YES 25.209 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
  ((plusFM :: Ord a => FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b) :: Ord a => FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b)

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

  addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b
addToFM fm key elt = addToFM_C (\old new ->new) fm 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_r) new_key new_elt 
 | new_key < key = 
mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
 | new_key > key = 
mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
 | otherwise = 
Branch new_key (combiner elt new_elt) size fm_l fm_r

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

  findMax :: FiniteMap a b  ->  (a,b)
findMax (Branch key elt _ _ EmptyFM) = (key,elt)
findMax (Branch key elt _ _ fm_r) = findMax 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 (\key elt rest ->(key,elt) : rest) [] fm

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

  mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkBalBranch key elt fm_L fm_R 
 | size_l + size_r < 2 = 
mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l = 
case fm_R of
  Branch _ _ _ fm_rl fm_rr
 | sizeFM fm_rl < 2 * sizeFM fm_rr -> 
single_L fm_L fm_R
 | otherwise -> 
double_L fm_L fm_R
 | size_l > sIZE_RATIO * size_r = 
case fm_L of
  Branch _ _ _ fm_ll fm_lr
 | sizeFM fm_lr < 2 * sizeFM fm_ll -> 
single_R fm_L fm_R
 | otherwise -> 
double_R fm_L fm_R
 | otherwise = 
mkBranch 2 key elt fm_L fm_R where 
double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_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 _ 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_rr) = mkBranch 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_lr) fm_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

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) 
 | sIZE_RATIO * size_l < size_r = 
mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r)
 | otherwise = 
mkBranch 13 key elt fm_l fm_r where 
size_l = sizeFM fm_l
size_r = sizeFM fm_r

  plusFM :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
plusFM EmptyFM fm2 = fm2
plusFM fm1 EmptyFM = fm1
plusFM fm1 (Branch split_key elt1 _ left right) = 
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right) where 
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

  splitGT :: Ord b => FiniteMap b a  ->  b  ->  FiniteMap b a
splitGT EmptyFM split_key = emptyFM
splitGT (Branch key elt _ fm_l fm_r) split_key 
 | split_key > key = 
splitGT fm_r split_key
 | split_key < key = 
mkVBalBranch key elt (splitGT fm_l split_key) fm_r
 | otherwise = 
fm_r

  splitLT :: Ord b => FiniteMap b a  ->  b  ->  FiniteMap b a
splitLT EmptyFM split_key = emptyFM
splitLT (Branch key elt _ fm_l fm_r) split_key 
 | split_key < key = 
splitLT fm_l split_key
 | split_key > key = 
mkVBalBranch key elt fm_l (splitLT fm_r split_key)
 | otherwise = 
fm_l

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

The following Lambda expression
\oldnew→new

is transformed to
addToFM0 old new = new



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

mainModule FiniteMap
  ((plusFM :: Ord b => FiniteMap (Maybe b) a  ->  FiniteMap (Maybe b) a  ->  FiniteMap (Maybe b) a) :: Ord b => FiniteMap (Maybe b) a  ->  FiniteMap (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

  addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM fm key elt = addToFM_C addToFM0 fm key elt

  
addToFM0 old new = new

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

  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_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 _ 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_rr) = mkBranch 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_lr) fm_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

  mkVBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) 
 | sIZE_RATIO * size_l < size_r = 
mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r)
 | otherwise = 
mkBranch 13 key elt fm_l fm_r where 
size_l = sizeFM fm_l
size_r = sizeFM fm_r

  plusFM :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
plusFM EmptyFM fm2 = fm2
plusFM fm1 EmptyFM = fm1
plusFM fm1 (Branch split_key elt1 _ left right) = 
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right) where 
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

  splitGT :: Ord b => FiniteMap b a  ->  b  ->  FiniteMap b a
splitGT EmptyFM split_key = emptyFM
splitGT (Branch key elt _ fm_l fm_r) split_key 
 | split_key > key = 
splitGT fm_r split_key
 | split_key < key = 
mkVBalBranch key elt (splitGT fm_l split_key) fm_r
 | otherwise = 
fm_r

  splitLT :: Ord a => FiniteMap a b  ->  a  ->  FiniteMap a b
splitLT EmptyFM split_key = emptyFM
splitLT (Branch key elt _ fm_l fm_r) split_key 
 | split_key < key = 
splitLT fm_l split_key
 | split_key > key = 
mkVBalBranch key elt fm_l (splitLT fm_r split_key)
 | otherwise = 
fm_l

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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

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

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

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

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

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



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

mainModule FiniteMap
  ((plusFM :: Ord b => FiniteMap (Maybe b) a  ->  FiniteMap (Maybe b) a  ->  FiniteMap (Maybe b) a) :: Ord b => FiniteMap (Maybe b) a  ->  FiniteMap (Maybe b) a  ->  FiniteMap (Maybe b) a)

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

  addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b
addToFM fm key elt = addToFM_C addToFM0 fm key elt

  
addToFM0 old new = new

  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_r) new_key new_elt 
 | new_key < key = 
mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
 | new_key > key = 
mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
 | otherwise = 
Branch new_key (combiner elt new_elt) size fm_l fm_r

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

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

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

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

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

  mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBalBranch key elt fm_L fm_R 
 | size_l + size_r < 2 = 
mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l = 
mkBalBranch0 fm_L fm_R fm_R
 | size_l > sIZE_RATIO * size_r = 
mkBalBranch1 fm_L fm_R fm_L
 | otherwise = 
mkBranch 2 key elt fm_L fm_R where 
double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_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 _ 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_rr) = mkBranch 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_lr) fm_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

  mkVBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) 
 | sIZE_RATIO * size_l < size_r = 
mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r)
 | otherwise = 
mkBranch 13 key elt fm_l fm_r where 
size_l = sizeFM fm_l
size_r = sizeFM fm_r

  plusFM :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
plusFM EmptyFM fm2 = fm2
plusFM fm1 EmptyFM = fm1
plusFM fm1 (Branch split_key elt1 _ left right) = 
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right) where 
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

  splitGT :: Ord b => FiniteMap b a  ->  b  ->  FiniteMap b a
splitGT EmptyFM split_key = emptyFM
splitGT (Branch key elt _ fm_l fm_r) split_key 
 | split_key > key = 
splitGT fm_r split_key
 | split_key < key = 
mkVBalBranch key elt (splitGT fm_l split_key) fm_r
 | otherwise = 
fm_r

  splitLT :: Ord b => FiniteMap b a  ->  b  ->  FiniteMap b a
splitLT EmptyFM split_key = emptyFM
splitLT (Branch key elt _ fm_l fm_r) split_key 
 | split_key < key = 
splitLT fm_l split_key
 | split_key > key = 
mkVBalBranch key elt fm_l (splitLT fm_r split_key)
 | otherwise = 
fm_l

  unitFM :: b  ->  a  ->  FiniteMap b a
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
  ((plusFM :: Ord a => FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b) :: Ord a => FiniteMap (Maybe a) b  ->  FiniteMap (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

  addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM fm key elt = addToFM_C addToFM0 fm key elt

  
addToFM0 old new = new

  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_r) new_key new_elt 
 | new_key < key = 
mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
 | new_key > key = 
mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
 | otherwise = 
Branch new_key (combiner elt new_elt) size fm_l fm_r

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

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

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

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

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

  mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkBalBranch key elt fm_L fm_R 
 | size_l + size_r < 2 = 
mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l = 
mkBalBranch0 fm_L fm_R fm_R
 | size_l > sIZE_RATIO * size_r = 
mkBalBranch1 fm_L fm_R fm_L
 | otherwise = 
mkBranch 2 key elt fm_L fm_R where 
double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_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 _ 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_rr) = mkBranch 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_lr) fm_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

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) 
 | sIZE_RATIO * size_l < size_r = 
mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r)
 | otherwise = 
mkBranch 13 key elt fm_l fm_r where 
size_l = sizeFM fm_l
size_r = sizeFM fm_r

  plusFM :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
plusFM EmptyFM fm2 = fm2
plusFM fm1 EmptyFM = fm1
plusFM fm1 (Branch split_key elt1 _ left right) = 
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right) where 
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

  splitGT :: Ord a => FiniteMap a b  ->  a  ->  FiniteMap a b
splitGT EmptyFM split_key = emptyFM
splitGT (Branch key elt _ fm_l fm_r) split_key 
 | split_key > key = 
splitGT fm_r split_key
 | split_key < key = 
mkVBalBranch key elt (splitGT fm_l split_key) fm_r
 | otherwise = 
fm_r

  splitLT :: Ord a => FiniteMap a b  ->  a  ->  FiniteMap a b
splitLT EmptyFM split_key = emptyFM
splitLT (Branch key elt _ fm_l fm_r) split_key 
 | split_key < key = 
splitLT fm_l split_key
 | split_key > key = 
mkVBalBranch key elt fm_l (splitLT fm_r split_key)
 | otherwise = 
fm_l

  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.
Binding Reductions:
The bind variable of the following binding Pattern
fm_l@(Branch yz zu zv zw zx)

is replaced by the following term
Branch yz zu zv zw zx

The bind variable of the following binding Pattern
fm_r@(Branch zz vuu vuv vuw vux)

is replaced by the following term
Branch zz vuu vuv vuw vux



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

mainModