), Float(xuu6000, xuu6001)) → new_esEs10(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_primCmpInt(Neg(Succ(xuu3300)), Pos(xuu340)) → LT
new_ltEs7(Right(xuu33000), Right(xuu34000), cd, ty_Int) → new_ltEs6(xuu33000, xuu34000)
new_not(True) → False
new_esEs15(False, False) → True
new_esEs19(xuu3110001, xuu6001, ty_Double) → new_esEs13(xuu3110001, xuu6001)

The set Q consists of the following terms:

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

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

new_addToFM_C1(xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_addToFM_C(xuu64, Nothing, xuu31101, h, ba)
new_addToFM_C(Branch(Just(xuu600), xuu61, xuu62, xuu63, xuu64), Nothing, xuu31101, h, ba) → new_addToFM_C2(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Just(xuu600), False, h), LT), h, ba)
new_addToFM_C20(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, False, h, ba) → new_addToFM_C11(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, new_esEs8(new_compare23(Just(xuu311000), Nothing, False, h), GT), h, ba)
new_addToFM_C21(xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, bb, bc) → new_addToFM_C(xuu20, Just(xuu22), xuu23, bb, bc)
new_addToFM_C(Branch(Just(xuu600), xuu61, xuu62, xuu63, xuu64), Just(xuu311000), xuu31101, h, ba) → new_addToFM_C21(xuu600, xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, new_esEs8(new_compare23(Just(xuu311000), Just(xuu600), new_esEs29(xuu311000, xuu600, h), h), LT), h, ba)
new_addToFM_C2(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_addToFM_C(xuu63, Nothing, xuu31101, h, ba)
new_addToFM_C(Branch(Nothing, xuu61, xuu62, xuu63, xuu64), Just(xuu311000), xuu31101, h, ba) → new_addToFM_C20(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, new_esEs8(new_compare23(Just(xuu311000), Nothing, False, h), LT), h, ba)
new_addToFM_C20(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, True, h, ba) → new_addToFM_C(xuu63, Just(xuu311000), xuu31101, h, ba)
new_addToFM_C2(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, False, h, ba) → new_addToFM_C10(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Just(xuu600), False, h), GT), h, ba)
new_addToFM_C11(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, True, h, ba) → new_addToFM_C(xuu64, Just(xuu311000), xuu31101, h, ba)
new_addToFM_C21(xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, False, bb, bc) → new_addToFM_C12(xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, new_esEs8(new_compare23(Just(xuu22), Just(xuu17), new_esEs30(xuu22, xuu17, bb), bb), GT), bb, bc)
new_addToFM_C(Branch(Nothing, xuu61, xuu62, xuu63, xuu64), Nothing, xuu31101, h, ba) → new_addToFM_C1(xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C10(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_addToFM_C(xuu64, Nothing, xuu31101, h, ba)
new_addToFM_C12(xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, bb, bc) → new_addToFM_C(xuu21, Just(xuu22), xuu23, bb, bc)

The TRS R consists of the following rules:

new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_ltEs19(xuu3300, xuu3400, app(ty_Ratio, hg)) → new_ltEs11(xuu3300, xuu3400, hg)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_@0, bdd) → new_ltEs14(xuu33000, xuu34000)
new_lt20(xuu33001, xuu34001, app(app(app(ty_@3, dcc), dcd), dce)) → new_lt12(xuu33001, xuu34001, dcc, dcd, dce)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(ty_Maybe, bfb)) → new_ltEs9(xuu33000, xuu34000, bfb)
new_esEs22(xuu3110002, xuu6002, app(ty_Ratio, cfb)) → new_esEs9(xuu3110002, xuu6002, cfb)
new_ltEs5(xuu33001, xuu34001, ty_@0) → new_ltEs14(xuu33001, xuu34001)
new_ltEs17(LT, LT) → True
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs17(Char(xuu3110000), Char(xuu6000)) → new_primEqNat0(xuu3110000, xuu6000)
new_esEs18(xuu33000, xuu34000, ty_Integer) → new_esEs16(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_ltEs20(xuu33002, xuu34002, app(ty_[], ddc)) → new_ltEs10(xuu33002, xuu34002, ddc)
new_esEs19(xuu3110001, xuu6001, ty_Bool) → new_esEs15(xuu3110001, xuu6001)
new_compare([], :(xuu34000, xuu34001), hf) → LT
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(app(app(ty_@3, gc), gd), ge)) → new_esEs6(xuu3110000, xuu6000, gc, gd, ge)
new_ltEs9(Nothing, Just(xuu34000), bhd) → True
new_ltEs4(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bd, be) → new_pePe(new_lt5(xuu33000, xuu34000, bd), new_asAs(new_esEs18(xuu33000, xuu34000, bd), new_ltEs5(xuu33001, xuu34001, be)))
new_ltEs8(xuu3300, xuu3400) → new_fsEs(new_compare30(xuu3300, xuu3400))
new_compare23(Just(xuu3300), Nothing, False, dbb) → GT
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(ty_Maybe, gb)) → new_esEs5(xuu3110000, xuu6000, gb)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(xuu33000), Right(xuu34000), beg, bdd) → True
new_compare(:(xuu33000, xuu33001), [], hf) → GT
new_lt5(xuu33000, xuu34000, ty_Ordering) → new_lt18(xuu33000, xuu34000)
new_compare28(xuu33000, xuu34000, False, bda, bdb) → new_compare19(xuu33000, xuu34000, new_ltEs4(xuu33000, xuu34000, bda, bdb), bda, bdb)
new_compare13(xuu33000, xuu34000, False, hc, hd, he) → GT
new_esEs18(xuu33000, xuu34000, ty_Double) → new_esEs13(xuu33000, xuu34000)
new_lt19(xuu33000, xuu34000, app(ty_Maybe, hb)) → new_lt9(xuu33000, xuu34000, hb)
new_esEs22(xuu3110002, xuu6002, ty_Char) → new_esEs17(xuu3110002, xuu6002)
new_ltEs5(xuu33001, xuu34001, ty_Float) → new_ltEs15(xuu33001, xuu34001)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(ty_[], ga)) → new_esEs12(xuu3110000, xuu6000, ga)
new_compare31(Float(xuu33000, xuu33001), Float(xuu34000, xuu34001)) → new_compare11(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_lt19(xuu33000, xuu34000, ty_Bool) → new_lt4(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(app(ty_@3, beb), bec), bed), bdd) → new_ltEs12(xuu33000, xuu34000, beb, bec, bed)
new_esEs29(xuu311000, xuu600, app(app(ty_Either, fg), ed)) → new_esEs4(xuu311000, xuu600, fg, ed)
new_lt5(xuu33000, xuu34000, app(app(ty_Either, bf), bg)) → new_lt7(xuu33000, xuu34000, bf, bg)
new_esEs24(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_compare16(@0, @0) → EQ
new_esEs30(xuu22, xuu17, ty_Int) → new_esEs10(xuu22, xuu17)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_ltEs19(xuu3300, xuu3400, ty_Bool) → new_ltEs18(xuu3300, xuu3400)
new_esEs20(xuu3110000, xuu6000, app(app(ty_Either, bcc), bcd)) → new_esEs4(xuu3110000, xuu6000, bcc, bcd)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(app(ty_@2, bfh), bga)) → new_ltEs4(xuu33000, xuu34000, bfh, bga)
new_esEs27(xuu33001, xuu34001, app(ty_Ratio, dcb)) → new_esEs9(xuu33001, xuu34001, dcb)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_esEs9(:%(xuu3110000, xuu3110001), :%(xuu6000, xuu6001), dah) → new_asAs(new_esEs26(xuu3110000, xuu6000, dah), new_esEs25(xuu3110001, xuu6001, dah))
new_esEs12([], [], ccb) → True
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Maybe, cbb)) → new_esEs5(xuu3110000, xuu6000, cbb)
new_esEs23(xuu3110001, xuu6001, ty_Double) → new_esEs13(xuu3110001, xuu6001)
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_@0) → new_ltEs14(xuu33000, xuu34000)
new_esEs18(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, ty_@0) → new_esEs14(xuu3110001, xuu6001)
new_esEs30(xuu22, xuu17, ty_Double) → new_esEs13(xuu22, xuu17)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Integer, bdd) → new_ltEs13(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, app(ty_Ratio, cea)) → new_compare9(xuu33000, xuu34000, cea)
new_esEs20(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_lt6(xuu330, xuu340) → new_esEs8(new_compare11(xuu330, xuu340), LT)
new_ltEs17(EQ, LT) → False
new_esEs24(xuu3110000, xuu6000, app(ty_[], chg)) → new_esEs12(xuu3110000, xuu6000, chg)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Ordering, ed) → new_esEs8(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Float) → new_lt15(xuu33000, xuu34000)
new_lt20(xuu33001, xuu34001, ty_Bool) → new_lt4(xuu33001, xuu34001)
new_pePe(False, xuu168) → xuu168
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Integer) → new_ltEs13(xuu33000, xuu34000)
new_esEs12([], :(xuu6000, xuu6001), ccb) → False
new_esEs12(:(xuu3110000, xuu3110001), [], ccb) → False
new_esEs27(xuu33001, xuu34001, ty_Float) → new_esEs11(xuu33001, xuu34001)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_esEs18(xuu33000, xuu34000, app(app(ty_@2, cf), cg)) → new_esEs7(xuu33000, xuu34000, cf, cg)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Integer) → new_ltEs13(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, app(app(ty_Either, cfh), cga)) → new_esEs4(xuu3110002, xuu6002, cfh, cga)
new_ltEs19(xuu3300, xuu3400, app(app(ty_@2, bd), be)) → new_ltEs4(xuu3300, xuu3400, bd, be)
new_ltEs10(xuu3300, xuu3400, hf) → new_fsEs(new_compare(xuu3300, xuu3400, hf))
new_compare32(xuu33000, xuu34000, ty_Double) → new_compare15(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, app(app(ty_@2, ea), eb)) → new_ltEs4(xuu33001, xuu34001, ea, eb)
new_esEs30(xuu22, xuu17, ty_Bool) → new_esEs15(xuu22, xuu17)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Char, bdd) → new_ltEs8(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, ty_Integer) → new_esEs16(xuu22, xuu17)
new_esEs22(xuu3110002, xuu6002, ty_Ordering) → new_esEs8(xuu3110002, xuu6002)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_[], cba)) → new_esEs12(xuu3110000, xuu6000, cba)
new_esEs30(xuu22, xuu17, app(ty_Ratio, bgb)) → new_esEs9(xuu22, xuu17, bgb)
new_lt20(xuu33001, xuu34001, app(app(ty_Either, dbf), dbg)) → new_lt7(xuu33001, xuu34001, dbf, dbg)
new_ltEs20(xuu33002, xuu34002, app(app(ty_@2, ddh), dea)) → new_ltEs4(xuu33002, xuu34002, ddh, dea)
new_primCmpNat0(Zero, Succ(xuu3400)) → LT
new_lt5(xuu33000, xuu34000, ty_Float) → new_lt15(xuu33000, xuu34000)
new_ltEs19(xuu3300, xuu3400, ty_Float) → new_ltEs15(xuu3300, xuu3400)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(app(ty_@2, gh), ha)) → new_esEs7(xuu3110000, xuu6000, gh, ha)
new_compare14(xuu33000, xuu34000, False) → GT
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_Ratio, bea), bdd) → new_ltEs11(xuu33000, xuu34000, bea)
new_esEs8(LT, LT) → True
new_compare25(xuu33000, xuu34000, True, hc, hd, he) → EQ
new_lt18(xuu33000, xuu34000) → new_esEs8(new_compare8(xuu33000, xuu34000), LT)
new_lt19(xuu33000, xuu34000, app(app(ty_@2, bda), bdb)) → new_lt16(xuu33000, xuu34000, bda, bdb)
new_esEs29(xuu311000, xuu600, app(app(ty_@2, baa), bab)) → new_esEs7(xuu311000, xuu600, baa, bab)
new_esEs18(xuu33000, xuu34000, app(ty_Ratio, cb)) → new_esEs9(xuu33000, xuu34000, cb)
new_ltEs20(xuu33002, xuu34002, app(ty_Maybe, ddb)) → new_ltEs9(xuu33002, xuu34002, ddb)
new_esEs28(xuu33000, xuu34000, ty_Integer) → new_esEs16(xuu33000, xuu34000)
new_esEs20(xuu3110000, xuu6000, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs6(xuu3110000, xuu6000, bbh, bca, bcb)
new_pePe(True, xuu168) → True
new_primEqNat0(Zero, Zero) → True
new_compare26(xuu33000, xuu34000, True) → EQ
new_compare23(Nothing, Just(xuu3400), False, dbb) → LT
new_ltEs20(xuu33002, xuu34002, app(app(app(ty_@3, dde), ddf), ddg)) → new_ltEs12(xuu33002, xuu34002, dde, ddf, ddg)
new_lt16(xuu33000, xuu34000, bda, bdb) → new_esEs8(new_compare27(xuu33000, xuu34000, bda, bdb), LT)
new_compare29(xuu33000, xuu34000, True, bcg, bch) → EQ
new_esEs14(@0, @0) → True
new_compare111(xuu33000, xuu34000, False, bcg, bch) → GT
new_esEs18(xuu33000, xuu34000, ty_Bool) → new_esEs15(xuu33000, xuu34000)
new_compare14(xuu33000, xuu34000, True) → LT
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Bool, bdd) → new_ltEs18(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, app(app(ty_@2, cgb), cgc)) → new_esEs7(xuu3110002, xuu6002, cgb, cgc)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Integer, ed) → new_esEs16(xuu3110000, xuu6000)
new_esEs19(xuu3110001, xuu6001, app(ty_[], bad)) → new_esEs12(xuu3110001, xuu6001, bad)
new_compare26(xuu33000, xuu34000, False) → new_compare14(xuu33000, xuu34000, new_ltEs17(xuu33000, xuu34000))
new_ltEs17(GT, LT) → False
new_compare(:(xuu33000, xuu33001), :(xuu34000, xuu34001), hf) → new_primCompAux1(xuu33000, xuu34000, new_compare(xuu33001, xuu34001, hf), hf)
new_lt5(xuu33000, xuu34000, ty_Char) → new_lt8(xuu33000, xuu34000)
new_sr(xuu3110001, xuu6001) → new_primMulInt(xuu3110001, xuu6001)
new_ltEs19(xuu3300, xuu3400, app(app(app(ty_@3, dbc), dbd), dbe)) → new_ltEs12(xuu3300, xuu3400, dbc, dbd, dbe)
new_esEs24(xuu3110000, xuu6000, app(app(ty_@2, daf), dag)) → new_esEs7(xuu3110000, xuu6000, daf, dag)
new_compare32(xuu33000, xuu34000, ty_Int) → new_compare11(xuu33000, xuu34000)
new_esEs8(GT, GT) → True
new_esEs18(xuu33000, xuu34000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs6(xuu33000, xuu34000, cc, cd, ce)
new_ltEs20(xuu33002, xuu34002, app(ty_Ratio, ddd)) → new_ltEs11(xuu33002, xuu34002, ddd)
new_compare32(xuu33000, xuu34000, ty_Bool) → new_compare6(xuu33000, xuu34000)
new_lt19(xuu33000, xuu34000, app(ty_Ratio, dba)) → new_lt11(xuu33000, xuu34000, dba)
new_lt20(xuu33001, xuu34001, ty_Double) → new_lt17(xuu33001, xuu34001)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs19(xuu3300, xuu3400, app(ty_Maybe, bhd)) → new_ltEs9(xuu3300, xuu3400, bhd)
new_esEs28(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(app(ty_Either, gf), gg)) → new_esEs4(xuu3110000, xuu6000, gf, gg)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Int, bdd) → new_ltEs6(xuu33000, xuu34000)
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_lt20(xuu33001, xuu34001, app(ty_Ratio, dcb)) → new_lt11(xuu33001, xuu34001, dcb)
new_esEs15(True, True) → True
new_esEs20(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_compare18(xuu33000, xuu34000, hc, hd, he) → new_compare25(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, hc, hd, he), hc, hd, he)
new_esEs22(xuu3110002, xuu6002, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs6(xuu3110002, xuu6002, cfe, cff, cfg)
new_esEs23(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(ty_Either, fb), fc), ed) → new_esEs4(xuu3110000, xuu6000, fb, fc)
new_ltEs17(LT, GT) → True
new_primPlusNat1(Zero, Succ(xuu9700)) → Succ(xuu9700)
new_primPlusNat1(Succ(xuu28200), Zero) → Succ(xuu28200)
new_esEs13(Double(xuu3110000, xuu3110001), Double(xuu6000, xuu6001)) → new_esEs10(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Float) → new_ltEs15(xuu33000, xuu34000)
new_esEs21(xuu3110000, xuu6000, app(ty_Ratio, ccc)) → new_esEs9(xuu3110000, xuu6000, ccc)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(ty_@2, cae), caf)) → new_ltEs4(xuu33000, xuu34000, cae, caf)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_Ratio, caa)) → new_ltEs11(xuu33000, xuu34000, caa)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Double, ed) → new_esEs13(xuu3110000, xuu6000)
new_ltEs18(True, True) → True
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Int, ed) → new_esEs10(xuu3110000, xuu6000)
new_compare32(xuu33000, xuu34000, app(app(ty_@2, cee), cef)) → new_compare27(xuu33000, xuu34000, cee, cef)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs5(xuu33001, xuu34001, ty_Double) → new_ltEs16(xuu33001, xuu34001)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_ltEs7(Right(xuu33000), Left(xuu34000), beg, bdd) → False
new_esEs24(xuu3110000, xuu6000, app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(xuu3110000, xuu6000, daa, dab, dac)
new_lt12(xuu33000, xuu34000, hc, hd, he) → new_esEs8(new_compare18(xuu33000, xuu34000, hc, hd, he), LT)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(ty_Either, bhe), bhf)) → new_ltEs7(xuu33000, xuu34000, bhe, bhf)
new_compare6(xuu33000, xuu34000) → new_compare24(xuu33000, xuu34000, new_esEs15(xuu33000, xuu34000))
new_esEs21(xuu3110000, xuu6000, app(app(ty_@2, cdc), cdd)) → new_esEs7(xuu3110000, xuu6000, cdc, cdd)
new_esEs28(xuu33000, xuu34000, ty_Double) → new_esEs13(xuu33000, xuu34000)
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu60000))) → False
new_ltEs18(False, False) → True
new_primCompAux0(xuu183, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs20(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_ltEs5(xuu33001, xuu34001, ty_Integer) → new_ltEs13(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_compare32(xuu33000, xuu34000, app(app(app(ty_@3, ceb), cec), ced)) → new_compare18(xuu33000, xuu34000, ceb, cec, ced)
new_compare32(xuu33000, xuu34000, app(app(ty_Either, cde), cdf)) → new_compare17(xuu33000, xuu34000, cde, cdf)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(ty_Ratio, bfd)) → new_ltEs11(xuu33000, xuu34000, bfd)
new_esEs20(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs21(xuu3110000, xuu6000, app(app(ty_Either, cda), cdb)) → new_esEs4(xuu3110000, xuu6000, cda, cdb)
new_compare23(Nothing, Nothing, False, dbb) → LT
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_compare([], [], hf) → EQ
new_ltEs17(EQ, EQ) → True
new_ltEs19(xuu3300, xuu3400, ty_Ordering) → new_ltEs17(xuu3300, xuu3400)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Char, ed) → new_esEs17(xuu3110000, xuu6000)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(ty_@2, bee), bef), bdd) → new_ltEs4(xuu33000, xuu34000, bee, bef)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_compare25(xuu33000, xuu34000, False, hc, hd, he) → new_compare13(xuu33000, xuu34000, new_ltEs12(xuu33000, xuu34000, hc, hd, he), hc, hd, he)
new_ltEs20(xuu33002, xuu34002, ty_Bool) → new_ltEs18(xuu33002, xuu34002)
new_lt20(xuu33001, xuu34001, ty_Char) → new_lt8(xuu33001, xuu34001)
new_esEs28(xuu33000, xuu34000, app(app(ty_@2, bda), bdb)) → new_esEs7(xuu33000, xuu34000, bda, bdb)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Int) → new_lt6(xuu33000, xuu34000)
new_primCmpNat0(Succ(xuu3300), Succ(xuu3400)) → new_primCmpNat0(xuu3300, xuu3400)
new_lt20(xuu33001, xuu34001, ty_Integer) → new_lt13(xuu33001, xuu34001)
new_lt8(xuu33000, xuu34000) → new_esEs8(new_compare30(xuu33000, xuu34000), LT)
new_esEs18(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_esEs26(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Double) → new_ltEs16(xuu33000, xuu34000)
new_esEs18(xuu33000, xuu34000, ty_Int) → new_esEs10(xuu33000, xuu34000)
new_esEs29(xuu311000, xuu600, app(ty_Maybe, cag)) → new_esEs5(xuu311000, xuu600, cag)
new_esEs28(xuu33000, xuu34000, ty_Char) → new_esEs17(xuu33000, xuu34000)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs23(xuu3110001, xuu6001, ty_Char) → new_esEs17(xuu3110001, xuu6001)
new_esEs23(xuu3110001, xuu6001, app(ty_[], cge)) → new_esEs12(xuu3110001, xuu6001, cge)
new_primEqNat0(Succ(xuu31100000), Succ(xuu60000)) → new_primEqNat0(xuu31100000, xuu60000)
new_esEs27(xuu33001, xuu34001, ty_Ordering) → new_esEs8(xuu33001, xuu34001)
new_esEs19(xuu3110001, xuu6001, app(app(app(ty_@3, baf), bag), bah)) → new_esEs6(xuu3110001, xuu6001, baf, bag, bah)
new_primCompAux1(xuu33000, xuu34000, xuu169, hf) → new_primCompAux0(xuu169, new_compare32(xuu33000, xuu34000, hf))
new_compare15(Double(xuu33000, xuu33001), Double(xuu34000, xuu34001)) → new_compare11(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_esEs29(xuu311000, xuu600, ty_Int) → new_esEs10(xuu311000, xuu600)
new_primCmpInt(Neg(Succ(xuu3300)), Neg(xuu340)) → new_primCmpNat0(xuu340, Succ(xuu3300))
new_ltEs19(xuu3300, xuu3400, app(app(ty_Either, beg), bdd)) → new_ltEs7(xuu3300, xuu3400, beg, bdd)
new_esEs24(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs18(xuu33000, xuu34000, ty_Char) → new_esEs17(xuu33000, xuu34000)
new_esEs23(xuu3110001, xuu6001, ty_Bool) → new_esEs15(xuu3110001, xuu6001)
new_lt19(xuu33000, xuu34000, app(app(ty_Either, bcg), bch)) → new_lt7(xuu33000, xuu34000, bcg, bch)
new_esEs28(xuu33000, xuu34000, ty_Ordering) → new_esEs8(xuu33000, xuu34000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu60000))) → False
new_esEs21(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_lt4(xuu33000, xuu34000) → new_esEs8(new_compare6(xuu33000, xuu34000), LT)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(app(ty_@3, cab), cac), cad)) → new_ltEs12(xuu33000, xuu34000, cab, cac, cad)
new_ltEs20(xuu33002, xuu34002, ty_Integer) → new_ltEs13(xuu33002, xuu34002)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Float, bdd) → new_ltEs15(xuu33000, xuu34000)
new_compare17(xuu33000, xuu34000, bcg, bch) → new_compare29(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, bcg, bch), bcg, bch)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu3300), Zero) → GT
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_Maybe, bhg)) → new_ltEs9(xuu33000, xuu34000, bhg)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3400))) → LT
new_ltEs20(xuu33002, xuu34002, ty_@0) → new_ltEs14(xuu33002, xuu34002)
new_esEs7(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), baa, bab) → new_asAs(new_esEs20(xuu3110000, xuu6000, baa), new_esEs19(xuu3110001, xuu6001, bab))
new_esEs21(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_sr0(Integer(xuu340000), Integer(xuu330010)) → Integer(new_primMulInt(xuu340000, xuu330010))
new_primPlusNat1(Succ(xuu28200), Succ(xuu9700)) → Succ(Succ(new_primPlusNat1(xuu28200, xuu9700)))
new_compare28(xuu33000, xuu34000, True, bda, bdb) → EQ
new_primEqInt(Pos(Succ(xuu31100000)), Neg(xuu6000)) → False
new_primEqInt(Neg(Succ(xuu31100000)), Pos(xuu6000)) → False
new_ltEs19(xuu3300, xuu3400, ty_Double) → new_ltEs16(xuu3300, xuu3400)
new_esEs25(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_compare9(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Int) → new_compare11(new_sr(xuu33000, xuu34001), new_sr(xuu34000, xuu33001))
new_esEs29(xuu311000, xuu600, app(ty_[], ccb)) → new_esEs12(xuu311000, xuu600, ccb)
new_esEs27(xuu33001, xuu34001, app(ty_Maybe, dbh)) → new_esEs5(xuu33001, xuu34001, dbh)
new_compare32(xuu33000, xuu34000, app(ty_[], cdh)) → new_compare(xuu33000, xuu34000, cdh)
new_esEs18(xuu33000, xuu34000, app(ty_[], ca)) → new_esEs12(xuu33000, xuu34000, ca)
new_compare23(Just(xuu3300), Just(xuu3400), False, dbb) → new_compare110(xuu3300, xuu3400, new_ltEs19(xuu3300, xuu3400, dbb), dbb)
new_lt11(xuu33000, xuu34000, dba) → new_esEs8(new_compare9(xuu33000, xuu34000, dba), LT)
new_lt19(xuu33000, xuu34000, ty_@0) → new_lt14(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, ty_Float) → new_ltEs15(xuu33002, xuu34002)
new_esEs29(xuu311000, xuu600, ty_@0) → new_esEs14(xuu311000, xuu600)
new_lt7(xuu33000, xuu34000, bcg, bch) → new_esEs8(new_compare17(xuu33000, xuu34000, bcg, bch), LT)
new_lt5(xuu33000, xuu34000, app(ty_Maybe, bh)) → new_lt9(xuu33000, xuu34000, bh)
new_esEs26(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_primEqInt(Pos(Zero), Neg(Succ(xuu60000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu60000))) → False
new_esEs20(xuu3110000, xuu6000, app(ty_[], bbf)) → new_esEs12(xuu3110000, xuu6000, bbf)
new_ltEs9(Just(xuu33000), Nothing, bhd) → False
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(ty_Ratio, fh)) → new_esEs9(xuu3110000, xuu6000, fh)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3400))) → new_primCmpNat0(Zero, Succ(xuu3400))
new_compare24(xuu33000, xuu34000, True) → EQ
new_esEs27(xuu33001, xuu34001, app(app(ty_@2, dcf), dcg)) → new_esEs7(xuu33001, xuu34001, dcf, dcg)
new_lt13(xuu33000, xuu34000) → new_esEs8(new_compare12(xuu33000, xuu34000), LT)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(app(app(ty_@3, bfe), bff), bfg)) → new_ltEs12(xuu33000, xuu34000, bfe, bff, bfg)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, ty_Char) → new_compare30(xuu33000, xuu34000)
new_lt15(xuu33000, xuu34000) → new_esEs8(new_compare31(xuu33000, xuu34000), LT)
new_primCompAux0(xuu183, LT) → LT
new_ltEs19(xuu3300, xuu3400, ty_Char) → new_ltEs8(xuu3300, xuu3400)
new_esEs23(xuu3110001, xuu6001, ty_Float) → new_esEs11(xuu3110001, xuu6001)
new_esEs20(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_not(False) → True
new_esEs30(xuu22, xuu17, ty_@0) → new_esEs14(xuu22, xuu17)
new_primCmpInt(Pos(Succ(xuu3300)), Pos(xuu340)) → new_primCmpNat0(Succ(xuu3300), xuu340)
new_compare110(xuu135, xuu136, True, bdc) → LT
new_esEs22(xuu3110002, xuu6002, ty_Float) → new_esEs11(xuu3110002, xuu6002)
new_esEs19(xuu3110001, xuu6001, app(app(ty_@2, bbc), bbd)) → new_esEs7(xuu3110001, xuu6001, bbc, bbd)
new_ltEs19(xuu3300, xuu3400, app(ty_[], hf)) → new_ltEs10(xuu3300, xuu3400, hf)
new_esEs30(xuu22, xuu17, app(app(ty_@2, bhb), bhc)) → new_esEs7(xuu22, xuu17, bhb, bhc)
new_ltEs5(xuu33001, xuu34001, app(ty_Ratio, de)) → new_ltEs11(xuu33001, xuu34001, de)
new_ltEs9(Nothing, Nothing, bhd) → True
new_esEs30(xuu22, xuu17, app(app(ty_Either, bgh), bha)) → new_esEs4(xuu22, xuu17, bgh, bha)
new_esEs19(xuu3110001, xuu6001, ty_Char) → new_esEs17(xuu3110001, xuu6001)
new_lt20(xuu33001, xuu34001, app(ty_[], dca)) → new_lt10(xuu33001, xuu34001, dca)
new_ltEs19(xuu3300, xuu3400, ty_Int) → new_ltEs6(xuu3300, xuu3400)
new_esEs27(xuu33001, xuu34001, ty_@0) → new_esEs14(xuu33001, xuu34001)
new_ltEs16(xuu3300, xuu3400) → new_fsEs(new_compare15(xuu3300, xuu3400))
new_lt19(xuu33000, xuu34000, app(app(app(ty_@3, hc), hd), he)) → new_lt12(xuu33000, xuu34000, hc, hd, he)
new_lt20(xuu33001, xuu34001, ty_Int) → new_lt6(xuu33001, xuu34001)
new_lt20(xuu33001, xuu34001, ty_Ordering) → new_lt18(xuu33001, xuu34001)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_compare12(Integer(xuu33000), Integer(xuu34000)) → new_primCmpInt(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, app(ty_Maybe, chh)) → new_esEs5(xuu3110000, xuu6000, chh)
new_lt5(xuu33000, xuu34000, app(app(ty_@2, cf), cg)) → new_lt16(xuu33000, xuu34000, cf, cg)
new_esEs18(xuu33000, xuu34000, app(app(ty_Either, bf), bg)) → new_esEs4(xuu33000, xuu34000, bf, bg)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(ty_[], bfc)) → new_ltEs10(xuu33000, xuu34000, bfc)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_primCmpInt(Pos(Succ(xuu3300)), Neg(xuu340)) → GT
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Double, bdd) → new_ltEs16(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, ty_Bool) → new_ltEs18(xuu33001, xuu34001)
new_esEs21(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs30(xuu22, xuu17, app(ty_[], bgc)) → new_esEs12(xuu22, xuu17, bgc)
new_compare32(xuu33000, xuu34000, ty_Ordering) → new_compare8(xuu33000, xuu34000)
new_lt5(xuu33000, xuu34000, app(ty_Ratio, cb)) → new_lt11(xuu33000, xuu34000, cb)
new_primMulInt(Pos(xuu31100010), Pos(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Bool, ed) → new_esEs15(xuu3110000, xuu6000)
new_esEs24(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs27(xuu33001, xuu34001, ty_Char) → new_esEs17(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, app(app(ty_Either, chb), chc)) → new_esEs4(xuu3110001, xuu6001, chb, chc)
new_esEs22(xuu3110002, xuu6002, ty_Double) → new_esEs13(xuu3110002, xuu6002)
new_esEs22(xuu3110002, xuu6002, ty_Int) → new_esEs10(xuu3110002, xuu6002)
new_compare32(xuu33000, xuu34000, ty_@0) → new_compare16(xuu33000, xuu34000)
new_primMulInt(Neg(xuu31100010), Neg(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_esEs24(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_esEs28(xuu33000, xuu34000, app(ty_Ratio, dba)) → new_esEs9(xuu33000, xuu34000, dba)
new_lt20(xuu33001, xuu34001, ty_@0) → new_lt14(xuu33001, xuu34001)
new_primEqNat0(Succ(xuu31100000), Zero) → False
new_primEqNat0(Zero, Succ(xuu60000)) → False
new_esEs21(xuu3110000, xuu6000, app(ty_[], ccd)) → new_esEs12(xuu3110000, xuu6000, ccd)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(ty_Either, bde), bdf), bdd) → new_ltEs7(xuu33000, xuu34000, bde, bdf)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(xuu3110000, xuu6000, app(app(ty_Either, dad), dae)) → new_esEs4(xuu3110000, xuu6000, dad, dae)
new_esEs28(xuu33000, xuu34000, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(xuu33000, xuu34000, hc, hd, he)
new_primPlusNat0(xuu107, xuu600100) → new_primPlusNat1(xuu107, Succ(xuu600100))
new_lt19(xuu33000, xuu34000, ty_Double) → new_lt17(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, ty_Integer) → new_compare12(xuu33000, xuu34000)
new_esEs27(xuu33001, xuu34001, app(app(ty_Either, dbf), dbg)) → new_esEs4(xuu33001, xuu34001, dbf, dbg)
new_esEs27(xuu33001, xuu34001, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs6(xuu33001, xuu34001, dcc, dcd, dce)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_lt5(xuu33000, xuu34000, ty_Integer) → new_lt13(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, app(ty_Maybe, bae)) → new_esEs5(xuu3110001, xuu6001, bae)
new_esEs27(xuu33001, xuu34001, ty_Integer) → new_esEs16(xuu33001, xuu34001)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Float, ed) → new_esEs11(xuu3110000, xuu6000)
new_ltEs5(xuu33001, xuu34001, ty_Int) → new_ltEs6(xuu33001, xuu34001)
new_ltEs14(xuu3300, xuu3400) → new_fsEs(new_compare16(xuu3300, xuu3400))
new_ltEs5(xuu33001, xuu34001, app(ty_Maybe, dc)) → new_ltEs9(xuu33001, xuu34001, dc)
new_esEs25(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_esEs21(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3400))) → new_primCmpNat0(Succ(xuu3400), Zero)
new_ltEs5(xuu33001, xuu34001, ty_Ordering) → new_ltEs17(xuu33001, xuu34001)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3400))) → GT
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Ordering) → new_ltEs17(xuu33000, xuu34000)
new_compare110(xuu135, xuu136, False, bdc) → GT
new_ltEs20(xuu33002, xuu34002, ty_Char) → new_ltEs8(xuu33002, xuu34002)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(app(ty_@3, cbc), cbd), cbe)) → new_esEs6(xuu3110000, xuu6000, cbc, cbd, cbe)
new_compare19(xuu33000, xuu34000, True, bda, bdb) → LT
new_lt20(xuu33001, xuu34001, app(ty_Maybe, dbh)) → new_lt9(xuu33001, xuu34001, dbh)
new_lt19(xuu33000, xuu34000, app(ty_[], hh)) → new_lt10(xuu33000, xuu34000, hh)
new_compare23(xuu330, xuu340, True, dbb) → EQ
new_esEs19(xuu3110001, xuu6001, ty_Float) → new_esEs11(xuu3110001, xuu6001)
new_esEs16(Integer(xuu3110000), Integer(xuu6000)) → new_primEqInt(xuu3110000, xuu6000)
new_ltEs20(xuu33002, xuu34002, ty_Ordering) → new_ltEs17(xuu33002, xuu34002)
new_lt5(xuu33000, xuu34000, ty_Bool) → new_lt4(xuu33000, xuu34000)
new_esEs29(xuu311000, xuu600, app(ty_Ratio, dah)) → new_esEs9(xuu311000, xuu600, dah)
new_esEs23(xuu3110001, xuu6001, ty_@0) → new_esEs14(xuu3110001, xuu6001)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs21(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Ordering, bdd) → new_ltEs17(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, app(ty_Maybe, bbg)) → new_esEs5(xuu3110000, xuu6000, bbg)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(app(ty_Either, beh), bfa)) → new_ltEs7(xuu33000, xuu34000, beh, bfa)
new_esEs29(xuu311000, xuu600, ty_Bool) → new_esEs15(xuu311000, xuu600)
new_asAs(False, xuu142) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Int) → new_ltEs6(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, ty_Double) → new_ltEs16(xuu33002, xuu34002)
new_lt17(xuu33000, xuu34000) → new_esEs8(new_compare15(xuu33000, xuu34000), LT)
new_primMulInt(Pos(xuu31100010), Neg(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_primMulInt(Neg(xuu31100010), Pos(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_ltEs11(xuu3300, xuu3400, hg) → new_fsEs(new_compare9(xuu3300, xuu3400, hg))
new_primMulNat0(Zero, Succ(xuu600100)) → Zero
new_primMulNat0(Succ(xuu311000100), Zero) → Zero
new_esEs27(xuu33001, xuu34001, ty_Double) → new_esEs13(xuu33001, xuu34001)
new_esEs24(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_lt5(xuu33000, xuu34000, ty_Int) → new_lt6(xuu33000, xuu34000)
new_esEs23(xuu3110001, xuu6001, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs6(xuu3110001, xuu6001, cgg, cgh, cha)
new_lt19(xuu33000, xuu34000, ty_Ordering) → new_lt18(xuu33000, xuu34000)
new_esEs21(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Char) → new_lt8(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, app(ty_Maybe, cdg)) → new_compare7(xuu33000, xuu34000, cdg)
new_esEs29(xuu311000, xuu600, ty_Float) → new_esEs11(xuu311000, xuu600)
new_esEs23(xuu3110001, xuu6001, app(app(ty_@2, chd), che)) → new_esEs7(xuu3110001, xuu6001, chd, che)
new_esEs29(xuu311000, xuu600, ty_Char) → new_esEs17(xuu311000, xuu600)
new_esEs29(xuu311000, xuu600, ty_Double) → new_esEs13(xuu311000, xuu600)
new_lt5(xuu33000, xuu34000, app(app(app(ty_@3, cc), cd), ce)) → new_lt12(xuu33000, xuu34000, cc, cd, ce)
new_esEs18(xuu33000, xuu34000, app(ty_Maybe, bh)) → new_esEs5(xuu33000, xuu34000, bh)
new_esEs24(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_compare27(xuu33000, xuu34000, bda, bdb) → new_compare28(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, bda, bdb), bda, bdb)
new_esEs18(xuu33000, xuu34000, ty_Ordering) → new_esEs8(xuu33000, xuu34000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_Maybe, ef), ed) → new_esEs5(xuu3110000, xuu6000, ef)
new_lt9(xuu33000, xuu34000, hb) → new_esEs8(new_compare7(xuu33000, xuu34000, hb), LT)
new_lt20(xuu33001, xuu34001, app(app(ty_@2, dcf), dcg)) → new_lt16(xuu33001, xuu34001, dcf, dcg)
new_esEs28(xuu33000, xuu34000, app(app(ty_Either, bcg), bch)) → new_esEs4(xuu33000, xuu34000, bcg, bch)
new_compare8(xuu33000, xuu34000) → new_compare26(xuu33000, xuu34000, new_esEs8(xuu33000, xuu34000))
new_esEs23(xuu3110001, xuu6001, app(ty_Maybe, cgf)) → new_esEs5(xuu3110001, xuu6001, cgf)
new_lt5(xuu33000, xuu34000, ty_Double) → new_lt17(xuu33000, xuu34000)
new_esEs6(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), ceg, ceh, cfa) → new_asAs(new_esEs24(xuu3110000, xuu6000, ceg), new_asAs(new_esEs23(xuu3110001, xuu6001, ceh), new_esEs22(xuu3110002, xuu6002, cfa)))
new_lt5(xuu33000, xuu34000, app(ty_[], ca)) → new_lt10(xuu33000, xuu34000, ca)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Char) → new_ltEs8(xuu33000, xuu34000)
new_ltEs17(GT, GT) → True
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Ordering) → new_ltEs17(xuu33000, xuu34000)
new_ltEs19(xuu3300, xuu3400, ty_@0) → new_ltEs14(xuu3300, xuu3400)
new_ltEs17(GT, EQ) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Char) → new_ltEs8(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, app(ty_[], cfc)) → new_esEs12(xuu3110002, xuu6002, cfc)
new_esEs5(Just(xuu3110000), Nothing, cag) → False
new_esEs5(Nothing, Just(xuu6000), cag) → False
new_ltEs15(xuu3300, xuu3400) → new_fsEs(new_compare31(xuu3300, xuu3400))
new_esEs22(xuu3110002, xuu6002, ty_Bool) → new_esEs15(xuu3110002, xuu6002)
new_esEs19(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_compare11(xuu33, xuu34) → new_primCmpInt(xuu33, xuu34)
new_esEs28(xuu33000, xuu34000, ty_Bool) → new_esEs15(xuu33000, xuu34000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(ty_@2, fd), ff), ed) → new_esEs7(xuu3110000, xuu6000, fd, ff)
new_ltEs5(xuu33001, xuu34001, app(ty_[], dd)) → new_ltEs10(xuu33001, xuu34001, dd)
new_lt19(xuu33000, xuu34000, ty_Integer) → new_lt13(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, app(app(ty_Either, dch), dda)) → new_ltEs7(xuu33002, xuu34002, dch, dda)
new_ltEs18(True, False) → False
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_Maybe, bdg), bdd) → new_ltEs9(xuu33000, xuu34000, bdg)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Double) → new_ltEs16(xuu33000, xuu34000)
new_lt10(xuu33000, xuu34000, hh) → new_esEs8(new_compare(xuu33000, xuu34000, hh), LT)
new_esEs20(xuu3110000, xuu6000, app(ty_Ratio, bbe)) → new_esEs9(xuu3110000, xuu6000, bbe)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_[], bhh)) → new_ltEs10(xuu33000, xuu34000, bhh)
new_ltEs12(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), dbc, dbd, dbe) → new_pePe(new_lt19(xuu33000, xuu34000, dbc), new_asAs(new_esEs28(xuu33000, xuu34000, dbc), new_pePe(new_lt20(xuu33001, xuu34001, dbd), new_asAs(new_esEs27(xuu33001, xuu34001, dbd), new_ltEs20(xuu33002, xuu34002, dbe)))))
new_esEs22(xuu3110002, xuu6002, ty_@0) → new_esEs14(xuu3110002, xuu6002)
new_esEs5(Nothing, Nothing, cag) → True
new_esEs23(xuu3110001, xuu6001, app(ty_Ratio, cgd)) → new_esEs9(xuu3110001, xuu6001, cgd)
new_esEs28(xuu33000, xuu34000, app(ty_Maybe, hb)) → new_esEs5(xuu33000, xuu34000, hb)
new_esEs29(xuu311000, xuu600, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs6(xuu311000, xuu600, ceg, ceh, cfa)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs28(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, ty_Integer) → new_esEs16(xuu3110002, xuu6002)
new_esEs30(xuu22, xuu17, ty_Char) → new_esEs17(xuu22, xuu17)
new_esEs30(xuu22, xuu17, ty_Float) → new_esEs11(xuu22, xuu17)
new_esEs28(xuu33000, xuu34000, ty_Int) → new_esEs10(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, app(ty_Ratio, bac)) → new_esEs9(xuu3110001, xuu6001, bac)
new_ltEs13(xuu3300, xuu3400) → new_fsEs(new_compare12(xuu3300, xuu3400))
new_esEs21(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_esEs30(xuu22, xuu17, ty_Ordering) → new_esEs8(xuu22, xuu17)
new_esEs29(xuu311000, xuu600, ty_Integer) → new_esEs16(xuu311000, xuu600)
new_compare24(xuu33000, xuu34000, False) → new_compare10(xuu33000, xuu34000, new_ltEs18(xuu33000, xuu34000))
new_esEs20(xuu3110000, xuu6000, app(app(ty_@2, bce), bcf)) → new_esEs7(xuu3110000, xuu6000, bce, bcf)
new_ltEs18(False, True) → True
new_esEs20(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_esEs22(xuu3110002, xuu6002, app(ty_Maybe, cfd)) → new_esEs5(xuu3110002, xuu6002, cfd)
new_esEs21(xuu3110000, xuu6000, app(ty_Maybe, cce)) → new_esEs5(xuu3110000, xuu6000, cce)
new_primPlusNat1(Zero, Zero) → Zero
new_compare111(xuu33000, xuu34000, True, bcg, bch) → LT
new_esEs21(xuu3110000, xuu6000, app(app(app(ty_@3, ccf), ccg), cch)) → new_esEs6(xuu3110000, xuu6000, ccf, ccg, cch)
new_lt14(xuu33000, xuu34000) → new_esEs8(new_compare16(xuu33000, xuu34000), LT)
new_lt20(xuu33001, xuu34001, ty_Float) → new_lt15(xuu33001, xuu34001)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_[], ee), ed) → new_esEs12(xuu3110000, xuu6000, ee)
new_ltEs5(xuu33001, xuu34001, app(app(ty_Either, da), db)) → new_ltEs7(xuu33001, xuu34001, da, db)
new_esEs12(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), ccb) → new_asAs(new_esEs21(xuu3110000, xuu6000, ccb), new_esEs12(xuu3110001, xuu6001, ccb))
new_asAs(True, xuu142) → xuu142
new_esEs28(xuu33000, xuu34000, app(ty_[], hh)) → new_esEs12(xuu33000, xuu34000, hh)
new_esEs27(xuu33001, xuu34001, app(ty_[], dca)) → new_esEs12(xuu33001, xuu34001, dca)
new_esEs19(xuu3110001, xuu6001, app(app(ty_Either, bba), bbb)) → new_esEs4(xuu3110001, xuu6001, bba, bbb)
new_primMulNat0(Succ(xuu311000100), Succ(xuu600100)) → new_primPlusNat0(new_primMulNat0(xuu311000100, Succ(xuu600100)), xuu600100)
new_ltEs17(LT, EQ) → True
new_compare30(Char(xuu33000), Char(xuu34000)) → new_primCmpNat0(xuu33000, xuu34000)
new_esEs4(Right(xuu3110000), Left(xuu6000), fg, ed) → False
new_esEs4(Left(xuu3110000), Right(xuu6000), fg, ed) → False
new_compare29(xuu33000, xuu34000, False, bcg, bch) → new_compare111(xuu33000, xuu34000, new_ltEs7(xuu33000, xuu34000, bcg, bch), bcg, bch)
new_esEs30(xuu22, xuu17, app(ty_Maybe, bgd)) → new_esEs5(xuu22, xuu17, bgd)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_@2, cbh), cca)) → new_esEs7(xuu3110000, xuu6000, cbh, cca)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_esEs27(xuu33001, xuu34001, ty_Int) → new_esEs10(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_esEs27(xuu33001, xuu34001, ty_Bool) → new_esEs15(xuu33001, xuu34001)
new_esEs21(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(app(ty_@3, eg), eh), fa), ed) → new_esEs6(xuu3110000, xuu6000, eg, eh, fa)
new_ltEs6(xuu3300, xuu3400) → new_fsEs(new_compare11(xuu3300, xuu3400))
new_fsEs(xuu152) → new_not(new_esEs8(xuu152, GT))
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Float) → new_ltEs15(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, ty_Char) → new_ltEs8(xuu33001, xuu34001)
new_ltEs19(xuu3300, xuu3400, ty_Integer) → new_ltEs13(xuu3300, xuu3400)
new_esEs19(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_Ratio, ec), ed) → new_esEs9(xuu3110000, xuu6000, ec)
new_compare7(xuu33000, xuu34000, hb) → new_compare23(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, hb), hb)
new_compare10(xuu33000, xuu34000, True) → LT
new_ltEs5(xuu33001, xuu34001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs12(xuu33001, xuu34001, df, dg, dh)
new_compare19(xuu33000, xuu34000, False, bda, bdb) → GT
new_ltEs20(xuu33002, xuu34002, ty_Int) → new_ltEs6(xuu33002, xuu34002)
new_ltEs17(EQ, GT) → True
new_compare13(xuu33000, xuu34000, True, hc, hd, he) → LT
new_compare10(xuu33000, xuu34000, False) → GT
new_esEs10(xuu311000, xuu600) → new_primEqInt(xuu311000, xuu600)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Ratio, cah)) → new_esEs9(xuu3110000, xuu6000, cah)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_@0, ed) → new_esEs14(xuu3110000, xuu6000)
new_esEs30(xuu22, xuu17, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs6(xuu22, xuu17, bge, bgf, bgg)
new_lt5(xuu33000, xuu34000, ty_@0) → new_lt14(xuu33000, xuu34000)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_Either, cbf), cbg)) → new_esEs4(xuu3110000, xuu6000, cbf, cbg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(xuu3110000, xuu6000, app(ty_Ratio, chf)) → new_esEs9(xuu3110000, xuu6000, chf)
new_primCompAux0(xuu183, EQ) → xuu183
new_esEs29(xuu311000, xuu600, ty_Ordering) → new_esEs8(xuu311000, xuu600)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_[], bdh), bdd) → new_ltEs10(xuu33000, xuu34000, bdh)
new_compare32(xuu33000, xuu34000, ty_Float) → new_compare31(xuu33000, xuu34000)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare9(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Integer) → new_compare12(new_sr0(xuu33000, xuu34001), new_sr0(xuu34000, xuu33001))
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_@0) → new_ltEs14(xuu33000, xuu34000)
new_esEs11(Float(xuu3110000, xuu3110001), Float(xuu6000, xuu6001)) → new_esEs10(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_primCmpInt(Neg(Succ(xuu3300)), Pos(xuu340)) → LT
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Int) → new_ltEs6(xuu33000, xuu34000)
new_not(True) → False
new_esEs15(False, False) → True
new_esEs19(xuu3110001, xuu6001, ty_Double) → new_esEs13(xuu3110001, xuu6001)

The set Q consists of the following terms:

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

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

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

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

new_addToFM_C20(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, False, h, ba) → new_addToFM_C11(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, new_esEs8(new_compare23(Just(xuu311000), Nothing, False, h), GT), h, ba)
new_addToFM_C21(xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, bb, bc) → new_addToFM_C(xuu20, Just(xuu22), xuu23, bb, bc)
new_addToFM_C(Branch(Just(xuu600), xuu61, xuu62, xuu63, xuu64), Just(xuu311000), xuu31101, h, ba) → new_addToFM_C21(xuu600, xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, new_esEs8(new_compare23(Just(xuu311000), Just(xuu600), new_esEs29(xuu311000, xuu600, h), h), LT), h, ba)
new_addToFM_C(Branch(Nothing, xuu61, xuu62, xuu63, xuu64), Just(xuu311000), xuu31101, h, ba) → new_addToFM_C20(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, new_esEs8(new_compare23(Just(xuu311000), Nothing, False, h), LT), h, ba)
new_addToFM_C11(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, True, h, ba) → new_addToFM_C(xuu64, Just(xuu311000), xuu31101, h, ba)
new_addToFM_C21(xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, False, bb, bc) → new_addToFM_C12(xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, new_esEs8(new_compare23(Just(xuu22), Just(xuu17), new_esEs30(xuu22, xuu17, bb), bb), GT), bb, bc)
new_addToFM_C12(xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, bb, bc) → new_addToFM_C(xuu21, Just(xuu22), xuu23, bb, bc)
new_addToFM_C20(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, True, h, ba) → new_addToFM_C(xuu63, Just(xuu311000), xuu31101, h, ba)

The TRS R consists of the following rules:

new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_ltEs19(xuu3300, xuu3400, app(ty_Ratio, hg)) → new_ltEs11(xuu3300, xuu3400, hg)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_@0, bdd) → new_ltEs14(xuu33000, xuu34000)
new_lt20(xuu33001, xuu34001, app(app(app(ty_@3, dcc), dcd), dce)) → new_lt12(xuu33001, xuu34001, dcc, dcd, dce)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(ty_Maybe, bfb)) → new_ltEs9(xuu33000, xuu34000, bfb)
new_esEs22(xuu3110002, xuu6002, app(ty_Ratio, cfb)) → new_esEs9(xuu3110002, xuu6002, cfb)
new_ltEs5(xuu33001, xuu34001, ty_@0) → new_ltEs14(xuu33001, xuu34001)
new_ltEs17(LT, LT) → True
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs17(Char(xuu3110000), Char(xuu6000)) → new_primEqNat0(xuu3110000, xuu6000)
new_esEs18(xuu33000, xuu34000, ty_Integer) → new_esEs16(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_ltEs20(xuu33002, xuu34002, app(ty_[], ddc)) → new_ltEs10(xuu33002, xuu34002, ddc)
new_esEs19(xuu3110001, xuu6001, ty_Bool) → new_esEs15(xuu3110001, xuu6001)
new_compare([], :(xuu34000, xuu34001), hf) → LT
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(app(app(ty_@3, gc), gd), ge)) → new_esEs6(xuu3110000, xuu6000, gc, gd, ge)
new_ltEs9(Nothing, Just(xuu34000), bhd) → True
new_ltEs4(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bd, be) → new_pePe(new_lt5(xuu33000, xuu34000, bd), new_asAs(new_esEs18(xuu33000, xuu34000, bd), new_ltEs5(xuu33001, xuu34001, be)))
new_ltEs8(xuu3300, xuu3400) → new_fsEs(new_compare30(xuu3300, xuu3400))
new_compare23(Just(xuu3300), Nothing, False, dbb) → GT
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(ty_Maybe, gb)) → new_esEs5(xuu3110000, xuu6000, gb)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(xuu33000), Right(xuu34000), beg, bdd) → True
new_compare(:(xuu33000, xuu33001), [], hf) → GT
new_lt5(xuu33000, xuu34000, ty_Ordering) → new_lt18(xuu33000, xuu34000)
new_compare28(xuu33000, xuu34000, False, bda, bdb) → new_compare19(xuu33000, xuu34000, new_ltEs4(xuu33000, xuu34000, bda, bdb), bda, bdb)
new_compare13(xuu33000, xuu34000, False, hc, hd, he) → GT
new_esEs18(xuu33000, xuu34000, ty_Double) → new_esEs13(xuu33000, xuu34000)
new_lt19(xuu33000, xuu34000, app(ty_Maybe, hb)) → new_lt9(xuu33000, xuu34000, hb)
new_esEs22(xuu3110002, xuu6002, ty_Char) → new_esEs17(xuu3110002, xuu6002)
new_ltEs5(xuu33001, xuu34001, ty_Float) → new_ltEs15(xuu33001, xuu34001)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(ty_[], ga)) → new_esEs12(xuu3110000, xuu6000, ga)
new_compare31(Float(xuu33000, xuu33001), Float(xuu34000, xuu34001)) → new_compare11(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_lt19(xuu33000, xuu34000, ty_Bool) → new_lt4(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(app(ty_@3, beb), bec), bed), bdd) → new_ltEs12(xuu33000, xuu34000, beb, bec, bed)
new_esEs29(xuu311000, xuu600, app(app(ty_Either, fg), ed)) → new_esEs4(xuu311000, xuu600, fg, ed)
new_lt5(xuu33000, xuu34000, app(app(ty_Either, bf), bg)) → new_lt7(xuu33000, xuu34000, bf, bg)
new_esEs24(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_compare16(@0, @0) → EQ
new_esEs30(xuu22, xuu17, ty_Int) → new_esEs10(xuu22, xuu17)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_ltEs19(xuu3300, xuu3400, ty_Bool) → new_ltEs18(xuu3300, xuu3400)
new_esEs20(xuu3110000, xuu6000, app(app(ty_Either, bcc), bcd)) → new_esEs4(xuu3110000, xuu6000, bcc, bcd)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(app(ty_@2, bfh), bga)) → new_ltEs4(xuu33000, xuu34000, bfh, bga)
new_esEs27(xuu33001, xuu34001, app(ty_Ratio, dcb)) → new_esEs9(xuu33001, xuu34001, dcb)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_esEs9(:%(xuu3110000, xuu3110001), :%(xuu6000, xuu6001), dah) → new_asAs(new_esEs26(xuu3110000, xuu6000, dah), new_esEs25(xuu3110001, xuu6001, dah))
new_esEs12([], [], ccb) → True
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Maybe, cbb)) → new_esEs5(xuu3110000, xuu6000, cbb)
new_esEs23(xuu3110001, xuu6001, ty_Double) → new_esEs13(xuu3110001, xuu6001)
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_@0) → new_ltEs14(xuu33000, xuu34000)
new_esEs18(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, ty_@0) → new_esEs14(xuu3110001, xuu6001)
new_esEs30(xuu22, xuu17, ty_Double) → new_esEs13(xuu22, xuu17)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Integer, bdd) → new_ltEs13(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, app(ty_Ratio, cea)) → new_compare9(xuu33000, xuu34000, cea)
new_esEs20(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_lt6(xuu330, xuu340) → new_esEs8(new_compare11(xuu330, xuu340), LT)
new_ltEs17(EQ, LT) → False
new_esEs24(xuu3110000, xuu6000, app(ty_[], chg)) → new_esEs12(xuu3110000, xuu6000, chg)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Ordering, ed) → new_esEs8(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Float) → new_lt15(xuu33000, xuu34000)
new_lt20(xuu33001, xuu34001, ty_Bool) → new_lt4(xuu33001, xuu34001)
new_pePe(False, xuu168) → xuu168
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Integer) → new_ltEs13(xuu33000, xuu34000)
new_esEs12([], :(xuu6000, xuu6001), ccb) → False
new_esEs12(:(xuu3110000, xuu3110001), [], ccb) → False
new_esEs27(xuu33001, xuu34001, ty_Float) → new_esEs11(xuu33001, xuu34001)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_esEs18(xuu33000, xuu34000, app(app(ty_@2, cf), cg)) → new_esEs7(xuu33000, xuu34000, cf, cg)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Integer) → new_ltEs13(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, app(app(ty_Either, cfh), cga)) → new_esEs4(xuu3110002, xuu6002, cfh, cga)
new_ltEs19(xuu3300, xuu3400, app(app(ty_@2, bd), be)) → new_ltEs4(xuu3300, xuu3400, bd, be)
new_ltEs10(xuu3300, xuu3400, hf) → new_fsEs(new_compare(xuu3300, xuu3400, hf))
new_compare32(xuu33000, xuu34000, ty_Double) → new_compare15(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, app(app(ty_@2, ea), eb)) → new_ltEs4(xuu33001, xuu34001, ea, eb)
new_esEs30(xuu22, xuu17, ty_Bool) → new_esEs15(xuu22, xuu17)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Char, bdd) → new_ltEs8(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, ty_Integer) → new_esEs16(xuu22, xuu17)
new_esEs22(xuu3110002, xuu6002, ty_Ordering) → new_esEs8(xuu3110002, xuu6002)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_[], cba)) → new_esEs12(xuu3110000, xuu6000, cba)
new_esEs30(xuu22, xuu17, app(ty_Ratio, bgb)) → new_esEs9(xuu22, xuu17, bgb)
new_lt20(xuu33001, xuu34001, app(app(ty_Either, dbf), dbg)) → new_lt7(xuu33001, xuu34001, dbf, dbg)
new_ltEs20(xuu33002, xuu34002, app(app(ty_@2, ddh), dea)) → new_ltEs4(xuu33002, xuu34002, ddh, dea)
new_primCmpNat0(Zero, Succ(xuu3400)) → LT
new_lt5(xuu33000, xuu34000, ty_Float) → new_lt15(xuu33000, xuu34000)
new_ltEs19(xuu3300, xuu3400, ty_Float) → new_ltEs15(xuu3300, xuu3400)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(app(ty_@2, gh), ha)) → new_esEs7(xuu3110000, xuu6000, gh, ha)
new_compare14(xuu33000, xuu34000, False) → GT
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_Ratio, bea), bdd) → new_ltEs11(xuu33000, xuu34000, bea)
new_esEs8(LT, LT) → True
new_compare25(xuu33000, xuu34000, True, hc, hd, he) → EQ
new_lt18(xuu33000, xuu34000) → new_esEs8(new_compare8(xuu33000, xuu34000), LT)
new_lt19(xuu33000, xuu34000, app(app(ty_@2, bda), bdb)) → new_lt16(xuu33000, xuu34000, bda, bdb)
new_esEs29(xuu311000, xuu600, app(app(ty_@2, baa), bab)) → new_esEs7(xuu311000, xuu600, baa, bab)
new_esEs18(xuu33000, xuu34000, app(ty_Ratio, cb)) → new_esEs9(xuu33000, xuu34000, cb)
new_ltEs20(xuu33002, xuu34002, app(ty_Maybe, ddb)) → new_ltEs9(xuu33002, xuu34002, ddb)
new_esEs28(xuu33000, xuu34000, ty_Integer) → new_esEs16(xuu33000, xuu34000)
new_esEs20(xuu3110000, xuu6000, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs6(xuu3110000, xuu6000, bbh, bca, bcb)
new_pePe(True, xuu168) → True
new_primEqNat0(Zero, Zero) → True
new_compare26(xuu33000, xuu34000, True) → EQ
new_compare23(Nothing, Just(xuu3400), False, dbb) → LT
new_ltEs20(xuu33002, xuu34002, app(app(app(ty_@3, dde), ddf), ddg)) → new_ltEs12(xuu33002, xuu34002, dde, ddf, ddg)
new_lt16(xuu33000, xuu34000, bda, bdb) → new_esEs8(new_compare27(xuu33000, xuu34000, bda, bdb), LT)
new_compare29(xuu33000, xuu34000, True, bcg, bch) → EQ
new_esEs14(@0, @0) → True
new_compare111(xuu33000, xuu34000, False, bcg, bch) → GT
new_esEs18(xuu33000, xuu34000, ty_Bool) → new_esEs15(xuu33000, xuu34000)
new_compare14(xuu33000, xuu34000, True) → LT
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Bool, bdd) → new_ltEs18(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, app(app(ty_@2, cgb), cgc)) → new_esEs7(xuu3110002, xuu6002, cgb, cgc)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Integer, ed) → new_esEs16(xuu3110000, xuu6000)
new_esEs19(xuu3110001, xuu6001, app(ty_[], bad)) → new_esEs12(xuu3110001, xuu6001, bad)
new_compare26(xuu33000, xuu34000, False) → new_compare14(xuu33000, xuu34000, new_ltEs17(xuu33000, xuu34000))
new_ltEs17(GT, LT) → False
new_compare(:(xuu33000, xuu33001), :(xuu34000, xuu34001), hf) → new_primCompAux1(xuu33000, xuu34000, new_compare(xuu33001, xuu34001, hf), hf)
new_lt5(xuu33000, xuu34000, ty_Char) → new_lt8(xuu33000, xuu34000)
new_sr(xuu3110001, xuu6001) → new_primMulInt(xuu3110001, xuu6001)
new_ltEs19(xuu3300, xuu3400, app(app(app(ty_@3, dbc), dbd), dbe)) → new_ltEs12(xuu3300, xuu3400, dbc, dbd, dbe)
new_esEs24(xuu3110000, xuu6000, app(app(ty_@2, daf), dag)) → new_esEs7(xuu3110000, xuu6000, daf, dag)
new_compare32(xuu33000, xuu34000, ty_Int) → new_compare11(xuu33000, xuu34000)
new_esEs8(GT, GT) → True
new_esEs18(xuu33000, xuu34000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs6(xuu33000, xuu34000, cc, cd, ce)
new_ltEs20(xuu33002, xuu34002, app(ty_Ratio, ddd)) → new_ltEs11(xuu33002, xuu34002, ddd)
new_compare32(xuu33000, xuu34000, ty_Bool) → new_compare6(xuu33000, xuu34000)
new_lt19(xuu33000, xuu34000, app(ty_Ratio, dba)) → new_lt11(xuu33000, xuu34000, dba)
new_lt20(xuu33001, xuu34001, ty_Double) → new_lt17(xuu33001, xuu34001)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs19(xuu3300, xuu3400, app(ty_Maybe, bhd)) → new_ltEs9(xuu3300, xuu3400, bhd)
new_esEs28(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(app(ty_Either, gf), gg)) → new_esEs4(xuu3110000, xuu6000, gf, gg)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Int, bdd) → new_ltEs6(xuu33000, xuu34000)
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_lt20(xuu33001, xuu34001, app(ty_Ratio, dcb)) → new_lt11(xuu33001, xuu34001, dcb)
new_esEs15(True, True) → True
new_esEs20(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_compare18(xuu33000, xuu34000, hc, hd, he) → new_compare25(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, hc, hd, he), hc, hd, he)
new_esEs22(xuu3110002, xuu6002, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs6(xuu3110002, xuu6002, cfe, cff, cfg)
new_esEs23(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(ty_Either, fb), fc), ed) → new_esEs4(xuu3110000, xuu6000, fb, fc)
new_ltEs17(LT, GT) → True
new_primPlusNat1(Zero, Succ(xuu9700)) → Succ(xuu9700)
new_primPlusNat1(Succ(xuu28200), Zero) → Succ(xuu28200)
new_esEs13(Double(xuu3110000, xuu3110001), Double(xuu6000, xuu6001)) → new_esEs10(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Float) → new_ltEs15(xuu33000, xuu34000)
new_esEs21(xuu3110000, xuu6000, app(ty_Ratio, ccc)) → new_esEs9(xuu3110000, xuu6000, ccc)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(ty_@2, cae), caf)) → new_ltEs4(xuu33000, xuu34000, cae, caf)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_Ratio, caa)) → new_ltEs11(xuu33000, xuu34000, caa)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Double, ed) → new_esEs13(xuu3110000, xuu6000)
new_ltEs18(True, True) → True
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Int, ed) → new_esEs10(xuu3110000, xuu6000)
new_compare32(xuu33000, xuu34000, app(app(ty_@2, cee), cef)) → new_compare27(xuu33000, xuu34000, cee, cef)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs5(xuu33001, xuu34001, ty_Double) → new_ltEs16(xuu33001, xuu34001)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_ltEs7(Right(xuu33000), Left(xuu34000), beg, bdd) → False
new_esEs24(xuu3110000, xuu6000, app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(xuu3110000, xuu6000, daa, dab, dac)
new_lt12(xuu33000, xuu34000, hc, hd, he) → new_esEs8(new_compare18(xuu33000, xuu34000, hc, hd, he), LT)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(ty_Either, bhe), bhf)) → new_ltEs7(xuu33000, xuu34000, bhe, bhf)
new_compare6(xuu33000, xuu34000) → new_compare24(xuu33000, xuu34000, new_esEs15(xuu33000, xuu34000))
new_esEs21(xuu3110000, xuu6000, app(app(ty_@2, cdc), cdd)) → new_esEs7(xuu3110000, xuu6000, cdc, cdd)
new_esEs28(xuu33000, xuu34000, ty_Double) → new_esEs13(xuu33000, xuu34000)
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu60000))) → False
new_ltEs18(False, False) → True
new_primCompAux0(xuu183, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs20(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_ltEs5(xuu33001, xuu34001, ty_Integer) → new_ltEs13(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_compare32(xuu33000, xuu34000, app(app(app(ty_@3, ceb), cec), ced)) → new_compare18(xuu33000, xuu34000, ceb, cec, ced)
new_compare32(xuu33000, xuu34000, app(app(ty_Either, cde), cdf)) → new_compare17(xuu33000, xuu34000, cde, cdf)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(ty_Ratio, bfd)) → new_ltEs11(xuu33000, xuu34000, bfd)
new_esEs20(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs21(xuu3110000, xuu6000, app(app(ty_Either, cda), cdb)) → new_esEs4(xuu3110000, xuu6000, cda, cdb)
new_compare23(Nothing, Nothing, False, dbb) → LT
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_compare([], [], hf) → EQ
new_ltEs17(EQ, EQ) → True
new_ltEs19(xuu3300, xuu3400, ty_Ordering) → new_ltEs17(xuu3300, xuu3400)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Char, ed) → new_esEs17(xuu3110000, xuu6000)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(ty_@2, bee), bef), bdd) → new_ltEs4(xuu33000, xuu34000, bee, bef)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_compare25(xuu33000, xuu34000, False, hc, hd, he) → new_compare13(xuu33000, xuu34000, new_ltEs12(xuu33000, xuu34000, hc, hd, he), hc, hd, he)
new_ltEs20(xuu33002, xuu34002, ty_Bool) → new_ltEs18(xuu33002, xuu34002)
new_lt20(xuu33001, xuu34001, ty_Char) → new_lt8(xuu33001, xuu34001)
new_esEs28(xuu33000, xuu34000, app(app(ty_@2, bda), bdb)) → new_esEs7(xuu33000, xuu34000, bda, bdb)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Int) → new_lt6(xuu33000, xuu34000)
new_primCmpNat0(Succ(xuu3300), Succ(xuu3400)) → new_primCmpNat0(xuu3300, xuu3400)
new_lt20(xuu33001, xuu34001, ty_Integer) → new_lt13(xuu33001, xuu34001)
new_lt8(xuu33000, xuu34000) → new_esEs8(new_compare30(xuu33000, xuu34000), LT)
new_esEs18(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_esEs26(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Double) → new_ltEs16(xuu33000, xuu34000)
new_esEs18(xuu33000, xuu34000, ty_Int) → new_esEs10(xuu33000, xuu34000)
new_esEs29(xuu311000, xuu600, app(ty_Maybe, cag)) → new_esEs5(xuu311000, xuu600, cag)
new_esEs28(xuu33000, xuu34000, ty_Char) → new_esEs17(xuu33000, xuu34000)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs23(xuu3110001, xuu6001, ty_Char) → new_esEs17(xuu3110001, xuu6001)
new_esEs23(xuu3110001, xuu6001, app(ty_[], cge)) → new_esEs12(xuu3110001, xuu6001, cge)
new_primEqNat0(Succ(xuu31100000), Succ(xuu60000)) → new_primEqNat0(xuu31100000, xuu60000)
new_esEs27(xuu33001, xuu34001, ty_Ordering) → new_esEs8(xuu33001, xuu34001)
new_esEs19(xuu3110001, xuu6001, app(app(app(ty_@3, baf), bag), bah)) → new_esEs6(xuu3110001, xuu6001, baf, bag, bah)
new_primCompAux1(xuu33000, xuu34000, xuu169, hf) → new_primCompAux0(xuu169, new_compare32(xuu33000, xuu34000, hf))
new_compare15(Double(xuu33000, xuu33001), Double(xuu34000, xuu34001)) → new_compare11(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_esEs29(xuu311000, xuu600, ty_Int) → new_esEs10(xuu311000, xuu600)
new_primCmpInt(Neg(Succ(xuu3300)), Neg(xuu340)) → new_primCmpNat0(xuu340, Succ(xuu3300))
new_ltEs19(xuu3300, xuu3400, app(app(ty_Either, beg), bdd)) → new_ltEs7(xuu3300, xuu3400, beg, bdd)
new_esEs24(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs18(xuu33000, xuu34000, ty_Char) → new_esEs17(xuu33000, xuu34000)
new_esEs23(xuu3110001, xuu6001, ty_Bool) → new_esEs15(xuu3110001, xuu6001)
new_lt19(xuu33000, xuu34000, app(app(ty_Either, bcg), bch)) → new_lt7(xuu33000, xuu34000, bcg, bch)
new_esEs28(xuu33000, xuu34000, ty_Ordering) → new_esEs8(xuu33000, xuu34000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu60000))) → False
new_esEs21(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_lt4(xuu33000, xuu34000) → new_esEs8(new_compare6(xuu33000, xuu34000), LT)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(app(ty_@3, cab), cac), cad)) → new_ltEs12(xuu33000, xuu34000, cab, cac, cad)
new_ltEs20(xuu33002, xuu34002, ty_Integer) → new_ltEs13(xuu33002, xuu34002)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Float, bdd) → new_ltEs15(xuu33000, xuu34000)
new_compare17(xuu33000, xuu34000, bcg, bch) → new_compare29(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, bcg, bch), bcg, bch)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu3300), Zero) → GT
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_Maybe, bhg)) → new_ltEs9(xuu33000, xuu34000, bhg)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3400))) → LT
new_ltEs20(xuu33002, xuu34002, ty_@0) → new_ltEs14(xuu33002, xuu34002)
new_esEs7(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), baa, bab) → new_asAs(new_esEs20(xuu3110000, xuu6000, baa), new_esEs19(xuu3110001, xuu6001, bab))
new_esEs21(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_sr0(Integer(xuu340000), Integer(xuu330010)) → Integer(new_primMulInt(xuu340000, xuu330010))
new_primPlusNat1(Succ(xuu28200), Succ(xuu9700)) → Succ(Succ(new_primPlusNat1(xuu28200, xuu9700)))
new_compare28(xuu33000, xuu34000, True, bda, bdb) → EQ
new_primEqInt(Pos(Succ(xuu31100000)), Neg(xuu6000)) → False
new_primEqInt(Neg(Succ(xuu31100000)), Pos(xuu6000)) → False
new_ltEs19(xuu3300, xuu3400, ty_Double) → new_ltEs16(xuu3300, xuu3400)
new_esEs25(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_compare9(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Int) → new_compare11(new_sr(xuu33000, xuu34001), new_sr(xuu34000, xuu33001))
new_esEs29(xuu311000, xuu600, app(ty_[], ccb)) → new_esEs12(xuu311000, xuu600, ccb)
new_esEs27(xuu33001, xuu34001, app(ty_Maybe, dbh)) → new_esEs5(xuu33001, xuu34001, dbh)
new_compare32(xuu33000, xuu34000, app(ty_[], cdh)) → new_compare(xuu33000, xuu34000, cdh)
new_esEs18(xuu33000, xuu34000, app(ty_[], ca)) → new_esEs12(xuu33000, xuu34000, ca)
new_compare23(Just(xuu3300), Just(xuu3400), False, dbb) → new_compare110(xuu3300, xuu3400, new_ltEs19(xuu3300, xuu3400, dbb), dbb)
new_lt11(xuu33000, xuu34000, dba) → new_esEs8(new_compare9(xuu33000, xuu34000, dba), LT)
new_lt19(xuu33000, xuu34000, ty_@0) → new_lt14(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, ty_Float) → new_ltEs15(xuu33002, xuu34002)
new_esEs29(xuu311000, xuu600, ty_@0) → new_esEs14(xuu311000, xuu600)
new_lt7(xuu33000, xuu34000, bcg, bch) → new_esEs8(new_compare17(xuu33000, xuu34000, bcg, bch), LT)
new_lt5(xuu33000, xuu34000, app(ty_Maybe, bh)) → new_lt9(xuu33000, xuu34000, bh)
new_esEs26(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_primEqInt(Pos(Zero), Neg(Succ(xuu60000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu60000))) → False
new_esEs20(xuu3110000, xuu6000, app(ty_[], bbf)) → new_esEs12(xuu3110000, xuu6000, bbf)
new_ltEs9(Just(xuu33000), Nothing, bhd) → False
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(ty_Ratio, fh)) → new_esEs9(xuu3110000, xuu6000, fh)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3400))) → new_primCmpNat0(Zero, Succ(xuu3400))
new_compare24(xuu33000, xuu34000, True) → EQ
new_esEs27(xuu33001, xuu34001, app(app(ty_@2, dcf), dcg)) → new_esEs7(xuu33001, xuu34001, dcf, dcg)
new_lt13(xuu33000, xuu34000) → new_esEs8(new_compare12(xuu33000, xuu34000), LT)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(app(app(ty_@3, bfe), bff), bfg)) → new_ltEs12(xuu33000, xuu34000, bfe, bff, bfg)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, ty_Char) → new_compare30(xuu33000, xuu34000)
new_lt15(xuu33000, xuu34000) → new_esEs8(new_compare31(xuu33000, xuu34000), LT)
new_primCompAux0(xuu183, LT) → LT
new_ltEs19(xuu3300, xuu3400, ty_Char) → new_ltEs8(xuu3300, xuu3400)
new_esEs23(xuu3110001, xuu6001, ty_Float) → new_esEs11(xuu3110001, xuu6001)
new_esEs20(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_not(False) → True
new_esEs30(xuu22, xuu17, ty_@0) → new_esEs14(xuu22, xuu17)
new_primCmpInt(Pos(Succ(xuu3300)), Pos(xuu340)) → new_primCmpNat0(Succ(xuu3300), xuu340)
new_compare110(xuu135, xuu136, True, bdc) → LT
new_esEs22(xuu3110002, xuu6002, ty_Float) → new_esEs11(xuu3110002, xuu6002)
new_esEs19(xuu3110001, xuu6001, app(app(ty_@2, bbc), bbd)) → new_esEs7(xuu3110001, xuu6001, bbc, bbd)
new_ltEs19(xuu3300, xuu3400, app(ty_[], hf)) → new_ltEs10(xuu3300, xuu3400, hf)
new_esEs30(xuu22, xuu17, app(app(ty_@2, bhb), bhc)) → new_esEs7(xuu22, xuu17, bhb, bhc)
new_ltEs5(xuu33001, xuu34001, app(ty_Ratio, de)) → new_ltEs11(xuu33001, xuu34001, de)
new_ltEs9(Nothing, Nothing, bhd) → True
new_esEs30(xuu22, xuu17, app(app(ty_Either, bgh), bha)) → new_esEs4(xuu22, xuu17, bgh, bha)
new_esEs19(xuu3110001, xuu6001, ty_Char) → new_esEs17(xuu3110001, xuu6001)
new_lt20(xuu33001, xuu34001, app(ty_[], dca)) → new_lt10(xuu33001, xuu34001, dca)
new_ltEs19(xuu3300, xuu3400, ty_Int) → new_ltEs6(xuu3300, xuu3400)
new_esEs27(xuu33001, xuu34001, ty_@0) → new_esEs14(xuu33001, xuu34001)
new_ltEs16(xuu3300, xuu3400) → new_fsEs(new_compare15(xuu3300, xuu3400))
new_lt19(xuu33000, xuu34000, app(app(app(ty_@3, hc), hd), he)) → new_lt12(xuu33000, xuu34000, hc, hd, he)
new_lt20(xuu33001, xuu34001, ty_Int) → new_lt6(xuu33001, xuu34001)
new_lt20(xuu33001, xuu34001, ty_Ordering) → new_lt18(xuu33001, xuu34001)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_compare12(Integer(xuu33000), Integer(xuu34000)) → new_primCmpInt(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, app(ty_Maybe, chh)) → new_esEs5(xuu3110000, xuu6000, chh)
new_lt5(xuu33000, xuu34000, app(app(ty_@2, cf), cg)) → new_lt16(xuu33000, xuu34000, cf, cg)
new_esEs18(xuu33000, xuu34000, app(app(ty_Either, bf), bg)) → new_esEs4(xuu33000, xuu34000, bf, bg)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(ty_[], bfc)) → new_ltEs10(xuu33000, xuu34000, bfc)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_primCmpInt(Pos(Succ(xuu3300)), Neg(xuu340)) → GT
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Double, bdd) → new_ltEs16(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, ty_Bool) → new_ltEs18(xuu33001, xuu34001)
new_esEs21(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs30(xuu22, xuu17, app(ty_[], bgc)) → new_esEs12(xuu22, xuu17, bgc)
new_compare32(xuu33000, xuu34000, ty_Ordering) → new_compare8(xuu33000, xuu34000)
new_lt5(xuu33000, xuu34000, app(ty_Ratio, cb)) → new_lt11(xuu33000, xuu34000, cb)
new_primMulInt(Pos(xuu31100010), Pos(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Bool, ed) → new_esEs15(xuu3110000, xuu6000)
new_esEs24(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs27(xuu33001, xuu34001, ty_Char) → new_esEs17(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, app(app(ty_Either, chb), chc)) → new_esEs4(xuu3110001, xuu6001, chb, chc)
new_esEs22(xuu3110002, xuu6002, ty_Double) → new_esEs13(xuu3110002, xuu6002)
new_esEs22(xuu3110002, xuu6002, ty_Int) → new_esEs10(xuu3110002, xuu6002)
new_compare32(xuu33000, xuu34000, ty_@0) → new_compare16(xuu33000, xuu34000)
new_primMulInt(Neg(xuu31100010), Neg(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_esEs24(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_esEs28(xuu33000, xuu34000, app(ty_Ratio, dba)) → new_esEs9(xuu33000, xuu34000, dba)
new_lt20(xuu33001, xuu34001, ty_@0) → new_lt14(xuu33001, xuu34001)
new_primEqNat0(Succ(xuu31100000), Zero) → False
new_primEqNat0(Zero, Succ(xuu60000)) → False
new_esEs21(xuu3110000, xuu6000, app(ty_[], ccd)) → new_esEs12(xuu3110000, xuu6000, ccd)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(ty_Either, bde), bdf), bdd) → new_ltEs7(xuu33000, xuu34000, bde, bdf)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(xuu3110000, xuu6000, app(app(ty_Either, dad), dae)) → new_esEs4(xuu3110000, xuu6000, dad, dae)
new_esEs28(xuu33000, xuu34000, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(xuu33000, xuu34000, hc, hd, he)
new_primPlusNat0(xuu107, xuu600100) → new_primPlusNat1(xuu107, Succ(xuu600100))
new_lt19(xuu33000, xuu34000, ty_Double) → new_lt17(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, ty_Integer) → new_compare12(xuu33000, xuu34000)
new_esEs27(xuu33001, xuu34001, app(app(ty_Either, dbf), dbg)) → new_esEs4(xuu33001, xuu34001, dbf, dbg)
new_esEs27(xuu33001, xuu34001, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs6(xuu33001, xuu34001, dcc, dcd, dce)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_lt5(xuu33000, xuu34000, ty_Integer) → new_lt13(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, app(ty_Maybe, bae)) → new_esEs5(xuu3110001, xuu6001, bae)
new_esEs27(xuu33001, xuu34001, ty_Integer) → new_esEs16(xuu33001, xuu34001)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Float, ed) → new_esEs11(xuu3110000, xuu6000)
new_ltEs5(xuu33001, xuu34001, ty_Int) → new_ltEs6(xuu33001, xuu34001)
new_ltEs14(xuu3300, xuu3400) → new_fsEs(new_compare16(xuu3300, xuu3400))
new_ltEs5(xuu33001, xuu34001, app(ty_Maybe, dc)) → new_ltEs9(xuu33001, xuu34001, dc)
new_esEs25(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_esEs21(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3400))) → new_primCmpNat0(Succ(xuu3400), Zero)
new_ltEs5(xuu33001, xuu34001, ty_Ordering) → new_ltEs17(xuu33001, xuu34001)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3400))) → GT
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Ordering) → new_ltEs17(xuu33000, xuu34000)
new_compare110(xuu135, xuu136, False, bdc) → GT
new_ltEs20(xuu33002, xuu34002, ty_Char) → new_ltEs8(xuu33002, xuu34002)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(app(ty_@3, cbc), cbd), cbe)) → new_esEs6(xuu3110000, xuu6000, cbc, cbd, cbe)
new_compare19(xuu33000, xuu34000, True, bda, bdb) → LT
new_lt20(xuu33001, xuu34001, app(ty_Maybe, dbh)) → new_lt9(xuu33001, xuu34001, dbh)
new_lt19(xuu33000, xuu34000, app(ty_[], hh)) → new_lt10(xuu33000, xuu34000, hh)
new_compare23(xuu330, xuu340, True, dbb) → EQ
new_esEs19(xuu3110001, xuu6001, ty_Float) → new_esEs11(xuu3110001, xuu6001)
new_esEs16(Integer(xuu3110000), Integer(xuu6000)) → new_primEqInt(xuu3110000, xuu6000)
new_ltEs20(xuu33002, xuu34002, ty_Ordering) → new_ltEs17(xuu33002, xuu34002)
new_lt5(xuu33000, xuu34000, ty_Bool) → new_lt4(xuu33000, xuu34000)
new_esEs29(xuu311000, xuu600, app(ty_Ratio, dah)) → new_esEs9(xuu311000, xuu600, dah)
new_esEs23(xuu3110001, xuu6001, ty_@0) → new_esEs14(xuu3110001, xuu6001)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs21(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Ordering, bdd) → new_ltEs17(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, app(ty_Maybe, bbg)) → new_esEs5(xuu3110000, xuu6000, bbg)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(app(ty_Either, beh), bfa)) → new_ltEs7(xuu33000, xuu34000, beh, bfa)
new_esEs29(xuu311000, xuu600, ty_Bool) → new_esEs15(xuu311000, xuu600)
new_asAs(False, xuu142) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Int) → new_ltEs6(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, ty_Double) → new_ltEs16(xuu33002, xuu34002)
new_lt17(xuu33000, xuu34000) → new_esEs8(new_compare15(xuu33000, xuu34000), LT)
new_primMulInt(Pos(xuu31100010), Neg(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_primMulInt(Neg(xuu31100010), Pos(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_ltEs11(xuu3300, xuu3400, hg) → new_fsEs(new_compare9(xuu3300, xuu3400, hg))
new_primMulNat0(Zero, Succ(xuu600100)) → Zero
new_primMulNat0(Succ(xuu311000100), Zero) → Zero
new_esEs27(xuu33001, xuu34001, ty_Double) → new_esEs13(xuu33001, xuu34001)
new_esEs24(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_lt5(xuu33000, xuu34000, ty_Int) → new_lt6(xuu33000, xuu34000)
new_esEs23(xuu3110001, xuu6001, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs6(xuu3110001, xuu6001, cgg, cgh, cha)
new_lt19(xuu33000, xuu34000, ty_Ordering) → new_lt18(xuu33000, xuu34000)
new_esEs21(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Char) → new_lt8(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, app(ty_Maybe, cdg)) → new_compare7(xuu33000, xuu34000, cdg)
new_esEs29(xuu311000, xuu600, ty_Float) → new_esEs11(xuu311000, xuu600)
new_esEs23(xuu3110001, xuu6001, app(app(ty_@2, chd), che)) → new_esEs7(xuu3110001, xuu6001, chd, che)
new_esEs29(xuu311000, xuu600, ty_Char) → new_esEs17(xuu311000, xuu600)
new_esEs29(xuu311000, xuu600, ty_Double) → new_esEs13(xuu311000, xuu600)
new_lt5(xuu33000, xuu34000, app(app(app(ty_@3, cc), cd), ce)) → new_lt12(xuu33000, xuu34000, cc, cd, ce)
new_esEs18(xuu33000, xuu34000, app(ty_Maybe, bh)) → new_esEs5(xuu33000, xuu34000, bh)
new_esEs24(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_compare27(xuu33000, xuu34000, bda, bdb) → new_compare28(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, bda, bdb), bda, bdb)
new_esEs18(xuu33000, xuu34000, ty_Ordering) → new_esEs8(xuu33000, xuu34000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_Maybe, ef), ed) → new_esEs5(xuu3110000, xuu6000, ef)
new_lt9(xuu33000, xuu34000, hb) → new_esEs8(new_compare7(xuu33000, xuu34000, hb), LT)
new_lt20(xuu33001, xuu34001, app(app(ty_@2, dcf), dcg)) → new_lt16(xuu33001, xuu34001, dcf, dcg)
new_esEs28(xuu33000, xuu34000, app(app(ty_Either, bcg), bch)) → new_esEs4(xuu33000, xuu34000, bcg, bch)
new_compare8(xuu33000, xuu34000) → new_compare26(xuu33000, xuu34000, new_esEs8(xuu33000, xuu34000))
new_esEs23(xuu3110001, xuu6001, app(ty_Maybe, cgf)) → new_esEs5(xuu3110001, xuu6001, cgf)
new_lt5(xuu33000, xuu34000, ty_Double) → new_lt17(xuu33000, xuu34000)
new_esEs6(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), ceg, ceh, cfa) → new_asAs(new_esEs24(xuu3110000, xuu6000, ceg), new_asAs(new_esEs23(xuu3110001, xuu6001, ceh), new_esEs22(xuu3110002, xuu6002, cfa)))
new_lt5(xuu33000, xuu34000, app(ty_[], ca)) → new_lt10(xuu33000, xuu34000, ca)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Char) → new_ltEs8(xuu33000, xuu34000)
new_ltEs17(GT, GT) → True
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Ordering) → new_ltEs17(xuu33000, xuu34000)
new_ltEs19(xuu3300, xuu3400, ty_@0) → new_ltEs14(xuu3300, xuu3400)
new_ltEs17(GT, EQ) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Char) → new_ltEs8(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, app(ty_[], cfc)) → new_esEs12(xuu3110002, xuu6002, cfc)
new_esEs5(Just(xuu3110000), Nothing, cag) → False
new_esEs5(Nothing, Just(xuu6000), cag) → False
new_ltEs15(xuu3300, xuu3400) → new_fsEs(new_compare31(xuu3300, xuu3400))
new_esEs22(xuu3110002, xuu6002, ty_Bool) → new_esEs15(xuu3110002, xuu6002)
new_esEs19(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_compare11(xuu33, xuu34) → new_primCmpInt(xuu33, xuu34)
new_esEs28(xuu33000, xuu34000, ty_Bool) → new_esEs15(xuu33000, xuu34000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(ty_@2, fd), ff), ed) → new_esEs7(xuu3110000, xuu6000, fd, ff)
new_ltEs5(xuu33001, xuu34001, app(ty_[], dd)) → new_ltEs10(xuu33001, xuu34001, dd)
new_lt19(xuu33000, xuu34000, ty_Integer) → new_lt13(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, app(app(ty_Either, dch), dda)) → new_ltEs7(xuu33002, xuu34002, dch, dda)
new_ltEs18(True, False) → False
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_Maybe, bdg), bdd) → new_ltEs9(xuu33000, xuu34000, bdg)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Double) → new_ltEs16(xuu33000, xuu34000)
new_lt10(xuu33000, xuu34000, hh) → new_esEs8(new_compare(xuu33000, xuu34000, hh), LT)
new_esEs20(xuu3110000, xuu6000, app(ty_Ratio, bbe)) → new_esEs9(xuu3110000, xuu6000, bbe)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_[], bhh)) → new_ltEs10(xuu33000, xuu34000, bhh)
new_ltEs12(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), dbc, dbd, dbe) → new_pePe(new_lt19(xuu33000, xuu34000, dbc), new_asAs(new_esEs28(xuu33000, xuu34000, dbc), new_pePe(new_lt20(xuu33001, xuu34001, dbd), new_asAs(new_esEs27(xuu33001, xuu34001, dbd), new_ltEs20(xuu33002, xuu34002, dbe)))))
new_esEs22(xuu3110002, xuu6002, ty_@0) → new_esEs14(xuu3110002, xuu6002)
new_esEs5(Nothing, Nothing, cag) → True
new_esEs23(xuu3110001, xuu6001, app(ty_Ratio, cgd)) → new_esEs9(xuu3110001, xuu6001, cgd)
new_esEs28(xuu33000, xuu34000, app(ty_Maybe, hb)) → new_esEs5(xuu33000, xuu34000, hb)
new_esEs29(xuu311000, xuu600, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs6(xuu311000, xuu600, ceg, ceh, cfa)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs28(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, ty_Integer) → new_esEs16(xuu3110002, xuu6002)
new_esEs30(xuu22, xuu17, ty_Char) → new_esEs17(xuu22, xuu17)
new_esEs30(xuu22, xuu17, ty_Float) → new_esEs11(xuu22, xuu17)
new_esEs28(xuu33000, xuu34000, ty_Int) → new_esEs10(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, app(ty_Ratio, bac)) → new_esEs9(xuu3110001, xuu6001, bac)
new_ltEs13(xuu3300, xuu3400) → new_fsEs(new_compare12(xuu3300, xuu3400))
new_esEs21(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_esEs30(xuu22, xuu17, ty_Ordering) → new_esEs8(xuu22, xuu17)
new_esEs29(xuu311000, xuu600, ty_Integer) → new_esEs16(xuu311000, xuu600)
new_compare24(xuu33000, xuu34000, False) → new_compare10(xuu33000, xuu34000, new_ltEs18(xuu33000, xuu34000))
new_esEs20(xuu3110000, xuu6000, app(app(ty_@2, bce), bcf)) → new_esEs7(xuu3110000, xuu6000, bce, bcf)
new_ltEs18(False, True) → True
new_esEs20(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_esEs22(xuu3110002, xuu6002, app(ty_Maybe, cfd)) → new_esEs5(xuu3110002, xuu6002, cfd)
new_esEs21(xuu3110000, xuu6000, app(ty_Maybe, cce)) → new_esEs5(xuu3110000, xuu6000, cce)
new_primPlusNat1(Zero, Zero) → Zero
new_compare111(xuu33000, xuu34000, True, bcg, bch) → LT
new_esEs21(xuu3110000, xuu6000, app(app(app(ty_@3, ccf), ccg), cch)) → new_esEs6(xuu3110000, xuu6000, ccf, ccg, cch)
new_lt14(xuu33000, xuu34000) → new_esEs8(new_compare16(xuu33000, xuu34000), LT)
new_lt20(xuu33001, xuu34001, ty_Float) → new_lt15(xuu33001, xuu34001)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_[], ee), ed) → new_esEs12(xuu3110000, xuu6000, ee)
new_ltEs5(xuu33001, xuu34001, app(app(ty_Either, da), db)) → new_ltEs7(xuu33001, xuu34001, da, db)
new_esEs12(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), ccb) → new_asAs(new_esEs21(xuu3110000, xuu6000, ccb), new_esEs12(xuu3110001, xuu6001, ccb))
new_asAs(True, xuu142) → xuu142
new_esEs28(xuu33000, xuu34000, app(ty_[], hh)) → new_esEs12(xuu33000, xuu34000, hh)
new_esEs27(xuu33001, xuu34001, app(ty_[], dca)) → new_esEs12(xuu33001, xuu34001, dca)
new_esEs19(xuu3110001, xuu6001, app(app(ty_Either, bba), bbb)) → new_esEs4(xuu3110001, xuu6001, bba, bbb)
new_primMulNat0(Succ(xuu311000100), Succ(xuu600100)) → new_primPlusNat0(new_primMulNat0(xuu311000100, Succ(xuu600100)), xuu600100)
new_ltEs17(LT, EQ) → True
new_compare30(Char(xuu33000), Char(xuu34000)) → new_primCmpNat0(xuu33000, xuu34000)
new_esEs4(Right(xuu3110000), Left(xuu6000), fg, ed) → False
new_esEs4(Left(xuu3110000), Right(xuu6000), fg, ed) → False
new_compare29(xuu33000, xuu34000, False, bcg, bch) → new_compare111(xuu33000, xuu34000, new_ltEs7(xuu33000, xuu34000, bcg, bch), bcg, bch)
new_esEs30(xuu22, xuu17, app(ty_Maybe, bgd)) → new_esEs5(xuu22, xuu17, bgd)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_@2, cbh), cca)) → new_esEs7(xuu3110000, xuu6000, cbh, cca)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_esEs27(xuu33001, xuu34001, ty_Int) → new_esEs10(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_esEs27(xuu33001, xuu34001, ty_Bool) → new_esEs15(xuu33001, xuu34001)
new_esEs21(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(app(ty_@3, eg), eh), fa), ed) → new_esEs6(xuu3110000, xuu6000, eg, eh, fa)
new_ltEs6(xuu3300, xuu3400) → new_fsEs(new_compare11(xuu3300, xuu3400))
new_fsEs(xuu152) → new_not(new_esEs8(xuu152, GT))
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Float) → new_ltEs15(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, ty_Char) → new_ltEs8(xuu33001, xuu34001)
new_ltEs19(xuu3300, xuu3400, ty_Integer) → new_ltEs13(xuu3300, xuu3400)
new_esEs19(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_Ratio, ec), ed) → new_esEs9(xuu3110000, xuu6000, ec)
new_compare7(xuu33000, xuu34000, hb) → new_compare23(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, hb), hb)
new_compare10(xuu33000, xuu34000, True) → LT
new_ltEs5(xuu33001, xuu34001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs12(xuu33001, xuu34001, df, dg, dh)
new_compare19(xuu33000, xuu34000, False, bda, bdb) → GT
new_ltEs20(xuu33002, xuu34002, ty_Int) → new_ltEs6(xuu33002, xuu34002)
new_ltEs17(EQ, GT) → True
new_compare13(xuu33000, xuu34000, True, hc, hd, he) → LT
new_compare10(xuu33000, xuu34000, False) → GT
new_esEs10(xuu311000, xuu600) → new_primEqInt(xuu311000, xuu600)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Ratio, cah)) → new_esEs9(xuu3110000, xuu6000, cah)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_@0, ed) → new_esEs14(xuu3110000, xuu6000)
new_esEs30(xuu22, xuu17, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs6(xuu22, xuu17, bge, bgf, bgg)
new_lt5(xuu33000, xuu34000, ty_@0) → new_lt14(xuu33000, xuu34000)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_Either, cbf), cbg)) → new_esEs4(xuu3110000, xuu6000, cbf, cbg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(xuu3110000, xuu6000, app(ty_Ratio, chf)) → new_esEs9(xuu3110000, xuu6000, chf)
new_primCompAux0(xuu183, EQ) → xuu183
new_esEs29(xuu311000, xuu600, ty_Ordering) → new_esEs8(xuu311000, xuu600)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_[], bdh), bdd) → new_ltEs10(xuu33000, xuu34000, bdh)
new_compare32(xuu33000, xuu34000, ty_Float) → new_compare31(xuu33000, xuu34000)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare9(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Integer) → new_compare12(new_sr0(xuu33000, xuu34001), new_sr0(xuu34000, xuu33001))
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_@0) → new_ltEs14(xuu33000, xuu34000)
new_esEs11(Float(xuu3110000, xuu3110001), Float(xuu6000, xuu6001)) → new_esEs10(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_primCmpInt(Neg(Succ(xuu3300)), Pos(xuu340)) → LT
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Int) → new_ltEs6(xuu33000, xuu34000)
new_not(True) → False
new_esEs15(False, False) → True
new_esEs19(xuu3110001, xuu6001, ty_Double) → new_esEs13(xuu3110001, xuu6001)

The set Q consists of the following terms:

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

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

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



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

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

new_addToFM_C1(xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_addToFM_C(xuu64, Nothing, xuu31101, h, ba)
new_addToFM_C(Branch(Just(xuu600), xuu61, xuu62, xuu63, xuu64), Nothing, xuu31101, h, ba) → new_addToFM_C2(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Just(xuu600), False, h), LT), h, ba)
new_addToFM_C2(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_addToFM_C(xuu63, Nothing, xuu31101, h, ba)
new_addToFM_C2(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, False, h, ba) → new_addToFM_C10(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Just(xuu600), False, h), GT), h, ba)
new_addToFM_C(Branch(Nothing, xuu61, xuu62, xuu63, xuu64), Nothing, xuu31101, h, ba) → new_addToFM_C1(xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C10(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_addToFM_C(xuu64, Nothing, xuu31101, h, ba)

The TRS R consists of the following rules:

new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_ltEs19(xuu3300, xuu3400, app(ty_Ratio, hg)) → new_ltEs11(xuu3300, xuu3400, hg)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_@0, bdd) → new_ltEs14(xuu33000, xuu34000)
new_lt20(xuu33001, xuu34001, app(app(app(ty_@3, dcc), dcd), dce)) → new_lt12(xuu33001, xuu34001, dcc, dcd, dce)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(ty_Maybe, bfb)) → new_ltEs9(xuu33000, xuu34000, bfb)
new_esEs22(xuu3110002, xuu6002, app(ty_Ratio, cfb)) → new_esEs9(xuu3110002, xuu6002, cfb)
new_ltEs5(xuu33001, xuu34001, ty_@0) → new_ltEs14(xuu33001, xuu34001)
new_ltEs17(LT, LT) → True
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs17(Char(xuu3110000), Char(xuu6000)) → new_primEqNat0(xuu3110000, xuu6000)
new_esEs18(xuu33000, xuu34000, ty_Integer) → new_esEs16(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_ltEs20(xuu33002, xuu34002, app(ty_[], ddc)) → new_ltEs10(xuu33002, xuu34002, ddc)
new_esEs19(xuu3110001, xuu6001, ty_Bool) → new_esEs15(xuu3110001, xuu6001)
new_compare([], :(xuu34000, xuu34001), hf) → LT
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(app(app(ty_@3, gc), gd), ge)) → new_esEs6(xuu3110000, xuu6000, gc, gd, ge)
new_ltEs9(Nothing, Just(xuu34000), bhd) → True
new_ltEs4(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bd, be) → new_pePe(new_lt5(xuu33000, xuu34000, bd), new_asAs(new_esEs18(xuu33000, xuu34000, bd), new_ltEs5(xuu33001, xuu34001, be)))
new_ltEs8(xuu3300, xuu3400) → new_fsEs(new_compare30(xuu3300, xuu3400))
new_compare23(Just(xuu3300), Nothing, False, dbb) → GT
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(ty_Maybe, gb)) → new_esEs5(xuu3110000, xuu6000, gb)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(xuu33000), Right(xuu34000), beg, bdd) → True
new_compare(:(xuu33000, xuu33001), [], hf) → GT
new_lt5(xuu33000, xuu34000, ty_Ordering) → new_lt18(xuu33000, xuu34000)
new_compare28(xuu33000, xuu34000, False, bda, bdb) → new_compare19(xuu33000, xuu34000, new_ltEs4(xuu33000, xuu34000, bda, bdb), bda, bdb)
new_compare13(xuu33000, xuu34000, False, hc, hd, he) → GT
new_esEs18(xuu33000, xuu34000, ty_Double) → new_esEs13(xuu33000, xuu34000)
new_lt19(xuu33000, xuu34000, app(ty_Maybe, hb)) → new_lt9(xuu33000, xuu34000, hb)
new_esEs22(xuu3110002, xuu6002, ty_Char) → new_esEs17(xuu3110002, xuu6002)
new_ltEs5(xuu33001, xuu34001, ty_Float) → new_ltEs15(xuu33001, xuu34001)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(ty_[], ga)) → new_esEs12(xuu3110000, xuu6000, ga)
new_compare31(Float(xuu33000, xuu33001), Float(xuu34000, xuu34001)) → new_compare11(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_lt19(xuu33000, xuu34000, ty_Bool) → new_lt4(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(app(ty_@3, beb), bec), bed), bdd) → new_ltEs12(xuu33000, xuu34000, beb, bec, bed)
new_esEs29(xuu311000, xuu600, app(app(ty_Either, fg), ed)) → new_esEs4(xuu311000, xuu600, fg, ed)
new_lt5(xuu33000, xuu34000, app(app(ty_Either, bf), bg)) → new_lt7(xuu33000, xuu34000, bf, bg)
new_esEs24(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_compare16(@0, @0) → EQ
new_esEs30(xuu22, xuu17, ty_Int) → new_esEs10(xuu22, xuu17)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_ltEs19(xuu3300, xuu3400, ty_Bool) → new_ltEs18(xuu3300, xuu3400)
new_esEs20(xuu3110000, xuu6000, app(app(ty_Either, bcc), bcd)) → new_esEs4(xuu3110000, xuu6000, bcc, bcd)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(app(ty_@2, bfh), bga)) → new_ltEs4(xuu33000, xuu34000, bfh, bga)
new_esEs27(xuu33001, xuu34001, app(ty_Ratio, dcb)) → new_esEs9(xuu33001, xuu34001, dcb)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_esEs9(:%(xuu3110000, xuu3110001), :%(xuu6000, xuu6001), dah) → new_asAs(new_esEs26(xuu3110000, xuu6000, dah), new_esEs25(xuu3110001, xuu6001, dah))
new_esEs12([], [], ccb) → True
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Maybe, cbb)) → new_esEs5(xuu3110000, xuu6000, cbb)
new_esEs23(xuu3110001, xuu6001, ty_Double) → new_esEs13(xuu3110001, xuu6001)
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_@0) → new_ltEs14(xuu33000, xuu34000)
new_esEs18(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, ty_@0) → new_esEs14(xuu3110001, xuu6001)
new_esEs30(xuu22, xuu17, ty_Double) → new_esEs13(xuu22, xuu17)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Integer, bdd) → new_ltEs13(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, app(ty_Ratio, cea)) → new_compare9(xuu33000, xuu34000, cea)
new_esEs20(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_lt6(xuu330, xuu340) → new_esEs8(new_compare11(xuu330, xuu340), LT)
new_ltEs17(EQ, LT) → False
new_esEs24(xuu3110000, xuu6000, app(ty_[], chg)) → new_esEs12(xuu3110000, xuu6000, chg)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Ordering, ed) → new_esEs8(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Float) → new_lt15(xuu33000, xuu34000)
new_lt20(xuu33001, xuu34001, ty_Bool) → new_lt4(xuu33001, xuu34001)
new_pePe(False, xuu168) → xuu168
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Integer) → new_ltEs13(xuu33000, xuu34000)
new_esEs12([], :(xuu6000, xuu6001), ccb) → False
new_esEs12(:(xuu3110000, xuu3110001), [], ccb) → False
new_esEs27(xuu33001, xuu34001, ty_Float) → new_esEs11(xuu33001, xuu34001)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_esEs18(xuu33000, xuu34000, app(app(ty_@2, cf), cg)) → new_esEs7(xuu33000, xuu34000, cf, cg)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Integer) → new_ltEs13(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, app(app(ty_Either, cfh), cga)) → new_esEs4(xuu3110002, xuu6002, cfh, cga)
new_ltEs19(xuu3300, xuu3400, app(app(ty_@2, bd), be)) → new_ltEs4(xuu3300, xuu3400, bd, be)
new_ltEs10(xuu3300, xuu3400, hf) → new_fsEs(new_compare(xuu3300, xuu3400, hf))
new_compare32(xuu33000, xuu34000, ty_Double) → new_compare15(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, app(app(ty_@2, ea), eb)) → new_ltEs4(xuu33001, xuu34001, ea, eb)
new_esEs30(xuu22, xuu17, ty_Bool) → new_esEs15(xuu22, xuu17)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Char, bdd) → new_ltEs8(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, ty_Integer) → new_esEs16(xuu22, xuu17)
new_esEs22(xuu3110002, xuu6002, ty_Ordering) → new_esEs8(xuu3110002, xuu6002)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_[], cba)) → new_esEs12(xuu3110000, xuu6000, cba)
new_esEs30(xuu22, xuu17, app(ty_Ratio, bgb)) → new_esEs9(xuu22, xuu17, bgb)
new_lt20(xuu33001, xuu34001, app(app(ty_Either, dbf), dbg)) → new_lt7(xuu33001, xuu34001, dbf, dbg)
new_ltEs20(xuu33002, xuu34002, app(app(ty_@2, ddh), dea)) → new_ltEs4(xuu33002, xuu34002, ddh, dea)
new_primCmpNat0(Zero, Succ(xuu3400)) → LT
new_lt5(xuu33000, xuu34000, ty_Float) → new_lt15(xuu33000, xuu34000)
new_ltEs19(xuu3300, xuu3400, ty_Float) → new_ltEs15(xuu3300, xuu3400)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(app(ty_@2, gh), ha)) → new_esEs7(xuu3110000, xuu6000, gh, ha)
new_compare14(xuu33000, xuu34000, False) → GT
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_Ratio, bea), bdd) → new_ltEs11(xuu33000, xuu34000, bea)
new_esEs8(LT, LT) → True
new_compare25(xuu33000, xuu34000, True, hc, hd, he) → EQ
new_lt18(xuu33000, xuu34000) → new_esEs8(new_compare8(xuu33000, xuu34000), LT)
new_lt19(xuu33000, xuu34000, app(app(ty_@2, bda), bdb)) → new_lt16(xuu33000, xuu34000, bda, bdb)
new_esEs29(xuu311000, xuu600, app(app(ty_@2, baa), bab)) → new_esEs7(xuu311000, xuu600, baa, bab)
new_esEs18(xuu33000, xuu34000, app(ty_Ratio, cb)) → new_esEs9(xuu33000, xuu34000, cb)
new_ltEs20(xuu33002, xuu34002, app(ty_Maybe, ddb)) → new_ltEs9(xuu33002, xuu34002, ddb)
new_esEs28(xuu33000, xuu34000, ty_Integer) → new_esEs16(xuu33000, xuu34000)
new_esEs20(xuu3110000, xuu6000, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs6(xuu3110000, xuu6000, bbh, bca, bcb)
new_pePe(True, xuu168) → True
new_primEqNat0(Zero, Zero) → True
new_compare26(xuu33000, xuu34000, True) → EQ
new_compare23(Nothing, Just(xuu3400), False, dbb) → LT
new_ltEs20(xuu33002, xuu34002, app(app(app(ty_@3, dde), ddf), ddg)) → new_ltEs12(xuu33002, xuu34002, dde, ddf, ddg)
new_lt16(xuu33000, xuu34000, bda, bdb) → new_esEs8(new_compare27(xuu33000, xuu34000, bda, bdb), LT)
new_compare29(xuu33000, xuu34000, True, bcg, bch) → EQ
new_esEs14(@0, @0) → True
new_compare111(xuu33000, xuu34000, False, bcg, bch) → GT
new_esEs18(xuu33000, xuu34000, ty_Bool) → new_esEs15(xuu33000, xuu34000)
new_compare14(xuu33000, xuu34000, True) → LT
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Bool, bdd) → new_ltEs18(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, app(app(ty_@2, cgb), cgc)) → new_esEs7(xuu3110002, xuu6002, cgb, cgc)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Integer, ed) → new_esEs16(xuu3110000, xuu6000)
new_esEs19(xuu3110001, xuu6001, app(ty_[], bad)) → new_esEs12(xuu3110001, xuu6001, bad)
new_compare26(xuu33000, xuu34000, False) → new_compare14(xuu33000, xuu34000, new_ltEs17(xuu33000, xuu34000))
new_ltEs17(GT, LT) → False
new_compare(:(xuu33000, xuu33001), :(xuu34000, xuu34001), hf) → new_primCompAux1(xuu33000, xuu34000, new_compare(xuu33001, xuu34001, hf), hf)
new_lt5(xuu33000, xuu34000, ty_Char) → new_lt8(xuu33000, xuu34000)
new_sr(xuu3110001, xuu6001) → new_primMulInt(xuu3110001, xuu6001)
new_ltEs19(xuu3300, xuu3400, app(app(app(ty_@3, dbc), dbd), dbe)) → new_ltEs12(xuu3300, xuu3400, dbc, dbd, dbe)
new_esEs24(xuu3110000, xuu6000, app(app(ty_@2, daf), dag)) → new_esEs7(xuu3110000, xuu6000, daf, dag)
new_compare32(xuu33000, xuu34000, ty_Int) → new_compare11(xuu33000, xuu34000)
new_esEs8(GT, GT) → True
new_esEs18(xuu33000, xuu34000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs6(xuu33000, xuu34000, cc, cd, ce)
new_ltEs20(xuu33002, xuu34002, app(ty_Ratio, ddd)) → new_ltEs11(xuu33002, xuu34002, ddd)
new_compare32(xuu33000, xuu34000, ty_Bool) → new_compare6(xuu33000, xuu34000)
new_lt19(xuu33000, xuu34000, app(ty_Ratio, dba)) → new_lt11(xuu33000, xuu34000, dba)
new_lt20(xuu33001, xuu34001, ty_Double) → new_lt17(xuu33001, xuu34001)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs19(xuu3300, xuu3400, app(ty_Maybe, bhd)) → new_ltEs9(xuu3300, xuu3400, bhd)
new_esEs28(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(app(ty_Either, gf), gg)) → new_esEs4(xuu3110000, xuu6000, gf, gg)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Int, bdd) → new_ltEs6(xuu33000, xuu34000)
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_lt20(xuu33001, xuu34001, app(ty_Ratio, dcb)) → new_lt11(xuu33001, xuu34001, dcb)
new_esEs15(True, True) → True
new_esEs20(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_compare18(xuu33000, xuu34000, hc, hd, he) → new_compare25(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, hc, hd, he), hc, hd, he)
new_esEs22(xuu3110002, xuu6002, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs6(xuu3110002, xuu6002, cfe, cff, cfg)
new_esEs23(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(ty_Either, fb), fc), ed) → new_esEs4(xuu3110000, xuu6000, fb, fc)
new_ltEs17(LT, GT) → True
new_primPlusNat1(Zero, Succ(xuu9700)) → Succ(xuu9700)
new_primPlusNat1(Succ(xuu28200), Zero) → Succ(xuu28200)
new_esEs13(Double(xuu3110000, xuu3110001), Double(xuu6000, xuu6001)) → new_esEs10(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Float) → new_ltEs15(xuu33000, xuu34000)
new_esEs21(xuu3110000, xuu6000, app(ty_Ratio, ccc)) → new_esEs9(xuu3110000, xuu6000, ccc)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(ty_@2, cae), caf)) → new_ltEs4(xuu33000, xuu34000, cae, caf)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_Ratio, caa)) → new_ltEs11(xuu33000, xuu34000, caa)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Double, ed) → new_esEs13(xuu3110000, xuu6000)
new_ltEs18(True, True) → True
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Int, ed) → new_esEs10(xuu3110000, xuu6000)
new_compare32(xuu33000, xuu34000, app(app(ty_@2, cee), cef)) → new_compare27(xuu33000, xuu34000, cee, cef)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs5(xuu33001, xuu34001, ty_Double) → new_ltEs16(xuu33001, xuu34001)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_ltEs7(Right(xuu33000), Left(xuu34000), beg, bdd) → False
new_esEs24(xuu3110000, xuu6000, app(app(app(ty_@3, daa), dab), dac)) → new_esEs6(xuu3110000, xuu6000, daa, dab, dac)
new_lt12(xuu33000, xuu34000, hc, hd, he) → new_esEs8(new_compare18(xuu33000, xuu34000, hc, hd, he), LT)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(ty_Either, bhe), bhf)) → new_ltEs7(xuu33000, xuu34000, bhe, bhf)
new_compare6(xuu33000, xuu34000) → new_compare24(xuu33000, xuu34000, new_esEs15(xuu33000, xuu34000))
new_esEs21(xuu3110000, xuu6000, app(app(ty_@2, cdc), cdd)) → new_esEs7(xuu3110000, xuu6000, cdc, cdd)
new_esEs28(xuu33000, xuu34000, ty_Double) → new_esEs13(xuu33000, xuu34000)
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu60000))) → False
new_ltEs18(False, False) → True
new_primCompAux0(xuu183, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs20(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_ltEs5(xuu33001, xuu34001, ty_Integer) → new_ltEs13(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_compare32(xuu33000, xuu34000, app(app(app(ty_@3, ceb), cec), ced)) → new_compare18(xuu33000, xuu34000, ceb, cec, ced)
new_compare32(xuu33000, xuu34000, app(app(ty_Either, cde), cdf)) → new_compare17(xuu33000, xuu34000, cde, cdf)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(ty_Ratio, bfd)) → new_ltEs11(xuu33000, xuu34000, bfd)
new_esEs20(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs21(xuu3110000, xuu6000, app(app(ty_Either, cda), cdb)) → new_esEs4(xuu3110000, xuu6000, cda, cdb)
new_compare23(Nothing, Nothing, False, dbb) → LT
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_compare([], [], hf) → EQ
new_ltEs17(EQ, EQ) → True
new_ltEs19(xuu3300, xuu3400, ty_Ordering) → new_ltEs17(xuu3300, xuu3400)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Char, ed) → new_esEs17(xuu3110000, xuu6000)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(ty_@2, bee), bef), bdd) → new_ltEs4(xuu33000, xuu34000, bee, bef)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_compare25(xuu33000, xuu34000, False, hc, hd, he) → new_compare13(xuu33000, xuu34000, new_ltEs12(xuu33000, xuu34000, hc, hd, he), hc, hd, he)
new_ltEs20(xuu33002, xuu34002, ty_Bool) → new_ltEs18(xuu33002, xuu34002)
new_lt20(xuu33001, xuu34001, ty_Char) → new_lt8(xuu33001, xuu34001)
new_esEs28(xuu33000, xuu34000, app(app(ty_@2, bda), bdb)) → new_esEs7(xuu33000, xuu34000, bda, bdb)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Int) → new_lt6(xuu33000, xuu34000)
new_primCmpNat0(Succ(xuu3300), Succ(xuu3400)) → new_primCmpNat0(xuu3300, xuu3400)
new_lt20(xuu33001, xuu34001, ty_Integer) → new_lt13(xuu33001, xuu34001)
new_lt8(xuu33000, xuu34000) → new_esEs8(new_compare30(xuu33000, xuu34000), LT)
new_esEs18(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_esEs26(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Double) → new_ltEs16(xuu33000, xuu34000)
new_esEs18(xuu33000, xuu34000, ty_Int) → new_esEs10(xuu33000, xuu34000)
new_esEs29(xuu311000, xuu600, app(ty_Maybe, cag)) → new_esEs5(xuu311000, xuu600, cag)
new_esEs28(xuu33000, xuu34000, ty_Char) → new_esEs17(xuu33000, xuu34000)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs23(xuu3110001, xuu6001, ty_Char) → new_esEs17(xuu3110001, xuu6001)
new_esEs23(xuu3110001, xuu6001, app(ty_[], cge)) → new_esEs12(xuu3110001, xuu6001, cge)
new_primEqNat0(Succ(xuu31100000), Succ(xuu60000)) → new_primEqNat0(xuu31100000, xuu60000)
new_esEs27(xuu33001, xuu34001, ty_Ordering) → new_esEs8(xuu33001, xuu34001)
new_esEs19(xuu3110001, xuu6001, app(app(app(ty_@3, baf), bag), bah)) → new_esEs6(xuu3110001, xuu6001, baf, bag, bah)
new_primCompAux1(xuu33000, xuu34000, xuu169, hf) → new_primCompAux0(xuu169, new_compare32(xuu33000, xuu34000, hf))
new_compare15(Double(xuu33000, xuu33001), Double(xuu34000, xuu34001)) → new_compare11(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_esEs29(xuu311000, xuu600, ty_Int) → new_esEs10(xuu311000, xuu600)
new_primCmpInt(Neg(Succ(xuu3300)), Neg(xuu340)) → new_primCmpNat0(xuu340, Succ(xuu3300))
new_ltEs19(xuu3300, xuu3400, app(app(ty_Either, beg), bdd)) → new_ltEs7(xuu3300, xuu3400, beg, bdd)
new_esEs24(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs18(xuu33000, xuu34000, ty_Char) → new_esEs17(xuu33000, xuu34000)
new_esEs23(xuu3110001, xuu6001, ty_Bool) → new_esEs15(xuu3110001, xuu6001)
new_lt19(xuu33000, xuu34000, app(app(ty_Either, bcg), bch)) → new_lt7(xuu33000, xuu34000, bcg, bch)
new_esEs28(xuu33000, xuu34000, ty_Ordering) → new_esEs8(xuu33000, xuu34000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu60000))) → False
new_esEs21(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_lt4(xuu33000, xuu34000) → new_esEs8(new_compare6(xuu33000, xuu34000), LT)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(app(ty_@3, cab), cac), cad)) → new_ltEs12(xuu33000, xuu34000, cab, cac, cad)
new_ltEs20(xuu33002, xuu34002, ty_Integer) → new_ltEs13(xuu33002, xuu34002)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Float, bdd) → new_ltEs15(xuu33000, xuu34000)
new_compare17(xuu33000, xuu34000, bcg, bch) → new_compare29(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, bcg, bch), bcg, bch)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu3300), Zero) → GT
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_Maybe, bhg)) → new_ltEs9(xuu33000, xuu34000, bhg)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3400))) → LT
new_ltEs20(xuu33002, xuu34002, ty_@0) → new_ltEs14(xuu33002, xuu34002)
new_esEs7(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), baa, bab) → new_asAs(new_esEs20(xuu3110000, xuu6000, baa), new_esEs19(xuu3110001, xuu6001, bab))
new_esEs21(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_sr0(Integer(xuu340000), Integer(xuu330010)) → Integer(new_primMulInt(xuu340000, xuu330010))
new_primPlusNat1(Succ(xuu28200), Succ(xuu9700)) → Succ(Succ(new_primPlusNat1(xuu28200, xuu9700)))
new_compare28(xuu33000, xuu34000, True, bda, bdb) → EQ
new_primEqInt(Pos(Succ(xuu31100000)), Neg(xuu6000)) → False
new_primEqInt(Neg(Succ(xuu31100000)), Pos(xuu6000)) → False
new_ltEs19(xuu3300, xuu3400, ty_Double) → new_ltEs16(xuu3300, xuu3400)
new_esEs25(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_compare9(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Int) → new_compare11(new_sr(xuu33000, xuu34001), new_sr(xuu34000, xuu33001))
new_esEs29(xuu311000, xuu600, app(ty_[], ccb)) → new_esEs12(xuu311000, xuu600, ccb)
new_esEs27(xuu33001, xuu34001, app(ty_Maybe, dbh)) → new_esEs5(xuu33001, xuu34001, dbh)
new_compare32(xuu33000, xuu34000, app(ty_[], cdh)) → new_compare(xuu33000, xuu34000, cdh)
new_esEs18(xuu33000, xuu34000, app(ty_[], ca)) → new_esEs12(xuu33000, xuu34000, ca)
new_compare23(Just(xuu3300), Just(xuu3400), False, dbb) → new_compare110(xuu3300, xuu3400, new_ltEs19(xuu3300, xuu3400, dbb), dbb)
new_lt11(xuu33000, xuu34000, dba) → new_esEs8(new_compare9(xuu33000, xuu34000, dba), LT)
new_lt19(xuu33000, xuu34000, ty_@0) → new_lt14(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, ty_Float) → new_ltEs15(xuu33002, xuu34002)
new_esEs29(xuu311000, xuu600, ty_@0) → new_esEs14(xuu311000, xuu600)
new_lt7(xuu33000, xuu34000, bcg, bch) → new_esEs8(new_compare17(xuu33000, xuu34000, bcg, bch), LT)
new_lt5(xuu33000, xuu34000, app(ty_Maybe, bh)) → new_lt9(xuu33000, xuu34000, bh)
new_esEs26(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_primEqInt(Pos(Zero), Neg(Succ(xuu60000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu60000))) → False
new_esEs20(xuu3110000, xuu6000, app(ty_[], bbf)) → new_esEs12(xuu3110000, xuu6000, bbf)
new_ltEs9(Just(xuu33000), Nothing, bhd) → False
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, app(ty_Ratio, fh)) → new_esEs9(xuu3110000, xuu6000, fh)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3400))) → new_primCmpNat0(Zero, Succ(xuu3400))
new_compare24(xuu33000, xuu34000, True) → EQ
new_esEs27(xuu33001, xuu34001, app(app(ty_@2, dcf), dcg)) → new_esEs7(xuu33001, xuu34001, dcf, dcg)
new_lt13(xuu33000, xuu34000) → new_esEs8(new_compare12(xuu33000, xuu34000), LT)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(app(app(ty_@3, bfe), bff), bfg)) → new_ltEs12(xuu33000, xuu34000, bfe, bff, bfg)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, ty_Char) → new_compare30(xuu33000, xuu34000)
new_lt15(xuu33000, xuu34000) → new_esEs8(new_compare31(xuu33000, xuu34000), LT)
new_primCompAux0(xuu183, LT) → LT
new_ltEs19(xuu3300, xuu3400, ty_Char) → new_ltEs8(xuu3300, xuu3400)
new_esEs23(xuu3110001, xuu6001, ty_Float) → new_esEs11(xuu3110001, xuu6001)
new_esEs20(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_not(False) → True
new_esEs30(xuu22, xuu17, ty_@0) → new_esEs14(xuu22, xuu17)
new_primCmpInt(Pos(Succ(xuu3300)), Pos(xuu340)) → new_primCmpNat0(Succ(xuu3300), xuu340)
new_compare110(xuu135, xuu136, True, bdc) → LT
new_esEs22(xuu3110002, xuu6002, ty_Float) → new_esEs11(xuu3110002, xuu6002)
new_esEs19(xuu3110001, xuu6001, app(app(ty_@2, bbc), bbd)) → new_esEs7(xuu3110001, xuu6001, bbc, bbd)
new_ltEs19(xuu3300, xuu3400, app(ty_[], hf)) → new_ltEs10(xuu3300, xuu3400, hf)
new_esEs30(xuu22, xuu17, app(app(ty_@2, bhb), bhc)) → new_esEs7(xuu22, xuu17, bhb, bhc)
new_ltEs5(xuu33001, xuu34001, app(ty_Ratio, de)) → new_ltEs11(xuu33001, xuu34001, de)
new_ltEs9(Nothing, Nothing, bhd) → True
new_esEs30(xuu22, xuu17, app(app(ty_Either, bgh), bha)) → new_esEs4(xuu22, xuu17, bgh, bha)
new_esEs19(xuu3110001, xuu6001, ty_Char) → new_esEs17(xuu3110001, xuu6001)
new_lt20(xuu33001, xuu34001, app(ty_[], dca)) → new_lt10(xuu33001, xuu34001, dca)
new_ltEs19(xuu3300, xuu3400, ty_Int) → new_ltEs6(xuu3300, xuu3400)
new_esEs27(xuu33001, xuu34001, ty_@0) → new_esEs14(xuu33001, xuu34001)
new_ltEs16(xuu3300, xuu3400) → new_fsEs(new_compare15(xuu3300, xuu3400))
new_lt19(xuu33000, xuu34000, app(app(app(ty_@3, hc), hd), he)) → new_lt12(xuu33000, xuu34000, hc, hd, he)
new_lt20(xuu33001, xuu34001, ty_Int) → new_lt6(xuu33001, xuu34001)
new_lt20(xuu33001, xuu34001, ty_Ordering) → new_lt18(xuu33001, xuu34001)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_compare12(Integer(xuu33000), Integer(xuu34000)) → new_primCmpInt(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, app(ty_Maybe, chh)) → new_esEs5(xuu3110000, xuu6000, chh)
new_lt5(xuu33000, xuu34000, app(app(ty_@2, cf), cg)) → new_lt16(xuu33000, xuu34000, cf, cg)
new_esEs18(xuu33000, xuu34000, app(app(ty_Either, bf), bg)) → new_esEs4(xuu33000, xuu34000, bf, bg)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(ty_[], bfc)) → new_ltEs10(xuu33000, xuu34000, bfc)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_primCmpInt(Pos(Succ(xuu3300)), Neg(xuu340)) → GT
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Double, bdd) → new_ltEs16(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, ty_Bool) → new_ltEs18(xuu33001, xuu34001)
new_esEs21(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs30(xuu22, xuu17, app(ty_[], bgc)) → new_esEs12(xuu22, xuu17, bgc)
new_compare32(xuu33000, xuu34000, ty_Ordering) → new_compare8(xuu33000, xuu34000)
new_lt5(xuu33000, xuu34000, app(ty_Ratio, cb)) → new_lt11(xuu33000, xuu34000, cb)
new_primMulInt(Pos(xuu31100010), Pos(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Bool, ed) → new_esEs15(xuu3110000, xuu6000)
new_esEs24(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs27(xuu33001, xuu34001, ty_Char) → new_esEs17(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, app(app(ty_Either, chb), chc)) → new_esEs4(xuu3110001, xuu6001, chb, chc)
new_esEs22(xuu3110002, xuu6002, ty_Double) → new_esEs13(xuu3110002, xuu6002)
new_esEs22(xuu3110002, xuu6002, ty_Int) → new_esEs10(xuu3110002, xuu6002)
new_compare32(xuu33000, xuu34000, ty_@0) → new_compare16(xuu33000, xuu34000)
new_primMulInt(Neg(xuu31100010), Neg(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_esEs24(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_esEs28(xuu33000, xuu34000, app(ty_Ratio, dba)) → new_esEs9(xuu33000, xuu34000, dba)
new_lt20(xuu33001, xuu34001, ty_@0) → new_lt14(xuu33001, xuu34001)
new_primEqNat0(Succ(xuu31100000), Zero) → False
new_primEqNat0(Zero, Succ(xuu60000)) → False
new_esEs21(xuu3110000, xuu6000, app(ty_[], ccd)) → new_esEs12(xuu3110000, xuu6000, ccd)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(ty_Either, bde), bdf), bdd) → new_ltEs7(xuu33000, xuu34000, bde, bdf)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(xuu3110000, xuu6000, app(app(ty_Either, dad), dae)) → new_esEs4(xuu3110000, xuu6000, dad, dae)
new_esEs28(xuu33000, xuu34000, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(xuu33000, xuu34000, hc, hd, he)
new_primPlusNat0(xuu107, xuu600100) → new_primPlusNat1(xuu107, Succ(xuu600100))
new_lt19(xuu33000, xuu34000, ty_Double) → new_lt17(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, ty_Integer) → new_compare12(xuu33000, xuu34000)
new_esEs27(xuu33001, xuu34001, app(app(ty_Either, dbf), dbg)) → new_esEs4(xuu33001, xuu34001, dbf, dbg)
new_esEs27(xuu33001, xuu34001, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs6(xuu33001, xuu34001, dcc, dcd, dce)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_lt5(xuu33000, xuu34000, ty_Integer) → new_lt13(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, app(ty_Maybe, bae)) → new_esEs5(xuu3110001, xuu6001, bae)
new_esEs27(xuu33001, xuu34001, ty_Integer) → new_esEs16(xuu33001, xuu34001)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Float, ed) → new_esEs11(xuu3110000, xuu6000)
new_ltEs5(xuu33001, xuu34001, ty_Int) → new_ltEs6(xuu33001, xuu34001)
new_ltEs14(xuu3300, xuu3400) → new_fsEs(new_compare16(xuu3300, xuu3400))
new_ltEs5(xuu33001, xuu34001, app(ty_Maybe, dc)) → new_ltEs9(xuu33001, xuu34001, dc)
new_esEs25(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_esEs21(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3400))) → new_primCmpNat0(Succ(xuu3400), Zero)
new_ltEs5(xuu33001, xuu34001, ty_Ordering) → new_ltEs17(xuu33001, xuu34001)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3400))) → GT
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Ordering) → new_ltEs17(xuu33000, xuu34000)
new_compare110(xuu135, xuu136, False, bdc) → GT
new_ltEs20(xuu33002, xuu34002, ty_Char) → new_ltEs8(xuu33002, xuu34002)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(app(ty_@3, cbc), cbd), cbe)) → new_esEs6(xuu3110000, xuu6000, cbc, cbd, cbe)
new_compare19(xuu33000, xuu34000, True, bda, bdb) → LT
new_lt20(xuu33001, xuu34001, app(ty_Maybe, dbh)) → new_lt9(xuu33001, xuu34001, dbh)
new_lt19(xuu33000, xuu34000, app(ty_[], hh)) → new_lt10(xuu33000, xuu34000, hh)
new_compare23(xuu330, xuu340, True, dbb) → EQ
new_esEs19(xuu3110001, xuu6001, ty_Float) → new_esEs11(xuu3110001, xuu6001)
new_esEs16(Integer(xuu3110000), Integer(xuu6000)) → new_primEqInt(xuu3110000, xuu6000)
new_ltEs20(xuu33002, xuu34002, ty_Ordering) → new_ltEs17(xuu33002, xuu34002)
new_lt5(xuu33000, xuu34000, ty_Bool) → new_lt4(xuu33000, xuu34000)
new_esEs29(xuu311000, xuu600, app(ty_Ratio, dah)) → new_esEs9(xuu311000, xuu600, dah)
new_esEs23(xuu3110001, xuu6001, ty_@0) → new_esEs14(xuu3110001, xuu6001)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs21(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Ordering, bdd) → new_ltEs17(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, app(ty_Maybe, bbg)) → new_esEs5(xuu3110000, xuu6000, bbg)
new_esEs4(Right(xuu3110000), Right(xuu6000), fg, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, app(app(ty_Either, beh), bfa)) → new_ltEs7(xuu33000, xuu34000, beh, bfa)
new_esEs29(xuu311000, xuu600, ty_Bool) → new_esEs15(xuu311000, xuu600)
new_asAs(False, xuu142) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Int) → new_ltEs6(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, ty_Double) → new_ltEs16(xuu33002, xuu34002)
new_lt17(xuu33000, xuu34000) → new_esEs8(new_compare15(xuu33000, xuu34000), LT)
new_primMulInt(Pos(xuu31100010), Neg(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_primMulInt(Neg(xuu31100010), Pos(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_ltEs11(xuu3300, xuu3400, hg) → new_fsEs(new_compare9(xuu3300, xuu3400, hg))
new_primMulNat0(Zero, Succ(xuu600100)) → Zero
new_primMulNat0(Succ(xuu311000100), Zero) → Zero
new_esEs27(xuu33001, xuu34001, ty_Double) → new_esEs13(xuu33001, xuu34001)
new_esEs24(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_lt5(xuu33000, xuu34000, ty_Int) → new_lt6(xuu33000, xuu34000)
new_esEs23(xuu3110001, xuu6001, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs6(xuu3110001, xuu6001, cgg, cgh, cha)
new_lt19(xuu33000, xuu34000, ty_Ordering) → new_lt18(xuu33000, xuu34000)
new_esEs21(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Char) → new_lt8(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, app(ty_Maybe, cdg)) → new_compare7(xuu33000, xuu34000, cdg)
new_esEs29(xuu311000, xuu600, ty_Float) → new_esEs11(xuu311000, xuu600)
new_esEs23(xuu3110001, xuu6001, app(app(ty_@2, chd), che)) → new_esEs7(xuu3110001, xuu6001, chd, che)
new_esEs29(xuu311000, xuu600, ty_Char) → new_esEs17(xuu311000, xuu600)
new_esEs29(xuu311000, xuu600, ty_Double) → new_esEs13(xuu311000, xuu600)
new_lt5(xuu33000, xuu34000, app(app(app(ty_@3, cc), cd), ce)) → new_lt12(xuu33000, xuu34000, cc, cd, ce)
new_esEs18(xuu33000, xuu34000, app(ty_Maybe, bh)) → new_esEs5(xuu33000, xuu34000, bh)
new_esEs24(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_compare27(xuu33000, xuu34000, bda, bdb) → new_compare28(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, bda, bdb), bda, bdb)
new_esEs18(xuu33000, xuu34000, ty_Ordering) → new_esEs8(xuu33000, xuu34000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_Maybe, ef), ed) → new_esEs5(xuu3110000, xuu6000, ef)
new_lt9(xuu33000, xuu34000, hb) → new_esEs8(new_compare7(xuu33000, xuu34000, hb), LT)
new_lt20(xuu33001, xuu34001, app(app(ty_@2, dcf), dcg)) → new_lt16(xuu33001, xuu34001, dcf, dcg)
new_esEs28(xuu33000, xuu34000, app(app(ty_Either, bcg), bch)) → new_esEs4(xuu33000, xuu34000, bcg, bch)
new_compare8(xuu33000, xuu34000) → new_compare26(xuu33000, xuu34000, new_esEs8(xuu33000, xuu34000))
new_esEs23(xuu3110001, xuu6001, app(ty_Maybe, cgf)) → new_esEs5(xuu3110001, xuu6001, cgf)
new_lt5(xuu33000, xuu34000, ty_Double) → new_lt17(xuu33000, xuu34000)
new_esEs6(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), ceg, ceh, cfa) → new_asAs(new_esEs24(xuu3110000, xuu6000, ceg), new_asAs(new_esEs23(xuu3110001, xuu6001, ceh), new_esEs22(xuu3110002, xuu6002, cfa)))
new_lt5(xuu33000, xuu34000, app(ty_[], ca)) → new_lt10(xuu33000, xuu34000, ca)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Char) → new_ltEs8(xuu33000, xuu34000)
new_ltEs17(GT, GT) → True
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Ordering) → new_ltEs17(xuu33000, xuu34000)
new_ltEs19(xuu3300, xuu3400, ty_@0) → new_ltEs14(xuu3300, xuu3400)
new_ltEs17(GT, EQ) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Char) → new_ltEs8(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, app(ty_[], cfc)) → new_esEs12(xuu3110002, xuu6002, cfc)
new_esEs5(Just(xuu3110000), Nothing, cag) → False
new_esEs5(Nothing, Just(xuu6000), cag) → False
new_ltEs15(xuu3300, xuu3400) → new_fsEs(new_compare31(xuu3300, xuu3400))
new_esEs22(xuu3110002, xuu6002, ty_Bool) → new_esEs15(xuu3110002, xuu6002)
new_esEs19(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_compare11(xuu33, xuu34) → new_primCmpInt(xuu33, xuu34)
new_esEs28(xuu33000, xuu34000, ty_Bool) → new_esEs15(xuu33000, xuu34000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(ty_@2, fd), ff), ed) → new_esEs7(xuu3110000, xuu6000, fd, ff)
new_ltEs5(xuu33001, xuu34001, app(ty_[], dd)) → new_ltEs10(xuu33001, xuu34001, dd)
new_lt19(xuu33000, xuu34000, ty_Integer) → new_lt13(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, app(app(ty_Either, dch), dda)) → new_ltEs7(xuu33002, xuu34002, dch, dda)
new_ltEs18(True, False) → False
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_Maybe, bdg), bdd) → new_ltEs9(xuu33000, xuu34000, bdg)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Double) → new_ltEs16(xuu33000, xuu34000)
new_lt10(xuu33000, xuu34000, hh) → new_esEs8(new_compare(xuu33000, xuu34000, hh), LT)
new_esEs20(xuu3110000, xuu6000, app(ty_Ratio, bbe)) → new_esEs9(xuu3110000, xuu6000, bbe)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_[], bhh)) → new_ltEs10(xuu33000, xuu34000, bhh)
new_ltEs12(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), dbc, dbd, dbe) → new_pePe(new_lt19(xuu33000, xuu34000, dbc), new_asAs(new_esEs28(xuu33000, xuu34000, dbc), new_pePe(new_lt20(xuu33001, xuu34001, dbd), new_asAs(new_esEs27(xuu33001, xuu34001, dbd), new_ltEs20(xuu33002, xuu34002, dbe)))))
new_esEs22(xuu3110002, xuu6002, ty_@0) → new_esEs14(xuu3110002, xuu6002)
new_esEs5(Nothing, Nothing, cag) → True
new_esEs23(xuu3110001, xuu6001, app(ty_Ratio, cgd)) → new_esEs9(xuu3110001, xuu6001, cgd)
new_esEs28(xuu33000, xuu34000, app(ty_Maybe, hb)) → new_esEs5(xuu33000, xuu34000, hb)
new_esEs29(xuu311000, xuu600, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs6(xuu311000, xuu600, ceg, ceh, cfa)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs28(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, ty_Integer) → new_esEs16(xuu3110002, xuu6002)
new_esEs30(xuu22, xuu17, ty_Char) → new_esEs17(xuu22, xuu17)
new_esEs30(xuu22, xuu17, ty_Float) → new_esEs11(xuu22, xuu17)
new_esEs28(xuu33000, xuu34000, ty_Int) → new_esEs10(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, app(ty_Ratio, bac)) → new_esEs9(xuu3110001, xuu6001, bac)
new_ltEs13(xuu3300, xuu3400) → new_fsEs(new_compare12(xuu3300, xuu3400))
new_esEs21(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_esEs30(xuu22, xuu17, ty_Ordering) → new_esEs8(xuu22, xuu17)
new_esEs29(xuu311000, xuu600, ty_Integer) → new_esEs16(xuu311000, xuu600)
new_compare24(xuu33000, xuu34000, False) → new_compare10(xuu33000, xuu34000, new_ltEs18(xuu33000, xuu34000))
new_esEs20(xuu3110000, xuu6000, app(app(ty_@2, bce), bcf)) → new_esEs7(xuu3110000, xuu6000, bce, bcf)
new_ltEs18(False, True) → True
new_esEs20(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_esEs22(xuu3110002, xuu6002, app(ty_Maybe, cfd)) → new_esEs5(xuu3110002, xuu6002, cfd)
new_esEs21(xuu3110000, xuu6000, app(ty_Maybe, cce)) → new_esEs5(xuu3110000, xuu6000, cce)
new_primPlusNat1(Zero, Zero) → Zero
new_compare111(xuu33000, xuu34000, True, bcg, bch) → LT
new_esEs21(xuu3110000, xuu6000, app(app(app(ty_@3, ccf), ccg), cch)) → new_esEs6(xuu3110000, xuu6000, ccf, ccg, cch)
new_lt14(xuu33000, xuu34000) → new_esEs8(new_compare16(xuu33000, xuu34000), LT)
new_lt20(xuu33001, xuu34001, ty_Float) → new_lt15(xuu33001, xuu34001)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_[], ee), ed) → new_esEs12(xuu3110000, xuu6000, ee)
new_ltEs5(xuu33001, xuu34001, app(app(ty_Either, da), db)) → new_ltEs7(xuu33001, xuu34001, da, db)
new_esEs12(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), ccb) → new_asAs(new_esEs21(xuu3110000, xuu6000, ccb), new_esEs12(xuu3110001, xuu6001, ccb))
new_asAs(True, xuu142) → xuu142
new_esEs28(xuu33000, xuu34000, app(ty_[], hh)) → new_esEs12(xuu33000, xuu34000, hh)
new_esEs27(xuu33001, xuu34001, app(ty_[], dca)) → new_esEs12(xuu33001, xuu34001, dca)
new_esEs19(xuu3110001, xuu6001, app(app(ty_Either, bba), bbb)) → new_esEs4(xuu3110001, xuu6001, bba, bbb)
new_primMulNat0(Succ(xuu311000100), Succ(xuu600100)) → new_primPlusNat0(new_primMulNat0(xuu311000100, Succ(xuu600100)), xuu600100)
new_ltEs17(LT, EQ) → True
new_compare30(Char(xuu33000), Char(xuu34000)) → new_primCmpNat0(xuu33000, xuu34000)
new_esEs4(Right(xuu3110000), Left(xuu6000), fg, ed) → False
new_esEs4(Left(xuu3110000), Right(xuu6000), fg, ed) → False
new_compare29(xuu33000, xuu34000, False, bcg, bch) → new_compare111(xuu33000, xuu34000, new_ltEs7(xuu33000, xuu34000, bcg, bch), bcg, bch)
new_esEs30(xuu22, xuu17, app(ty_Maybe, bgd)) → new_esEs5(xuu22, xuu17, bgd)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_@2, cbh), cca)) → new_esEs7(xuu3110000, xuu6000, cbh, cca)
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_esEs27(xuu33001, xuu34001, ty_Int) → new_esEs10(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_esEs27(xuu33001, xuu34001, ty_Bool) → new_esEs15(xuu33001, xuu34001)
new_esEs21(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(app(ty_@3, eg), eh), fa), ed) → new_esEs6(xuu3110000, xuu6000, eg, eh, fa)
new_ltEs6(xuu3300, xuu3400) → new_fsEs(new_compare11(xuu3300, xuu3400))
new_fsEs(xuu152) → new_not(new_esEs8(xuu152, GT))
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Float) → new_ltEs15(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, ty_Char) → new_ltEs8(xuu33001, xuu34001)
new_ltEs19(xuu3300, xuu3400, ty_Integer) → new_ltEs13(xuu3300, xuu3400)
new_esEs19(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_Ratio, ec), ed) → new_esEs9(xuu3110000, xuu6000, ec)
new_compare7(xuu33000, xuu34000, hb) → new_compare23(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, hb), hb)
new_compare10(xuu33000, xuu34000, True) → LT
new_ltEs5(xuu33001, xuu34001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs12(xuu33001, xuu34001, df, dg, dh)
new_compare19(xuu33000, xuu34000, False, bda, bdb) → GT
new_ltEs20(xuu33002, xuu34002, ty_Int) → new_ltEs6(xuu33002, xuu34002)
new_ltEs17(EQ, GT) → True
new_compare13(xuu33000, xuu34000, True, hc, hd, he) → LT
new_compare10(xuu33000, xuu34000, False) → GT
new_esEs10(xuu311000, xuu600) → new_primEqInt(xuu311000, xuu600)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Ratio, cah)) → new_esEs9(xuu3110000, xuu6000, cah)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_@0, ed) → new_esEs14(xuu3110000, xuu6000)
new_esEs30(xuu22, xuu17, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs6(xuu22, xuu17, bge, bgf, bgg)
new_lt5(xuu33000, xuu34000, ty_@0) → new_lt14(xuu33000, xuu34000)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_Either, cbf), cbg)) → new_esEs4(xuu3110000, xuu6000, cbf, cbg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs24(xuu3110000, xuu6000, app(ty_Ratio, chf)) → new_esEs9(xuu3110000, xuu6000, chf)
new_primCompAux0(xuu183, EQ) → xuu183
new_esEs29(xuu311000, xuu600, ty_Ordering) → new_esEs8(xuu311000, xuu600)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_[], bdh), bdd) → new_ltEs10(xuu33000, xuu34000, bdh)
new_compare32(xuu33000, xuu34000, ty_Float) → new_compare31(xuu33000, xuu34000)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare9(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Integer) → new_compare12(new_sr0(xuu33000, xuu34001), new_sr0(xuu34000, xuu33001))
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_@0) → new_ltEs14(xuu33000, xuu34000)
new_esEs11(Float(xuu3110000, xuu3110001), Float(xuu6000, xuu6001)) → new_esEs10(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_primCmpInt(Neg(Succ(xuu3300)), Pos(xuu340)) → LT
new_ltEs7(Right(xuu33000), Right(xuu34000), beg, ty_Int) → new_ltEs6(xuu33000, xuu34000)
new_not(True) → False
new_esEs15(False, False) → True
new_esEs19(xuu3110001, xuu6001, ty_Double) → new_esEs13(xuu3110001, xuu6001)

The set Q consists of the following terms:

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

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

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

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

new_addToFM_C1(xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_addToFM_C(xuu64, Nothing, xuu31101, h, ba)
new_addToFM_C(Branch(Just(xuu600), xuu61, xuu62, xuu63, xuu64), Nothing, xuu31101, h, ba) → new_addToFM_C2(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Just(xuu600), False, h), LT), h, ba)
new_addToFM_C2(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_addToFM_C(xuu63, Nothing, xuu31101, h, ba)
new_addToFM_C2(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, False, h, ba) → new_addToFM_C10(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Just(xuu600), False, h), GT), h, ba)
new_addToFM_C(Branch(Nothing, xuu61, xuu62, xuu63, xuu64), Nothing, xuu31101, h, ba) → new_addToFM_C1(xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C10(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_addToFM_C(xuu64, Nothing, xuu31101, h, ba)

The TRS R consists of the following rules:

new_compare23(Nothing, Just(xuu3400), False, dbb) → LT
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_compare23(xuu330, xuu340, True, dbb) → EQ
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False

The set Q consists of the following terms:

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

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

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



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

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

new_addToFM_C(Branch(Just(xuu600), xuu61, xuu62, xuu63, xuu64), Nothing, xuu31101, h, ba) → new_addToFM_C2(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Just(xuu600), False, h), LT), h, ba)
new_addToFM_C1(xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_addToFM_C(xuu64, Nothing, xuu31101, h, ba)
new_addToFM_C2(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_addToFM_C(xuu63, Nothing, xuu31101, h, ba)
new_addToFM_C2(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, False, h, ba) → new_addToFM_C10(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Just(xuu600), False, h), GT), h, ba)
new_addToFM_C(Branch(Nothing, xuu61, xuu62, xuu63, xuu64), Nothing, xuu31101, h, ba) → new_addToFM_C1(xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C10(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_addToFM_C(xuu64, Nothing, xuu31101, h, ba)

The TRS R consists of the following rules:

new_compare23(Nothing, Just(xuu3400), False, dbb) → LT
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_compare23(xuu330, xuu340, True, dbb) → EQ
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False

The set Q consists of the following terms:

new_compare23(Nothing, Just(x0), False, x1)
new_compare23(Nothing, Nothing, False, x0)
new_esEs8(GT, GT)
new_esEs8(LT, LT)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_compare23(x0, x1, True, x2)
new_compare23(Just(x0), Nothing, False, x1)
new_compare23(Just(x0), Just(x1), False, x2)
new_esEs8(EQ, EQ)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)

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(xuu6, :(xuu3110, xuu3111), h, ba) → new_foldl(new_addListToFM_CAdd(xuu6, xuu3110, h, ba), xuu3111, h, ba)

The TRS R consists of the following rules:

new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_ltEs19(xuu3300, xuu3400, app(ty_Ratio, bef)) → new_ltEs11(xuu3300, xuu3400, bef)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_@0, eh) → new_ltEs14(xuu33000, xuu34000)
new_lt20(xuu33001, xuu34001, app(app(app(ty_@3, dce), dcf), dcg)) → new_lt12(xuu33001, xuu34001, dce, dcf, dcg)
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, app(ty_Maybe, gg)) → new_ltEs9(xuu33000, xuu34000, gg)
new_esEs22(xuu3110002, xuu6002, app(ty_Ratio, ceb)) → new_esEs9(xuu3110002, xuu6002, ceb)
new_ltEs5(xuu33001, xuu34001, ty_@0) → new_ltEs14(xuu33001, xuu34001)
new_ltEs17(LT, LT) → True
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_mkBalBranch6Size_l(xuu64, xuu600, xuu61, xuu28, h, ba) → new_sizeFM(xuu28, h, ba)
new_esEs17(Char(xuu3110000), Char(xuu6000)) → new_primEqNat0(xuu3110000, xuu6000)
new_addToFM_C24(xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, chh, daa) → new_mkBalBranch0(xuu17, xuu18, new_addToFM_C0(xuu20, Just(xuu22), xuu23, chh, daa), xuu21, chh, daa)
new_esEs18(xuu33000, xuu34000, ty_Integer) → new_esEs16(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_ltEs20(xuu33002, xuu34002, app(ty_[], dde)) → new_ltEs10(xuu33002, xuu34002, dde)
new_esEs19(xuu3110001, xuu6001, ty_Bool) → new_esEs15(xuu3110001, xuu6001)
new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs6(xuu3110000, xuu6000, bdg, bdh, bea)
new_compare([], :(xuu34000, xuu34001), eb) → LT
new_ltEs9(Nothing, Just(xuu34000), cac) → True
new_ltEs4(@2(xuu33000, xuu33001), @2(xuu34000, xuu34001), bb, bc) → new_pePe(new_lt5(xuu33000, xuu34000, bb), new_asAs(new_esEs18(xuu33000, xuu34000, bb), new_ltEs5(xuu33001, xuu34001, bc)))
new_ltEs8(xuu3300, xuu3400) → new_fsEs(new_compare30(xuu3300, xuu3400))
new_sizeFM0(Branch(xuu2150, xuu2151, xuu2152, xuu2153, xuu2154), baa, bab) → xuu2152
new_compare23(Just(xuu3300), Nothing, False, dab) → GT
new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, app(ty_Maybe, bdf)) → new_esEs5(xuu3110000, xuu6000, bdf)
new_primCmpInt1(Branch(xuu280, xuu281, xuu282, xuu283, xuu284), xuu64, xuu600, xuu61, h, ba) → new_primCmpInt(new_primPlusInt(xuu282, new_mkBalBranch6Size_r0(xuu64, xuu600, xuu61, Branch(xuu280, xuu281, xuu282, xuu283, xuu284), h, ba)), Pos(Succ(Succ(Zero))))
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(xuu33000), Right(xuu34000), gd, eh) → True
new_lt5(xuu33000, xuu34000, ty_Ordering) → new_lt18(xuu33000, xuu34000)
new_compare28(xuu33000, xuu34000, False, ef, eg) → new_compare19(xuu33000, xuu34000, new_ltEs4(xuu33000, xuu34000, ef, eg), ef, eg)
new_compare(:(xuu33000, xuu33001), [], eb) → GT
new_compare13(xuu33000, xuu34000, False, ec, ed, ee) → GT
new_esEs18(xuu33000, xuu34000, ty_Double) → new_esEs13(xuu33000, xuu34000)
new_mkBalBranch6MkBalBranch40(Branch(xuu640, xuu641, xuu642, xuu643, xuu644), xuu61, xuu36, True, h, ba) → new_mkBalBranch6MkBalBranch01(xuu640, xuu641, xuu642, xuu643, xuu644, xuu61, xuu36, new_lt6(new_sizeFM(xuu643, h, ba), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM(xuu644, h, ba))), h, ba)
new_lt19(xuu33000, xuu34000, app(ty_Maybe, ea)) → new_lt9(xuu33000, xuu34000, ea)
new_esEs22(xuu3110002, xuu6002, ty_Char) → new_esEs17(xuu3110002, xuu6002)
new_ltEs5(xuu33001, xuu34001, ty_Float) → new_ltEs15(xuu33001, xuu34001)
new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, app(ty_[], bde)) → new_esEs12(xuu3110000, xuu6000, bde)
new_compare31(Float(xuu33000, xuu33001), Float(xuu34000, xuu34001)) → new_compare11(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_mkBalBranch6MkBalBranch4(xuu64, xuu600, xuu61, xuu28, False, h, ba) → new_mkBalBranch6MkBalBranch3(xuu64, xuu600, xuu61, xuu28, new_gt(new_mkBalBranch6Size_l(xuu64, xuu600, xuu61, xuu28, h, ba), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_r0(xuu64, xuu600, xuu61, xuu28, h, ba))), h, ba)
new_lt19(xuu33000, xuu34000, ty_Bool) → new_lt4(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(app(ty_@3, fg), fh), ga), eh) → new_ltEs12(xuu33000, xuu34000, fg, fh, ga)
new_esEs29(xuu311000, xuu600, app(app(ty_Either, bdc), bca)) → new_esEs4(xuu311000, xuu600, bdc, bca)
new_lt5(xuu33000, xuu34000, app(app(ty_Either, bd), be)) → new_lt7(xuu33000, xuu34000, bd, be)
new_esEs24(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_compare16(@0, @0) → EQ
new_esEs30(xuu22, xuu17, ty_Int) → new_esEs10(xuu22, xuu17)
new_addToFM_C23(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, True, h, ba) → new_mkBalBranch(xuu61, new_addToFM_C0(xuu63, Just(xuu311000), xuu31101, h, ba), xuu64, h, ba)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_ltEs19(xuu3300, xuu3400, ty_Bool) → new_ltEs18(xuu3300, xuu3400)
new_esEs20(xuu3110000, xuu6000, app(app(ty_Either, bhb), bhc)) → new_esEs4(xuu3110000, xuu6000, bhb, bhc)
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, app(app(ty_@2, he), hf)) → new_ltEs4(xuu33000, xuu34000, he, hf)
new_esEs27(xuu33001, xuu34001, app(ty_Ratio, dcd)) → new_esEs9(xuu33001, xuu34001, dcd)
new_esEs20(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_esEs9(:%(xuu3110000, xuu3110001), :%(xuu6000, xuu6001), bbf) → new_asAs(new_esEs26(xuu3110000, xuu6000, bbf), new_esEs25(xuu3110001, xuu6001, bbf))
new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs12([], [], bhg) → True
new_primCmpInt0(Branch(xuu360, xuu361, xuu362, xuu363, xuu364), xuu64, xuu61, h, ba) → new_primCmpInt(new_primPlusInt(xuu362, new_mkBalBranch6Size_r(xuu64, xuu61, Branch(xuu360, xuu361, xuu362, xuu363, xuu364), h, ba)), Pos(Succ(Succ(Zero))))
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Maybe, baf)) → new_esEs5(xuu3110000, xuu6000, baf)
new_esEs23(xuu3110001, xuu6001, ty_Double) → new_esEs13(xuu3110001, xuu6001)
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_@0) → new_ltEs14(xuu33000, xuu34000)
new_mkBranch(xuu211, xuu212, xuu213, xuu214, xuu215, baa, bab) → Branch(xuu212, xuu213, new_primPlusInt(new_primPlusInt(Pos(Succ(Zero)), new_sizeFM0(xuu214, baa, bab)), new_sizeFM0(xuu215, baa, bab)), xuu214, xuu215)
new_esEs18(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, ty_@0) → new_esEs14(xuu3110001, xuu6001)
new_esEs30(xuu22, xuu17, ty_Double) → new_esEs13(xuu22, xuu17)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Integer, eh) → new_ltEs13(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, app(ty_Ratio, cdd)) → new_compare9(xuu33000, xuu34000, cdd)
new_esEs20(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_lt6(xuu330, xuu340) → new_esEs8(new_compare11(xuu330, xuu340), LT)
new_ltEs17(EQ, LT) → False
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Ordering, bca) → new_esEs8(xuu3110000, xuu6000)
new_esEs24(xuu3110000, xuu6000, app(ty_[], cgg)) → new_esEs12(xuu3110000, xuu6000, cgg)
new_lt19(xuu33000, xuu34000, ty_Float) → new_lt15(xuu33000, xuu34000)
new_lt20(xuu33001, xuu34001, ty_Bool) → new_lt4(xuu33001, xuu34001)
new_pePe(False, xuu168) → xuu168
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Integer) → new_ltEs13(xuu33000, xuu34000)
new_esEs12([], :(xuu6000, xuu6001), bhg) → False
new_esEs12(:(xuu3110000, xuu3110001), [], bhg) → False
new_esEs27(xuu33001, xuu34001, ty_Float) → new_esEs11(xuu33001, xuu34001)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_esEs18(xuu33000, xuu34000, app(app(ty_@2, cd), ce)) → new_esEs7(xuu33000, xuu34000, cd, ce)
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, ty_Integer) → new_ltEs13(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, app(app(ty_Either, ceh), cfa)) → new_esEs4(xuu3110002, xuu6002, ceh, cfa)
new_ltEs19(xuu3300, xuu3400, app(app(ty_@2, bb), bc)) → new_ltEs4(xuu3300, xuu3400, bb, bc)
new_addToFM_C16(xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, False, chh, daa) → Branch(Just(xuu22), new_addListToFM0(xuu18, xuu23, daa), xuu19, xuu20, xuu21)
new_mkBalBranch6MkBalBranch01(xuu640, xuu641, xuu642, xuu643, xuu644, xuu61, xuu36, True, h, ba) → new_mkBranch(Succ(Succ(Zero)), xuu640, xuu641, new_mkBranch(Succ(Succ(Succ(Zero))), Nothing, xuu61, xuu36, xuu643, app(ty_Maybe, h), ba), xuu644, app(ty_Maybe, h), ba)
new_ltEs10(xuu3300, xuu3400, eb) → new_fsEs(new_compare(xuu3300, xuu3400, eb))
new_compare32(xuu33000, xuu34000, ty_Double) → new_compare15(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, app(app(ty_@2, dg), dh)) → new_ltEs4(xuu33001, xuu34001, dg, dh)
new_esEs30(xuu22, xuu17, ty_Bool) → new_esEs15(xuu22, xuu17)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Char, eh) → new_ltEs8(xuu33000, xuu34000)
new_esEs30(xuu22, xuu17, ty_Integer) → new_esEs16(xuu22, xuu17)
new_esEs22(xuu3110002, xuu6002, ty_Ordering) → new_esEs8(xuu3110002, xuu6002)
new_addToFM_C23(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, False, h, ba) → new_addToFM_C15(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, new_esEs8(new_compare23(Just(xuu311000), Nothing, False, h), GT), h, ba)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_[], bae)) → new_esEs12(xuu3110000, xuu6000, bae)
new_esEs30(xuu22, xuu17, app(ty_Ratio, daf)) → new_esEs9(xuu22, xuu17, daf)
new_lt20(xuu33001, xuu34001, app(app(ty_Either, dbh), dca)) → new_lt7(xuu33001, xuu34001, dbh, dca)
new_ltEs20(xuu33002, xuu34002, app(app(ty_@2, deb), dec)) → new_ltEs4(xuu33002, xuu34002, deb, dec)
new_primCmpNat0(Zero, Succ(xuu3400)) → LT
new_lt5(xuu33000, xuu34000, ty_Float) → new_lt15(xuu33000, xuu34000)
new_ltEs19(xuu3300, xuu3400, ty_Float) → new_ltEs15(xuu3300, xuu3400)
new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, app(app(ty_@2, bed), bee)) → new_esEs7(xuu3110000, xuu6000, bed, bee)
new_compare14(xuu33000, xuu34000, False) → GT
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_Ratio, ff), eh) → new_ltEs11(xuu33000, xuu34000, ff)
new_esEs8(LT, LT) → True
new_compare25(xuu33000, xuu34000, True, ec, ed, ee) → EQ
new_lt18(xuu33000, xuu34000) → new_esEs8(new_compare8(xuu33000, xuu34000), LT)
new_lt19(xuu33000, xuu34000, app(app(ty_@2, ef), eg)) → new_lt16(xuu33000, xuu34000, ef, eg)
new_mkBalBranch6MkBalBranch010(xuu640, xuu641, xuu642, EmptyFM, xuu644, xuu600, xuu61, xuu28, False, h, ba) → error([])
new_esEs29(xuu311000, xuu600, app(app(ty_@2, beh), bfa)) → new_esEs7(xuu311000, xuu600, beh, bfa)
new_mkBalBranch6MkBalBranch110(xuu64, xuu61, xuu360, xuu361, xuu362, xuu363, xuu364, True, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), xuu360, xuu361, xuu363, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Nothing, xuu61, xuu364, xuu64, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_esEs18(xuu33000, xuu34000, app(ty_Ratio, bh)) → new_esEs9(xuu33000, xuu34000, bh)
new_primCmpInt0(EmptyFM, xuu64, xuu61, h, ba) → new_primCmpInt(new_primPlusInt(Pos(Zero), new_mkBalBranch6Size_r(xuu64, xuu61, EmptyFM, h, ba)), Pos(Succ(Succ(Zero))))
new_ltEs20(xuu33002, xuu34002, app(ty_Maybe, ddd)) → new_ltEs9(xuu33002, xuu34002, ddd)
new_esEs28(xuu33000, xuu34000, ty_Integer) → new_esEs16(xuu33000, xuu34000)
new_esEs20(xuu3110000, xuu6000, app(app(app(ty_@3, bgg), bgh), bha)) → new_esEs6(xuu3110000, xuu6000, bgg, bgh, bha)
new_pePe(True, xuu168) → True
new_primEqNat0(Zero, Zero) → True
new_mkBalBranch6MkBalBranch30(xuu64, xuu61, EmptyFM, True, h, ba) → error([])
new_compare26(xuu33000, xuu34000, True) → EQ
new_compare23(Nothing, Just(xuu3400), False, dab) → LT
new_ltEs20(xuu33002, xuu34002, app(app(app(ty_@3, ddg), ddh), dea)) → new_ltEs12(xuu33002, xuu34002, ddg, ddh, dea)
new_lt16(xuu33000, xuu34000, ef, eg) → new_esEs8(new_compare27(xuu33000, xuu34000, ef, eg), LT)
new_compare29(xuu33000, xuu34000, True, hg, hh) → EQ
new_esEs14(@0, @0) → True
new_esEs18(xuu33000, xuu34000, ty_Bool) → new_esEs15(xuu33000, xuu34000)
new_compare111(xuu33000, xuu34000, False, hg, hh) → GT
new_compare14(xuu33000, xuu34000, True) → LT
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Bool, eh) → new_ltEs18(xuu33000, xuu34000)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Integer, bca) → new_esEs16(xuu3110000, xuu6000)
new_esEs22(xuu3110002, xuu6002, app(app(ty_@2, cfb), cfc)) → new_esEs7(xuu3110002, xuu6002, cfb, cfc)
new_esEs19(xuu3110001, xuu6001, app(ty_[], bfc)) → new_esEs12(xuu3110001, xuu6001, bfc)
new_mkBalBranch6MkBalBranch5(xuu64, xuu61, xuu36, True, h, ba) → new_mkBranch(Zero, Nothing, xuu61, xuu36, xuu64, app(ty_Maybe, h), ba)
new_compare26(xuu33000, xuu34000, False) → new_compare14(xuu33000, xuu34000, new_ltEs17(xuu33000, xuu34000))
new_ltEs17(GT, LT) → False
new_compare(:(xuu33000, xuu33001), :(xuu34000, xuu34001), eb) → new_primCompAux1(xuu33000, xuu34000, new_compare(xuu33001, xuu34001, eb), eb)
new_lt5(xuu33000, xuu34000, ty_Char) → new_lt8(xuu33000, xuu34000)
new_sr(xuu3110001, xuu6001) → new_primMulInt(xuu3110001, xuu6001)
new_ltEs19(xuu3300, xuu3400, app(app(app(ty_@3, dac), dad), dae)) → new_ltEs12(xuu3300, xuu3400, dac, dad, dae)
new_primPlusInt(Neg(xuu2820), Neg(xuu970)) → Neg(new_primPlusNat1(xuu2820, xuu970))
new_esEs24(xuu3110000, xuu6000, app(app(ty_@2, chf), chg)) → new_esEs7(xuu3110000, xuu6000, chf, chg)
new_compare32(xuu33000, xuu34000, ty_Int) → new_compare11(xuu33000, xuu34000)
new_esEs8(GT, GT) → True
new_esEs18(xuu33000, xuu34000, app(app(app(ty_@3, ca), cb), cc)) → new_esEs6(xuu33000, xuu34000, ca, cb, cc)
new_ltEs20(xuu33002, xuu34002, app(ty_Ratio, ddf)) → new_ltEs11(xuu33002, xuu34002, ddf)
new_compare32(xuu33000, xuu34000, ty_Bool) → new_compare6(xuu33000, xuu34000)
new_lt19(xuu33000, xuu34000, app(ty_Ratio, bbg)) → new_lt11(xuu33000, xuu34000, bbg)
new_lt20(xuu33001, xuu34001, ty_Double) → new_lt17(xuu33001, xuu34001)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs19(xuu3300, xuu3400, app(ty_Maybe, cac)) → new_ltEs9(xuu3300, xuu3400, cac)
new_esEs28(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, app(app(ty_Either, beb), bec)) → new_esEs4(xuu3110000, xuu6000, beb, bec)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Int, eh) → new_ltEs6(xuu33000, xuu34000)
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_lt20(xuu33001, xuu34001, app(ty_Ratio, dcd)) → new_lt11(xuu33001, xuu34001, dcd)
new_esEs15(True, True) → True
new_esEs20(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_compare18(xuu33000, xuu34000, ec, ed, ee) → new_compare25(xuu33000, xuu34000, new_esEs6(xuu33000, xuu34000, ec, ed, ee), ec, ed, ee)
new_esEs22(xuu3110002, xuu6002, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs6(xuu3110002, xuu6002, cee, cef, ceg)
new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_esEs23(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(ty_Either, bcg), bch), bca) → new_esEs4(xuu3110000, xuu6000, bcg, bch)
new_ltEs17(LT, GT) → True
new_primPlusNat1(Succ(xuu28200), Zero) → Succ(xuu28200)
new_primPlusNat1(Zero, Succ(xuu9700)) → Succ(xuu9700)
new_esEs13(Double(xuu3110000, xuu3110001), Double(xuu6000, xuu6001)) → new_esEs10(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Float) → new_ltEs15(xuu33000, xuu34000)
new_esEs21(xuu3110000, xuu6000, app(ty_Ratio, cbf)) → new_esEs9(xuu3110000, xuu6000, cbf)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(ty_@2, cbd), cbe)) → new_ltEs4(xuu33000, xuu34000, cbd, cbe)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_Ratio, cah)) → new_ltEs11(xuu33000, xuu34000, cah)
new_addToFM_C0(Branch(Just(xuu600), xuu61, xuu62, xuu63, xuu64), Nothing, xuu31101, h, ba) → new_addToFM_C22(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Just(xuu600), False, h), LT), h, ba)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Double, bca) → new_esEs13(xuu3110000, xuu6000)
new_ltEs18(True, True) → True
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Int, bca) → new_esEs10(xuu3110000, xuu6000)
new_compare32(xuu33000, xuu34000, app(app(ty_@2, cdh), cea)) → new_compare27(xuu33000, xuu34000, cdh, cea)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs5(xuu33001, xuu34001, ty_Double) → new_ltEs16(xuu33001, xuu34001)
new_ltEs7(Right(xuu33000), Left(xuu34000), gd, eh) → False
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs24(xuu3110000, xuu6000, app(app(app(ty_@3, cha), chb), chc)) → new_esEs6(xuu3110000, xuu6000, cha, chb, chc)
new_lt12(xuu33000, xuu34000, ec, ed, ee) → new_esEs8(new_compare18(xuu33000, xuu34000, ec, ed, ee), LT)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(ty_Either, cad), cae)) → new_ltEs7(xuu33000, xuu34000, cad, cae)
new_compare6(xuu33000, xuu34000) → new_compare24(xuu33000, xuu34000, new_esEs15(xuu33000, xuu34000))
new_esEs21(xuu3110000, xuu6000, app(app(ty_@2, ccf), ccg)) → new_esEs7(xuu3110000, xuu6000, ccf, ccg)
new_esEs28(xuu33000, xuu34000, ty_Double) → new_esEs13(xuu33000, xuu34000)
new_mkBalBranch6MkBalBranch5(xuu64, xuu61, xuu36, False, h, ba) → new_mkBalBranch6MkBalBranch40(xuu64, xuu61, xuu36, new_gt(new_mkBalBranch6Size_r(xuu64, xuu61, xuu36, h, ba), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_l0(xuu64, xuu61, xuu36, h, ba))), h, ba)
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu60000))) → False
new_ltEs18(False, False) → True
new_primCompAux0(xuu183, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs20(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_addListToFM0(xuu61, xuu31101, ba) → xuu31101
new_ltEs5(xuu33001, xuu34001, ty_Integer) → new_ltEs13(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_compare32(xuu33000, xuu34000, app(app(app(ty_@3, cde), cdf), cdg)) → new_compare18(xuu33000, xuu34000, cde, cdf, cdg)
new_compare32(xuu33000, xuu34000, app(app(ty_Either, cch), cda)) → new_compare17(xuu33000, xuu34000, cch, cda)
new_mkBalBranch6Size_r0(xuu64, xuu600, xuu61, xuu28, h, ba) → new_sizeFM(xuu64, h, ba)
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, app(ty_Ratio, ha)) → new_ltEs11(xuu33000, xuu34000, ha)
new_addToFM_C13(xuu61, xuu62, xuu63, xuu64, xuu31101, False, h, ba) → Branch(Nothing, new_addListToFM0(xuu61, xuu31101, ba), xuu62, xuu63, xuu64)
new_esEs20(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs21(xuu3110000, xuu6000, app(app(ty_Either, ccd), cce)) → new_esEs4(xuu3110000, xuu6000, ccd, cce)
new_compare23(Nothing, Nothing, False, dab) → LT
new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_compare([], [], eb) → EQ
new_ltEs17(EQ, EQ) → True
new_ltEs19(xuu3300, xuu3400, ty_Ordering) → new_ltEs17(xuu3300, xuu3400)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(ty_@2, gb), gc), eh) → new_ltEs4(xuu33000, xuu34000, gb, gc)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Char, bca) → new_esEs17(xuu3110000, xuu6000)
new_compare25(xuu33000, xuu34000, False, ec, ed, ee) → new_compare13(xuu33000, xuu34000, new_ltEs12(xuu33000, xuu34000, ec, ed, ee), ec, ed, ee)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_mkBalBranch6MkBalBranch30(xuu64, xuu61, xuu36, False, h, ba) → new_mkBranch(Succ(Zero), Nothing, xuu61, xuu36, xuu64, app(ty_Maybe, h), ba)
new_ltEs20(xuu33002, xuu34002, ty_Bool) → new_ltEs18(xuu33002, xuu34002)
new_lt20(xuu33001, xuu34001, ty_Char) → new_lt8(xuu33001, xuu34001)
new_esEs28(xuu33000, xuu34000, app(app(ty_@2, ef), eg)) → new_esEs7(xuu33000, xuu34000, ef, eg)
new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Int) → new_lt6(xuu33000, xuu34000)
new_primMinusNat0(Succ(xuu28200), Zero) → Pos(Succ(xuu28200))
new_primCmpNat0(Succ(xuu3300), Succ(xuu3400)) → new_primCmpNat0(xuu3300, xuu3400)
new_lt20(xuu33001, xuu34001, ty_Integer) → new_lt13(xuu33001, xuu34001)
new_esEs18(xuu33000, xuu34000, ty_@0) → new_esEs14(xuu33000, xuu34000)
new_lt8(xuu33000, xuu34000) → new_esEs8(new_compare30(xuu33000, xuu34000), LT)
new_sizeFM(EmptyFM, h, ba) → Pos(Zero)
new_esEs26(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Double) → new_ltEs16(xuu33000, xuu34000)
new_esEs18(xuu33000, xuu34000, ty_Int) → new_esEs10(xuu33000, xuu34000)
new_esEs29(xuu311000, xuu600, app(ty_Maybe, bac)) → new_esEs5(xuu311000, xuu600, bac)
new_esEs28(xuu33000, xuu34000, ty_Char) → new_esEs17(xuu33000, xuu34000)
new_esEs20(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_esEs23(xuu3110001, xuu6001, app(ty_[], cfe)) → new_esEs12(xuu3110001, xuu6001, cfe)
new_esEs23(xuu3110001, xuu6001, ty_Char) → new_esEs17(xuu3110001, xuu6001)
new_addToFM_C0(Branch(Just(xuu600), xuu61, xuu62, xuu63, xuu64), Just(xuu311000), xuu31101, h, ba) → new_addToFM_C24(xuu600, xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, new_esEs8(new_compare23(Just(xuu311000), Just(xuu600), new_esEs29(xuu311000, xuu600, h), h), LT), h, ba)
new_primEqNat0(Succ(xuu31100000), Succ(xuu60000)) → new_primEqNat0(xuu31100000, xuu60000)
new_esEs27(xuu33001, xuu34001, ty_Ordering) → new_esEs8(xuu33001, xuu34001)
new_esEs19(xuu3110001, xuu6001, app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs6(xuu3110001, xuu6001, bfe, bff, bfg)
new_mkBalBranch6MkBalBranch30(xuu64, xuu61, Branch(xuu360, xuu361, xuu362, xuu363, xuu364), True, h, ba) → new_mkBalBranch6MkBalBranch110(xuu64, xuu61, xuu360, xuu361, xuu362, xuu363, xuu364, new_lt6(new_sizeFM(xuu364, h, ba), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM(xuu363, h, ba))), h, ba)
new_primCompAux1(xuu33000, xuu34000, xuu169, eb) → new_primCompAux0(xuu169, new_compare32(xuu33000, xuu34000, eb))
new_compare15(Double(xuu33000, xuu33001), Double(xuu34000, xuu34001)) → new_compare11(new_sr(xuu33000, xuu34000), new_sr(xuu33001, xuu34001))
new_mkBalBranch6MkBalBranch110(xuu64, xuu61, xuu360, xuu361, xuu362, xuu363, EmptyFM, False, h, ba) → error([])
new_esEs29(xuu311000, xuu600, ty_Int) → new_esEs10(xuu311000, xuu600)
new_primCmpInt(Neg(Succ(xuu3300)), Neg(xuu340)) → new_primCmpNat0(xuu340, Succ(xuu3300))
new_ltEs19(xuu3300, xuu3400, app(app(ty_Either, gd), eh)) → new_ltEs7(xuu3300, xuu3400, gd, eh)
new_esEs18(xuu33000, xuu34000, ty_Char) → new_esEs17(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs23(xuu3110001, xuu6001, ty_Bool) → new_esEs15(xuu3110001, xuu6001)
new_addToFM_C13(xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_mkBalBranch(xuu61, xuu63, new_addToFM_C0(xuu64, Nothing, xuu31101, h, ba), h, ba)
new_addListToFM_CAdd(xuu6, @2(xuu31100, xuu31101), h, ba) → new_addToFM_C0(xuu6, xuu31100, xuu31101, h, ba)
new_lt19(xuu33000, xuu34000, app(app(ty_Either, hg), hh)) → new_lt7(xuu33000, xuu34000, hg, hh)
new_mkBalBranch6MkBalBranch110(xuu64, xuu61, xuu360, xuu361, xuu362, xuu363, Branch(xuu3640, xuu3641, xuu3642, xuu3643, xuu3644), False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), xuu3640, xuu3641, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), xuu360, xuu361, xuu363, xuu3643, app(ty_Maybe, h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), Nothing, xuu61, xuu3644, xuu64, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_esEs28(xuu33000, xuu34000, ty_Ordering) → new_esEs8(xuu33000, xuu34000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu60000))) → False
new_esEs21(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_lt4(xuu33000, xuu34000) → new_esEs8(new_compare6(xuu33000, xuu34000), LT)
new_mkBalBranch(xuu61, xuu36, xuu64, h, ba) → new_mkBalBranch6MkBalBranch5(xuu64, xuu61, xuu36, new_esEs8(new_primCmpInt0(xuu36, xuu64, xuu61, h, ba), LT), h, ba)
new_mkBalBranch6MkBalBranch3(xuu64, xuu600, xuu61, xuu28, False, h, ba) → new_mkBranch(Succ(Zero), Just(xuu600), xuu61, xuu28, xuu64, app(ty_Maybe, h), ba)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(app(app(ty_@3, cba), cbb), cbc)) → new_ltEs12(xuu33000, xuu34000, cba, cbb, cbc)
new_ltEs20(xuu33002, xuu34002, ty_Integer) → new_ltEs13(xuu33002, xuu34002)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Float, eh) → new_ltEs15(xuu33000, xuu34000)
new_compare17(xuu33000, xuu34000, hg, hh) → new_compare29(xuu33000, xuu34000, new_esEs4(xuu33000, xuu34000, hg, hh), hg, hh)
new_mkBalBranch6MkBalBranch11(xuu64, xuu600, xuu61, xuu280, xuu281, xuu282, xuu283, Branch(xuu2840, xuu2841, xuu2842, xuu2843, xuu2844), False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), xuu2840, xuu2841, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), xuu280, xuu281, xuu283, xuu2843, app(ty_Maybe, h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), Just(xuu600), xuu61, xuu2844, xuu64, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(xuu3300), Zero) → GT
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_Maybe, caf)) → new_ltEs9(xuu33000, xuu34000, caf)
new_mkBalBranch6MkBalBranch50(xuu64, xuu600, xuu61, xuu28, False, h, ba) → new_mkBalBranch6MkBalBranch4(xuu64, xuu600, xuu61, xuu28, new_gt(new_mkBalBranch6Size_r0(xuu64, xuu600, xuu61, xuu28, h, ba), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_l(xuu64, xuu600, xuu61, xuu28, h, ba))), h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu3400))) → LT
new_ltEs20(xuu33002, xuu34002, ty_@0) → new_ltEs14(xuu33002, xuu34002)
new_esEs7(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), beh, bfa) → new_asAs(new_esEs20(xuu3110000, xuu6000, beh), new_esEs19(xuu3110001, xuu6001, bfa))
new_esEs21(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_sr0(Integer(xuu340000), Integer(xuu330010)) → Integer(new_primMulInt(xuu340000, xuu330010))
new_primPlusNat1(Succ(xuu28200), Succ(xuu9700)) → Succ(Succ(new_primPlusNat1(xuu28200, xuu9700)))
new_compare28(xuu33000, xuu34000, True, ef, eg) → EQ
new_primEqInt(Pos(Succ(xuu31100000)), Neg(xuu6000)) → False
new_primEqInt(Neg(Succ(xuu31100000)), Pos(xuu6000)) → False
new_ltEs19(xuu3300, xuu3400, ty_Double) → new_ltEs16(xuu3300, xuu3400)
new_esEs25(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_addToFM_C15(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, False, h, ba) → Branch(Just(xuu311000), new_addListToFM0(xuu61, xuu31101, ba), xuu62, xuu63, xuu64)
new_esEs29(xuu311000, xuu600, app(ty_[], bhg)) → new_esEs12(xuu311000, xuu600, bhg)
new_compare9(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Int) → new_compare11(new_sr(xuu33000, xuu34001), new_sr(xuu34000, xuu33001))
new_esEs27(xuu33001, xuu34001, app(ty_Maybe, dcb)) → new_esEs5(xuu33001, xuu34001, dcb)
new_compare32(xuu33000, xuu34000, app(ty_[], cdc)) → new_compare(xuu33000, xuu34000, cdc)
new_esEs18(xuu33000, xuu34000, app(ty_[], bg)) → new_esEs12(xuu33000, xuu34000, bg)
new_mkBalBranch6MkBalBranch01(xuu640, xuu641, xuu642, EmptyFM, xuu644, xuu61, xuu36, False, h, ba) → error([])
new_compare23(Just(xuu3300), Just(xuu3400), False, dab) → new_compare110(xuu3300, xuu3400, new_ltEs19(xuu3300, xuu3400, dab), dab)
new_lt11(xuu33000, xuu34000, bbg) → new_esEs8(new_compare9(xuu33000, xuu34000, bbg), LT)
new_primPlusInt(Neg(xuu2820), Pos(xuu970)) → new_primMinusNat0(xuu970, xuu2820)
new_primPlusInt(Pos(xuu2820), Neg(xuu970)) → new_primMinusNat0(xuu2820, xuu970)
new_mkBalBranch6MkBalBranch3(xuu64, xuu600, xuu61, EmptyFM, True, h, ba) → error([])
new_lt19(xuu33000, xuu34000, ty_@0) → new_lt14(xuu33000, xuu34000)
new_mkBalBranch6MkBalBranch010(xuu640, xuu641, xuu642, Branch(xuu6430, xuu6431, xuu6432, xuu6433, xuu6434), xuu644, xuu600, xuu61, xuu28, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), xuu6430, xuu6431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), Just(xuu600), xuu61, xuu28, xuu6433, app(ty_Maybe, h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), xuu640, xuu641, xuu6434, xuu644, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_gt(xuu91, xuu90) → new_esEs8(new_compare11(xuu91, xuu90), GT)
new_ltEs20(xuu33002, xuu34002, ty_Float) → new_ltEs15(xuu33002, xuu34002)
new_esEs29(xuu311000, xuu600, ty_@0) → new_esEs14(xuu311000, xuu600)
new_lt7(xuu33000, xuu34000, hg, hh) → new_esEs8(new_compare17(xuu33000, xuu34000, hg, hh), LT)
new_lt5(xuu33000, xuu34000, app(ty_Maybe, bf)) → new_lt9(xuu33000, xuu34000, bf)
new_mkBalBranch6MkBalBranch40(xuu64, xuu61, xuu36, False, h, ba) → new_mkBalBranch6MkBalBranch30(xuu64, xuu61, xuu36, new_gt(new_mkBalBranch6Size_l0(xuu64, xuu61, xuu36, h, ba), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_r(xuu64, xuu61, xuu36, h, ba))), h, ba)
new_esEs26(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_primEqInt(Pos(Zero), Neg(Succ(xuu60000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu60000))) → False
new_esEs20(xuu3110000, xuu6000, app(ty_[], bge)) → new_esEs12(xuu3110000, xuu6000, bge)
new_ltEs9(Just(xuu33000), Nothing, cac) → False
new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, app(ty_Ratio, bdd)) → new_esEs9(xuu3110000, xuu6000, bdd)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu3400))) → new_primCmpNat0(Zero, Succ(xuu3400))
new_compare24(xuu33000, xuu34000, True) → EQ
new_esEs27(xuu33001, xuu34001, app(app(ty_@2, dch), dda)) → new_esEs7(xuu33001, xuu34001, dch, dda)
new_lt13(xuu33000, xuu34000) → new_esEs8(new_compare12(xuu33000, xuu34000), LT)
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs12(xuu33000, xuu34000, hb, hc, hd)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, ty_Char) → new_compare30(xuu33000, xuu34000)
new_emptyFM(h, ba) → EmptyFM
new_mkBalBranch6Size_l0(xuu64, xuu61, xuu36, h, ba) → new_sizeFM(xuu36, h, ba)
new_lt15(xuu33000, xuu34000) → new_esEs8(new_compare31(xuu33000, xuu34000), LT)
new_primCompAux0(xuu183, LT) → LT
new_ltEs19(xuu3300, xuu3400, ty_Char) → new_ltEs8(xuu3300, xuu3400)
new_esEs23(xuu3110001, xuu6001, ty_Float) → new_esEs11(xuu3110001, xuu6001)
new_esEs20(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_not(False) → True
new_mkBalBranch6MkBalBranch010(xuu640, xuu641, xuu642, xuu643, xuu644, xuu600, xuu61, xuu28, True, h, ba) → new_mkBranch(Succ(Succ(Zero)), xuu640, xuu641, new_mkBranch(Succ(Succ(Succ(Zero))), Just(xuu600), xuu61, xuu28, xuu643, app(ty_Maybe, h), ba), xuu644, app(ty_Maybe, h), ba)
new_esEs30(xuu22, xuu17, ty_@0) → new_esEs14(xuu22, xuu17)
new_primCmpInt(Pos(Succ(xuu3300)), Pos(xuu340)) → new_primCmpNat0(Succ(xuu3300), xuu340)
new_compare110(xuu135, xuu136, True, bhf) → LT
new_esEs19(xuu3110001, xuu6001, app(app(ty_@2, bgb), bgc)) → new_esEs7(xuu3110001, xuu6001, bgb, bgc)
new_esEs22(xuu3110002, xuu6002, ty_Float) → new_esEs11(xuu3110002, xuu6002)
new_ltEs19(xuu3300, xuu3400, app(ty_[], eb)) → new_ltEs10(xuu3300, xuu3400, eb)
new_esEs30(xuu22, xuu17, app(app(ty_@2, dbf), dbg)) → new_esEs7(xuu22, xuu17, dbf, dbg)
new_ltEs5(xuu33001, xuu34001, app(ty_Ratio, dc)) → new_ltEs11(xuu33001, xuu34001, dc)
new_ltEs9(Nothing, Nothing, cac) → True
new_esEs30(xuu22, xuu17, app(app(ty_Either, dbd), dbe)) → new_esEs4(xuu22, xuu17, dbd, dbe)
new_esEs19(xuu3110001, xuu6001, ty_Char) → new_esEs17(xuu3110001, xuu6001)
new_lt20(xuu33001, xuu34001, app(ty_[], dcc)) → new_lt10(xuu33001, xuu34001, dcc)
new_ltEs19(xuu3300, xuu3400, ty_Int) → new_ltEs6(xuu3300, xuu3400)
new_esEs27(xuu33001, xuu34001, ty_@0) → new_esEs14(xuu33001, xuu34001)
new_ltEs16(xuu3300, xuu3400) → new_fsEs(new_compare15(xuu3300, xuu3400))
new_lt19(xuu33000, xuu34000, app(app(app(ty_@3, ec), ed), ee)) → new_lt12(xuu33000, xuu34000, ec, ed, ee)
new_lt20(xuu33001, xuu34001, ty_Int) → new_lt6(xuu33001, xuu34001)
new_lt20(xuu33001, xuu34001, ty_Ordering) → new_lt18(xuu33001, xuu34001)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_compare12(Integer(xuu33000), Integer(xuu34000)) → new_primCmpInt(xuu33000, xuu34000)
new_esEs24(xuu3110000, xuu6000, app(ty_Maybe, cgh)) → new_esEs5(xuu3110000, xuu6000, cgh)
new_lt5(xuu33000, xuu34000, app(app(ty_@2, cd), ce)) → new_lt16(xuu33000, xuu34000, cd, ce)
new_esEs18(xuu33000, xuu34000, app(app(ty_Either, bd), be)) → new_esEs4(xuu33000, xuu34000, bd, be)
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, app(ty_[], gh)) → new_ltEs10(xuu33000, xuu34000, gh)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_mkBalBranch6MkBalBranch4(Branch(xuu640, xuu641, xuu642, xuu643, xuu644), xuu600, xuu61, xuu28, True, h, ba) → new_mkBalBranch6MkBalBranch010(xuu640, xuu641, xuu642, xuu643, xuu644, xuu600, xuu61, xuu28, new_lt6(new_sizeFM(xuu643, h, ba), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM(xuu644, h, ba))), h, ba)
new_primCmpInt(Pos(Succ(xuu3300)), Neg(xuu340)) → GT
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Double, eh) → new_ltEs16(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, ty_Bool) → new_ltEs18(xuu33001, xuu34001)
new_esEs21(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs30(xuu22, xuu17, app(ty_[], dag)) → new_esEs12(xuu22, xuu17, dag)
new_mkBalBranch6MkBalBranch3(xuu64, xuu600, xuu61, Branch(xuu280, xuu281, xuu282, xuu283, xuu284), True, h, ba) → new_mkBalBranch6MkBalBranch11(xuu64, xuu600, xuu61, xuu280, xuu281, xuu282, xuu283, xuu284, new_lt6(new_sizeFM(xuu284, h, ba), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM(xuu283, h, ba))), h, ba)
new_compare32(xuu33000, xuu34000, ty_Ordering) → new_compare8(xuu33000, xuu34000)
new_lt5(xuu33000, xuu34000, app(ty_Ratio, bh)) → new_lt11(xuu33000, xuu34000, bh)
new_primMulInt(Pos(xuu31100010), Pos(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Bool, bca) → new_esEs15(xuu3110000, xuu6000)
new_esEs24(xuu3110000, xuu6000, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs27(xuu33001, xuu34001, ty_Char) → new_esEs17(xuu33001, xuu34001)
new_esEs22(xuu3110002, xuu6002, ty_Int) → new_esEs10(xuu3110002, xuu6002)
new_esEs22(xuu3110002, xuu6002, ty_Double) → new_esEs13(xuu3110002, xuu6002)
new_esEs23(xuu3110001, xuu6001, app(app(ty_Either, cgb), cgc)) → new_esEs4(xuu3110001, xuu6001, cgb, cgc)
new_compare32(xuu33000, xuu34000, ty_@0) → new_compare16(xuu33000, xuu34000)
new_primMulInt(Neg(xuu31100010), Neg(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_esEs24(xuu3110000, xuu6000, ty_Bool) → new_esEs15(xuu3110000, xuu6000)
new_esEs28(xuu33000, xuu34000, app(ty_Ratio, bbg)) → new_esEs9(xuu33000, xuu34000, bbg)
new_lt20(xuu33001, xuu34001, ty_@0) → new_lt14(xuu33001, xuu34001)
new_primEqNat0(Zero, Succ(xuu60000)) → False
new_primEqNat0(Succ(xuu31100000), Zero) → False
new_esEs21(xuu3110000, xuu6000, app(ty_[], cbg)) → new_esEs12(xuu3110000, xuu6000, cbg)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(app(ty_Either, fa), fb), eh) → new_ltEs7(xuu33000, xuu34000, fa, fb)
new_addToFM_C16(xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, True, chh, daa) → new_mkBalBranch0(xuu17, xuu18, xuu20, new_addToFM_C0(xuu21, Just(xuu22), xuu23, chh, daa), chh, daa)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(xuu3110000, xuu6000, app(app(ty_Either, chd), che)) → new_esEs4(xuu3110000, xuu6000, chd, che)
new_esEs28(xuu33000, xuu34000, app(app(app(ty_@3, ec), ed), ee)) → new_esEs6(xuu33000, xuu34000, ec, ed, ee)
new_primPlusNat0(xuu107, xuu600100) → new_primPlusNat1(xuu107, Succ(xuu600100))
new_lt19(xuu33000, xuu34000, ty_Double) → new_lt17(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, ty_Integer) → new_compare12(xuu33000, xuu34000)
new_esEs27(xuu33001, xuu34001, app(app(ty_Either, dbh), dca)) → new_esEs4(xuu33001, xuu34001, dbh, dca)
new_esEs27(xuu33001, xuu34001, app(app(app(ty_@3, dce), dcf), dcg)) → new_esEs6(xuu33001, xuu34001, dce, dcf, dcg)
new_addToFM_C0(Branch(Nothing, xuu61, xuu62, xuu63, xuu64), Nothing, xuu31101, h, ba) → new_addToFM_C13(xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Nothing, True, h), GT), h, ba)
new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_lt5(xuu33000, xuu34000, ty_Integer) → new_lt13(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, app(ty_Maybe, bfd)) → new_esEs5(xuu3110001, xuu6001, bfd)
new_esEs27(xuu33001, xuu34001, ty_Integer) → new_esEs16(xuu33001, xuu34001)
new_sizeFM(Branch(xuu640, xuu641, xuu642, xuu643, xuu644), h, ba) → xuu642
new_sizeFM0(EmptyFM, baa, bab) → Pos(Zero)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_Float, bca) → new_esEs11(xuu3110000, xuu6000)
new_ltEs5(xuu33001, xuu34001, ty_Int) → new_ltEs6(xuu33001, xuu34001)
new_ltEs14(xuu3300, xuu3400) → new_fsEs(new_compare16(xuu3300, xuu3400))
new_ltEs5(xuu33001, xuu34001, app(ty_Maybe, da)) → new_ltEs9(xuu33001, xuu34001, da)
new_esEs25(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_esEs21(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_ltEs5(xuu33001, xuu34001, ty_Ordering) → new_ltEs17(xuu33001, xuu34001)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu3400))) → new_primCmpNat0(Succ(xuu3400), Zero)
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Ordering) → new_ltEs17(xuu33000, xuu34000)
new_primCmpInt(Pos(Zero), Neg(Succ(xuu3400))) → GT
new_compare110(xuu135, xuu136, False, bhf) → GT
new_ltEs20(xuu33002, xuu34002, ty_Char) → new_ltEs8(xuu33002, xuu34002)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(app(ty_@3, bag), bah), bba)) → new_esEs6(xuu3110000, xuu6000, bag, bah, bba)
new_compare19(xuu33000, xuu34000, True, ef, eg) → LT
new_lt20(xuu33001, xuu34001, app(ty_Maybe, dcb)) → new_lt9(xuu33001, xuu34001, dcb)
new_lt19(xuu33000, xuu34000, app(ty_[], beg)) → new_lt10(xuu33000, xuu34000, beg)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_compare23(xuu330, xuu340, True, dab) → EQ
new_mkBalBranch6MkBalBranch40(EmptyFM, xuu61, xuu36, True, h, ba) → error([])
new_mkBalBranch6MkBalBranch4(EmptyFM, xuu600, xuu61, xuu28, True, h, ba) → error([])
new_addToFM_C22(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, False, h, ba) → new_addToFM_C14(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, new_esEs8(new_compare23(Nothing, Just(xuu600), False, h), GT), h, ba)
new_esEs19(xuu3110001, xuu6001, ty_Float) → new_esEs11(xuu3110001, xuu6001)
new_esEs16(Integer(xuu3110000), Integer(xuu6000)) → new_primEqInt(xuu3110000, xuu6000)
new_addToFM_C24(xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, False, chh, daa) → new_addToFM_C16(xuu17, xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, new_esEs8(new_compare23(Just(xuu22), Just(xuu17), new_esEs30(xuu22, xuu17, chh), chh), GT), chh, daa)
new_ltEs20(xuu33002, xuu34002, ty_Ordering) → new_ltEs17(xuu33002, xuu34002)
new_esEs29(xuu311000, xuu600, app(ty_Ratio, bbf)) → new_esEs9(xuu311000, xuu600, bbf)
new_lt5(xuu33000, xuu34000, ty_Bool) → new_lt4(xuu33000, xuu34000)
new_esEs23(xuu3110001, xuu6001, ty_@0) → new_esEs14(xuu3110001, xuu6001)
new_primPlusInt(Pos(xuu2820), Pos(xuu970)) → Pos(new_primPlusNat1(xuu2820, xuu970))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs21(xuu3110000, xuu6000, ty_@0) → new_esEs14(xuu3110000, xuu6000)
new_ltEs7(Left(xuu33000), Left(xuu34000), ty_Ordering, eh) → new_ltEs17(xuu33000, xuu34000)
new_esEs20(xuu3110000, xuu6000, app(ty_Maybe, bgf)) → new_esEs5(xuu3110000, xuu6000, bgf)
new_esEs24(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_esEs4(Right(xuu3110000), Right(xuu6000), bdc, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, app(app(ty_Either, ge), gf)) → new_ltEs7(xuu33000, xuu34000, ge, gf)
new_esEs29(xuu311000, xuu600, ty_Bool) → new_esEs15(xuu311000, xuu600)
new_asAs(False, xuu142) → False
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Int) → new_ltEs6(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, ty_Double) → new_ltEs16(xuu33002, xuu34002)
new_lt17(xuu33000, xuu34000) → new_esEs8(new_compare15(xuu33000, xuu34000), LT)
new_primMulInt(Neg(xuu31100010), Pos(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_primMulInt(Pos(xuu31100010), Neg(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_ltEs11(xuu3300, xuu3400, bef) → new_fsEs(new_compare9(xuu3300, xuu3400, bef))
new_primMulNat0(Zero, Succ(xuu600100)) → Zero
new_primMulNat0(Succ(xuu311000100), Zero) → Zero
new_esEs27(xuu33001, xuu34001, ty_Double) → new_esEs13(xuu33001, xuu34001)
new_esEs24(xuu3110000, xuu6000, ty_Double) → new_esEs13(xuu3110000, xuu6000)
new_lt5(xuu33000, xuu34000, ty_Int) → new_lt6(xuu33000, xuu34000)
new_esEs23(xuu3110001, xuu6001, app(app(app(ty_@3, cfg), cfh), cga)) → new_esEs6(xuu3110001, xuu6001, cfg, cfh, cga)
new_lt19(xuu33000, xuu34000, ty_Ordering) → new_lt18(xuu33000, xuu34000)
new_esEs21(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_lt19(xuu33000, xuu34000, ty_Char) → new_lt8(xuu33000, xuu34000)
new_compare32(xuu33000, xuu34000, app(ty_Maybe, cdb)) → new_compare7(xuu33000, xuu34000, cdb)
new_esEs29(xuu311000, xuu600, ty_Float) → new_esEs11(xuu311000, xuu600)
new_addToFM_C15(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, True, h, ba) → new_mkBalBranch(xuu61, xuu63, new_addToFM_C0(xuu64, Just(xuu311000), xuu31101, h, ba), h, ba)
new_esEs23(xuu3110001, xuu6001, app(app(ty_@2, cgd), cge)) → new_esEs7(xuu3110001, xuu6001, cgd, cge)
new_esEs29(xuu311000, xuu600, ty_Char) → new_esEs17(xuu311000, xuu600)
new_esEs29(xuu311000, xuu600, ty_Double) → new_esEs13(xuu311000, xuu600)
new_lt5(xuu33000, xuu34000, app(app(app(ty_@3, ca), cb), cc)) → new_lt12(xuu33000, xuu34000, ca, cb, cc)
new_primCmpInt1(EmptyFM, xuu64, xuu600, xuu61, h, ba) → new_primCmpInt(new_primPlusInt(Pos(Zero), new_mkBalBranch6Size_r0(xuu64, xuu600, xuu61, EmptyFM, h, ba)), Pos(Succ(Succ(Zero))))
new_esEs18(xuu33000, xuu34000, app(ty_Maybe, bf)) → new_esEs5(xuu33000, xuu34000, bf)
new_compare27(xuu33000, xuu34000, ef, eg) → new_compare28(xuu33000, xuu34000, new_esEs7(xuu33000, xuu34000, ef, eg), ef, eg)
new_esEs24(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_esEs18(xuu33000, xuu34000, ty_Ordering) → new_esEs8(xuu33000, xuu34000)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_Maybe, bcc), bca) → new_esEs5(xuu3110000, xuu6000, bcc)
new_lt9(xuu33000, xuu34000, ea) → new_esEs8(new_compare7(xuu33000, xuu34000, ea), LT)
new_lt20(xuu33001, xuu34001, app(app(ty_@2, dch), dda)) → new_lt16(xuu33001, xuu34001, dch, dda)
new_esEs28(xuu33000, xuu34000, app(app(ty_Either, hg), hh)) → new_esEs4(xuu33000, xuu34000, hg, hh)
new_compare8(xuu33000, xuu34000) → new_compare26(xuu33000, xuu34000, new_esEs8(xuu33000, xuu34000))
new_esEs23(xuu3110001, xuu6001, app(ty_Maybe, cff)) → new_esEs5(xuu3110001, xuu6001, cff)
new_lt5(xuu33000, xuu34000, ty_Double) → new_lt17(xuu33000, xuu34000)
new_addToFM_C22(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_mkBalBranch0(xuu600, xuu61, new_addToFM_C0(xuu63, Nothing, xuu31101, h, ba), xuu64, h, ba)
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, ty_Char) → new_ltEs8(xuu33000, xuu34000)
new_lt5(xuu33000, xuu34000, app(ty_[], bg)) → new_lt10(xuu33000, xuu34000, bg)
new_esEs6(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), bhh, caa, cab) → new_asAs(new_esEs24(xuu3110000, xuu6000, bhh), new_asAs(new_esEs23(xuu3110001, xuu6001, caa), new_esEs22(xuu3110002, xuu6002, cab)))
new_ltEs17(GT, GT) → True
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, ty_Ordering) → new_ltEs17(xuu33000, xuu34000)
new_ltEs19(xuu3300, xuu3400, ty_@0) → new_ltEs14(xuu3300, xuu3400)
new_ltEs9(Just(xuu33000), Just(xuu34000), ty_Char) → new_ltEs8(xuu33000, xuu34000)
new_ltEs17(GT, EQ) → False
new_esEs5(Nothing, Just(xuu6000), bac) → False
new_esEs5(Just(xuu3110000), Nothing, bac) → False
new_esEs22(xuu3110002, xuu6002, app(ty_[], cec)) → new_esEs12(xuu3110002, xuu6002, cec)
new_ltEs15(xuu3300, xuu3400) → new_fsEs(new_compare31(xuu3300, xuu3400))
new_esEs19(xuu3110001, xuu6001, ty_Integer) → new_esEs16(xuu3110001, xuu6001)
new_esEs22(xuu3110002, xuu6002, ty_Bool) → new_esEs15(xuu3110002, xuu6002)
new_primMinusNat0(Zero, Succ(xuu9700)) → Neg(Succ(xuu9700))
new_compare11(xuu33, xuu34) → new_primCmpInt(xuu33, xuu34)
new_mkBalBranch6MkBalBranch50(xuu64, xuu600, xuu61, xuu28, True, h, ba) → new_mkBranch(Zero, Just(xuu600), xuu61, xuu28, xuu64, app(ty_Maybe, h), ba)
new_esEs28(xuu33000, xuu34000, ty_Bool) → new_esEs15(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, app(ty_[], db)) → new_ltEs10(xuu33001, xuu34001, db)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(ty_@2, bda), bdb), bca) → new_esEs7(xuu3110000, xuu6000, bda, bdb)
new_lt19(xuu33000, xuu34000, ty_Integer) → new_lt13(xuu33000, xuu34000)
new_ltEs20(xuu33002, xuu34002, app(app(ty_Either, ddb), ddc)) → new_ltEs7(xuu33002, xuu34002, ddb, ddc)
new_ltEs18(True, False) → False
new_mkBalBranch6Size_r(xuu64, xuu61, xuu36, h, ba) → new_sizeFM(xuu64, h, ba)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_Maybe, fc), eh) → new_ltEs9(xuu33000, xuu34000, fc)
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, ty_Double) → new_ltEs16(xuu33000, xuu34000)
new_lt10(xuu33000, xuu34000, beg) → new_esEs8(new_compare(xuu33000, xuu34000, beg), LT)
new_esEs20(xuu3110000, xuu6000, app(ty_Ratio, bgd)) → new_esEs9(xuu3110000, xuu6000, bgd)
new_ltEs9(Just(xuu33000), Just(xuu34000), app(ty_[], cag)) → new_ltEs10(xuu33000, xuu34000, cag)
new_ltEs12(@3(xuu33000, xuu33001, xuu33002), @3(xuu34000, xuu34001, xuu34002), dac, dad, dae) → new_pePe(new_lt19(xuu33000, xuu34000, dac), new_asAs(new_esEs28(xuu33000, xuu34000, dac), new_pePe(new_lt20(xuu33001, xuu34001, dad), new_asAs(new_esEs27(xuu33001, xuu34001, dad), new_ltEs20(xuu33002, xuu34002, dae)))))
new_esEs22(xuu3110002, xuu6002, ty_@0) → new_esEs14(xuu3110002, xuu6002)
new_esEs5(Nothing, Nothing, bac) → True
new_esEs23(xuu3110001, xuu6001, app(ty_Ratio, cfd)) → new_esEs9(xuu3110001, xuu6001, cfd)
new_esEs28(xuu33000, xuu34000, app(ty_Maybe, ea)) → new_esEs5(xuu33000, xuu34000, ea)
new_esEs29(xuu311000, xuu600, app(app(app(ty_@3, bhh), caa), cab)) → new_esEs6(xuu311000, xuu600, bhh, caa, cab)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Integer) → new_esEs16(xuu3110000, xuu6000)
new_esEs28(xuu33000, xuu34000, ty_Float) → new_esEs11(xuu33000, xuu34000)
new_esEs22(xuu3110002, xuu6002, ty_Integer) → new_esEs16(xuu3110002, xuu6002)
new_esEs30(xuu22, xuu17, ty_Float) → new_esEs11(xuu22, xuu17)
new_esEs30(xuu22, xuu17, ty_Char) → new_esEs17(xuu22, xuu17)
new_esEs28(xuu33000, xuu34000, ty_Int) → new_esEs10(xuu33000, xuu34000)
new_esEs19(xuu3110001, xuu6001, app(ty_Ratio, bfb)) → new_esEs9(xuu3110001, xuu6001, bfb)
new_ltEs13(xuu3300, xuu3400) → new_fsEs(new_compare12(xuu3300, xuu3400))
new_esEs21(xuu3110000, xuu6000, ty_Float) → new_esEs11(xuu3110000, xuu6000)
new_mkBalBranch6MkBalBranch11(xuu64, xuu600, xuu61, xuu280, xuu281, xuu282, xuu283, EmptyFM, False, h, ba) → error([])
new_mkBalBranch6MkBalBranch11(xuu64, xuu600, xuu61, xuu280, xuu281, xuu282, xuu283, xuu284, True, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), xuu280, xuu281, xuu283, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Just(xuu600), xuu61, xuu284, xuu64, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_esEs30(xuu22, xuu17, ty_Ordering) → new_esEs8(xuu22, xuu17)
new_esEs29(xuu311000, xuu600, ty_Integer) → new_esEs16(xuu311000, xuu600)
new_esEs20(xuu3110000, xuu6000, app(app(ty_@2, bhd), bhe)) → new_esEs7(xuu3110000, xuu6000, bhd, bhe)
new_compare24(xuu33000, xuu34000, False) → new_compare10(xuu33000, xuu34000, new_ltEs18(xuu33000, xuu34000))
new_ltEs18(False, True) → True
new_esEs20(xuu3110000, xuu6000, ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_esEs22(xuu3110002, xuu6002, app(ty_Maybe, ced)) → new_esEs5(xuu3110002, xuu6002, ced)
new_esEs21(xuu3110000, xuu6000, app(ty_Maybe, cbh)) → new_esEs5(xuu3110000, xuu6000, cbh)
new_compare111(xuu33000, xuu34000, True, hg, hh) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs21(xuu3110000, xuu6000, app(app(app(ty_@3, cca), ccb), ccc)) → new_esEs6(xuu3110000, xuu6000, cca, ccb, ccc)
new_addToFM_C0(EmptyFM, xuu31100, xuu31101, h, ba) → Branch(xuu31100, xuu31101, Pos(Succ(Zero)), new_emptyFM(h, ba), new_emptyFM(h, ba))
new_lt14(xuu33000, xuu34000) → new_esEs8(new_compare16(xuu33000, xuu34000), LT)
new_lt20(xuu33001, xuu34001, ty_Float) → new_lt15(xuu33001, xuu34001)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_[], bcb), bca) → new_esEs12(xuu3110000, xuu6000, bcb)
new_ltEs5(xuu33001, xuu34001, app(app(ty_Either, cf), cg)) → new_ltEs7(xuu33001, xuu34001, cf, cg)
new_esEs12(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), bhg) → new_asAs(new_esEs21(xuu3110000, xuu6000, bhg), new_esEs12(xuu3110001, xuu6001, bhg))
new_asAs(True, xuu142) → xuu142
new_esEs28(xuu33000, xuu34000, app(ty_[], beg)) → new_esEs12(xuu33000, xuu34000, beg)
new_esEs27(xuu33001, xuu34001, app(ty_[], dcc)) → new_esEs12(xuu33001, xuu34001, dcc)
new_esEs19(xuu3110001, xuu6001, app(app(ty_Either, bfh), bga)) → new_esEs4(xuu3110001, xuu6001, bfh, bga)
new_primMulNat0(Succ(xuu311000100), Succ(xuu600100)) → new_primPlusNat0(new_primMulNat0(xuu311000100, Succ(xuu600100)), xuu600100)
new_ltEs17(LT, EQ) → True
new_compare30(Char(xuu33000), Char(xuu34000)) → new_primCmpNat0(xuu33000, xuu34000)
new_esEs4(Left(xuu3110000), Right(xuu6000), bdc, bca) → False
new_esEs4(Right(xuu3110000), Left(xuu6000), bdc, bca) → False
new_compare29(xuu33000, xuu34000, False, hg, hh) → new_compare111(xuu33000, xuu34000, new_ltEs7(xuu33000, xuu34000, hg, hh), hg, hh)
new_esEs30(xuu22, xuu17, app(ty_Maybe, dah)) → new_esEs5(xuu22, xuu17, dah)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_@2, bbd), bbe)) → new_esEs7(xuu3110000, xuu6000, bbd, bbe)
new_addToFM_C0(Branch(Nothing, xuu61, xuu62, xuu63, xuu64), Just(xuu311000), xuu31101, h, ba) → new_addToFM_C23(xuu61, xuu62, xuu63, xuu64, xuu311000, xuu31101, new_esEs8(new_compare23(Just(xuu311000), Nothing, False, h), LT), h, ba)
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, ty_Bool) → new_ltEs18(xuu33000, xuu34000)
new_esEs27(xuu33001, xuu34001, ty_Int) → new_esEs10(xuu33001, xuu34001)
new_esEs23(xuu3110001, xuu6001, ty_Int) → new_esEs10(xuu3110001, xuu6001)
new_esEs27(xuu33001, xuu34001, ty_Bool) → new_esEs15(xuu33001, xuu34001)
new_addToFM_C14(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, False, h, ba) → Branch(Nothing, new_addListToFM0(xuu61, xuu31101, ba), xuu62, xuu63, xuu64)
new_esEs21(xuu3110000, xuu6000, ty_Int) → new_esEs10(xuu3110000, xuu6000)
new_addToFM_C14(xuu600, xuu61, xuu62, xuu63, xuu64, xuu31101, True, h, ba) → new_mkBalBranch0(xuu600, xuu61, xuu63, new_addToFM_C0(xuu64, Nothing, xuu31101, h, ba), h, ba)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(app(app(ty_@3, bcd), bce), bcf), bca) → new_esEs6(xuu3110000, xuu6000, bcd, bce, bcf)
new_ltEs6(xuu3300, xuu3400) → new_fsEs(new_compare11(xuu3300, xuu3400))
new_fsEs(xuu152) → new_not(new_esEs8(xuu152, GT))
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, ty_Float) → new_ltEs15(xuu33000, xuu34000)
new_ltEs5(xuu33001, xuu34001, ty_Char) → new_ltEs8(xuu33001, xuu34001)
new_ltEs19(xuu3300, xuu3400, ty_Integer) → new_ltEs13(xuu3300, xuu3400)
new_mkBalBranch0(xuu600, xuu61, xuu28, xuu64, h, ba) → new_mkBalBranch6MkBalBranch50(xuu64, xuu600, xuu61, xuu28, new_esEs8(new_primCmpInt1(xuu28, xuu64, xuu600, xuu61, h, ba), LT), h, ba)
new_esEs19(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs4(Left(xuu3110000), Left(xuu6000), app(ty_Ratio, bbh), bca) → new_esEs9(xuu3110000, xuu6000, bbh)
new_compare7(xuu33000, xuu34000, ea) → new_compare23(xuu33000, xuu34000, new_esEs5(xuu33000, xuu34000, ea), ea)
new_compare10(xuu33000, xuu34000, True) → LT
new_ltEs5(xuu33001, xuu34001, app(app(app(ty_@3, dd), de), df)) → new_ltEs12(xuu33001, xuu34001, dd, de, df)
new_compare19(xuu33000, xuu34000, False, ef, eg) → GT
new_ltEs20(xuu33002, xuu34002, ty_Int) → new_ltEs6(xuu33002, xuu34002)
new_ltEs17(EQ, GT) → True
new_compare13(xuu33000, xuu34000, True, ec, ed, ee) → LT
new_compare10(xuu33000, xuu34000, False) → GT
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Ratio, bad)) → new_esEs9(xuu3110000, xuu6000, bad)
new_esEs10(xuu311000, xuu600) → new_primEqInt(xuu311000, xuu600)
new_esEs4(Left(xuu3110000), Left(xuu6000), ty_@0, bca) → new_esEs14(xuu3110000, xuu6000)
new_esEs30(xuu22, xuu17, app(app(app(ty_@3, dba), dbb), dbc)) → new_esEs6(xuu22, xuu17, dba, dbb, dbc)
new_lt5(xuu33000, xuu34000, ty_@0) → new_lt14(xuu33000, xuu34000)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_Either, bbb), bbc)) → new_esEs4(xuu3110000, xuu6000, bbb, bbc)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(xuu183, EQ) → xuu183
new_esEs24(xuu3110000, xuu6000, app(ty_Ratio, cgf)) → new_esEs9(xuu3110000, xuu6000, cgf)
new_esEs29(xuu311000, xuu600, ty_Ordering) → new_esEs8(xuu311000, xuu600)
new_ltEs7(Left(xuu33000), Left(xuu34000), app(ty_[], fd), eh) → new_ltEs10(xuu33000, xuu34000, fd)
new_mkBalBranch6MkBalBranch01(xuu640, xuu641, xuu642, Branch(xuu6430, xuu6431, xuu6432, xuu6433, xuu6434), xuu644, xuu61, xuu36, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), xuu6430, xuu6431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), Nothing, xuu61, xuu36, xuu6433, app(ty_Maybe, h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), xuu640, xuu641, xuu6434, xuu644, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_compare32(xuu33000, xuu34000, ty_Float) → new_compare31(xuu33000, xuu34000)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Char) → new_esEs17(xuu3110000, xuu6000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare9(:%(xuu33000, xuu33001), :%(xuu34000, xuu34001), ty_Integer) → new_compare12(new_sr0(xuu33000, xuu34001), new_sr0(xuu34000, xuu33001))
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, ty_@0) → new_ltEs14(xuu33000, xuu34000)
new_esEs11(Float(xuu3110000, xuu3110001), Float(xuu6000, xuu6001)) → new_esEs10(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_primCmpInt(Neg(Succ(xuu3300)), Pos(xuu340)) → LT
new_ltEs7(Right(xuu33000), Right(xuu34000), gd, ty_Int) → new_ltEs6(xuu33000, xuu34000)
new_not(True) → False
new_esEs15(False, False) → True
new_primMinusNat0(Succ(xuu28200), Succ(xuu9700)) → new_primMinusNat0(xuu28200, xuu9700)
new_esEs19(xuu3110001, xuu6001, ty_Double) → new_esEs13(xuu3110001, xuu6001)

The set Q consists of the following terms:

new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs23(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_gt(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, EmptyFM, False, x7, x8)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_addToFM_C15(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_compare32(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt5(x0, x1, ty_Float)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare32(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primEqNat0(Zero, Succ(x0))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMinusNat0(Zero, Zero)
new_addListToFM0(x0, x1, x2)
new_esEs18(x0, x1, ty_Int)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt13(x0, x1)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(Integer(x0), Integer(x1))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Ordering)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, EmptyFM, x3, x4, x5, x6, False, x7, x8)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_mkBalBranch6MkBalBranch5(x0, x1, x2, True, x3, x4)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, EmptyFM, False, x6, x7)
new_esEs15(True, True)
new_ltEs17(EQ, GT)
new_ltEs17(GT, EQ)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, False)
new_compare17(x0, x1, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt5(x0, x1, ty_Double)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare23(Just(x0), Just(x1), False, x2)
new_ltEs10(x0, x1, x2)
new_esEs11(Float(x0, x1), Float(x2, x3))
new_ltEs15(x0, x1)
new_primCmpInt0(EmptyFM, x0, x1, x2, x3)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10, x11, False, x12, x13)
new_esEs19(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, True, x4, x5)
new_ltEs20(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt1(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8, x9)
new_esEs19(x0, x1, ty_@0)
new_ltEs9(Just(x0), Nothing, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs15(False, False)
new_esEs8(GT, GT)
new_mkBalBranch6Size_r0(x0, x1, x2, x3, x4, x5)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_sizeFM(EmptyFM, x0, x1)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare32(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_@0)
new_esEs8(LT, LT)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs30(x0, x1, ty_Int)
new_compare([], :(x0, x1), x2)
new_esEs20(x0, x1, ty_Double)
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs27(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs8(x0, x1)
new_esEs30(x0, x1, ty_Integer)
new_esEs12(:(x0, x1), [], x2)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), False, x12, x13)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs5(x0, x1, app(ty_[], x2))
new_addToFM_C16(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_primEqNat0(Zero, Zero)
new_esEs25(x0, x1, ty_Int)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Double)
new_lt5(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_addToFM_C0(Branch(Nothing, x0, x1, x2, x3), Just(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), False, x11, x12)
new_esEs30(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare26(x0, x1, True)
new_asAs(True, x0)
new_compare110(x0, x1, False, x2)
new_primPlusInt(Pos(x0), Pos(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_mkBalBranch6MkBalBranch3(x0, x1, x2, EmptyFM, True, x3, x4)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10, False, x11, x12)
new_compare26(x0, x1, False)
new_primMulNat0(Zero, Zero)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare32(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare23(Nothing, Just(x0), False, x1)
new_mkBalBranch6MkBalBranch4(Branch(x0, x1, x2, x3, x4), x5, x6, x7, True, x8, x9)
new_compare8(x0, x1)
new_addToFM_C13(x0, x1, x2, x3, x4, True, x5, x6)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs5(x0, x1, ty_Integer)
new_ltEs16(x0, x1)
new_lt20(x0, x1, ty_Int)
new_mkBalBranch0(x0, x1, x2, x3, x4, x5)
new_sIZE_RATIO
new_lt5(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9)
new_compare(:(x0, x1), :(x2, x3), x4)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, False, x3, x4)
new_compare15(Double(x0, x1), Double(x2, x3))
new_addToFM_C0(Branch(Nothing, x0, x1, x2, x3), Nothing, x4, x5, x6)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_compare32(x0, x1, ty_Ordering)
new_lt18(x0, x1)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, ty_Char)
new_esEs14(@0, @0)
new_primMulNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare14(x0, x1, False)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, False, x3, x4)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare111(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Float)
new_mkBalBranch6MkBalBranch40(Branch(x0, x1, x2, x3, x4), x5, x6, True, x7, x8)
new_primPlusNat1(Zero, Succ(x0))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Float)
new_emptyFM(x0, x1)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_addToFM_C14(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_ltEs20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Ordering)
new_compare16(@0, @0)
new_compare32(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(x0, x1)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_Integer)
new_addToFM_C0(EmptyFM, x0, x1, x2, x3)
new_compare29(x0, x1, True, x2, x3)
new_esEs22(x0, x1, ty_Bool)
new_primPlusInt(Pos(x0), Neg(x1))
new_primPlusInt(Neg(x0), Pos(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs28(x0, x1, ty_Bool)
new_primPlusNat1(Zero, Zero)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs18(True, True)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs5(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Float)
new_compare31(Float(x0, x1), Float(x2, x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_compare32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs9(Nothing, Just(x0), x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs19(x0, x1, ty_Integer)
new_lt4(x0, x1)
new_addToFM_C13(x0, x1, x2, x3, x4, False, x5, x6)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_mkBalBranch6Size_l0(x0, x1, x2, x3, x4)
new_compare24(x0, x1, True)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_compare13(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4)
new_lt19(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Ordering)
new_addToFM_C22(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_esEs28(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_pePe(False, x0)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_addToFM_C0(Branch(Just(x0), x1, x2, x3, x4), Nothing, x5, x6, x7)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare23(Just(x0), Nothing, False, x1)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_primMinusNat0(Zero, Succ(x0))
new_lt16(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Int)
new_lt11(x0, x1, x2)
new_ltEs13(x0, x1)
new_lt14(x0, x1)
new_esEs24(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, ty_Ordering)
new_mkBalBranch6MkBalBranch30(x0, x1, EmptyFM, True, x2, x3)
new_lt5(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_fsEs(x0)
new_esEs27(x0, x1, ty_Float)
new_ltEs17(GT, GT)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare18(x0, x1, x2, x3, x4)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs18(False, False)
new_lt20(x0, x1, ty_Bool)
new_ltEs5(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primCompAux1(x0, x1, x2, x3)
new_primPlusNat0(x0, x1)
new_lt20(x0, x1, ty_@0)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Double)
new_primCompAux0(x0, EQ)
new_esEs5(Nothing, Nothing, x0)
new_esEs20(x0, x1, ty_Int)
new_esEs5(Nothing, Just(x0), x1)
new_lt7(x0, x1, x2, x3)
new_sr(x0, x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs8(EQ, EQ)
new_primCompAux0(x0, LT)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare32(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt15(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, EmptyFM, x3, x4, x5, False, x6, x7)
new_compare111(x0, x1, True, x2, x3)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs12([], [], x0)
new_esEs22(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, x2, x3, x4)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Int)
new_esEs17(Char(x0), Char(x1))
new_esEs30(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Succ(x1))
new_compare28(x0, x1, False, x2, x3)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, ty_Integer)
new_lt6(x0, x1)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare25(x0, x1, False, x2, x3, x4)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs24(x0, x1, ty_@0)
new_ltEs5(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Bool)
new_compare28(x0, x1, True, x2, x3)
new_compare12(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Bool)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, False, x4, x5)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_esEs21(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs24(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Char)
new_primMinusNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Neg(x1))
new_compare19(x0, x1, True, x2, x3)
new_primPlusInt(Neg(x0), Neg(x1))
new_primCompAux0(x0, GT)
new_esEs28(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Zero)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Double)
new_compare32(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Float)
new_primCmpNat0(Zero, Zero)
new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_ltEs6(x0, x1)
new_compare6(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_compare32(x0, x1, ty_Bool)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_mkBalBranch(x0, x1, x2, x3, x4)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Char)
new_ltEs17(LT, GT)
new_ltEs17(GT, LT)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs28(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_addToFM_C22(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs19(x0, x1, ty_Char)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_compare27(x0, x1, x2, x3)
new_primCmpInt0(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_mkBalBranch6MkBalBranch30(x0, x1, Branch(x2, x3, x4, x5, x6), True, x7, x8)
new_esEs20(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_addToFM_C14(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs10(x0, x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, ty_Int)
new_mkBalBranch6MkBalBranch4(EmptyFM, x0, x1, x2, True, x3, x4)
new_lt9(x0, x1, x2)
new_esEs22(x0, x1, ty_Integer)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Int)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs21(x0, x1, ty_Bool)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_@0)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_lt19(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_Ordering)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs18(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs18(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_not(True)
new_esEs24(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Float)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs9(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_compare32(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_compare7(x0, x1, x2)
new_compare19(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Integer)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Char)
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs29(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_ltEs19(x0, x1, ty_Double)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_mkBalBranch6MkBalBranch3(x0, x1, x2, Branch(x3, x4, x5, x6, x7), True, x8, x9)
new_ltEs18(False, True)
new_ltEs18(True, False)
new_lt20(x0, x1, ty_Double)
new_addToFM_C16(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare14(x0, x1, True)
new_compare([], [], x0)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_addToFM_C0(Branch(Just(x0), x1, x2, x3, x4), Just(x5), x6, x7, x8)
new_ltEs20(x0, x1, ty_Bool)
new_compare10(x0, x1, False)
new_compare23(Nothing, Nothing, False, x0)
new_compare32(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt17(x0, x1)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, x3, False, x4, x5)
new_compare110(x0, x1, True, x2)
new_lt5(x0, x1, ty_Bool)
new_primCmpInt1(EmptyFM, x0, x1, x2, x3, x4)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs27(x0, x1, ty_@0)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs20(x0, x1, ty_Char)
new_compare29(x0, x1, False, x2, x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_mkBalBranch6MkBalBranch40(EmptyFM, x0, x1, True, x2, x3)
new_compare(:(x0, x1), [], x2)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_primMinusNat0(Succ(x0), Succ(x1))
new_ltEs17(LT, EQ)
new_ltEs17(EQ, LT)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_mkBalBranch6MkBalBranch4(x0, x1, x2, x3, False, x4, x5)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs5(x0, x1, ty_Double)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(Char(x0), Char(x1))
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_compare23(x0, x1, True, x2)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_addToFM_C15(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_compare13(x0, x1, True, x2, x3, x4)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_mkBalBranch6MkBalBranch30(x0, x1, x2, False, x3, x4)
new_ltEs5(x0, x1, ty_Bool)
new_primMulNat0(Succ(x0), Zero)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, x2)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs19(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Char)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Float)
new_compare32(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Bool)
new_esEs12([], :(x0, x1), x2)
new_ltEs17(EQ, EQ)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(LT, LT)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, ty_Double)
new_lt8(x0, x1)
new_esEs29(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_addListToFM_CAdd(x0, @2(x1, x2), x3, x4)
new_compare32(x0, x1, ty_Float)
new_primCmpNat0(Succ(x0), Zero)
new_esEs18(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_[], 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: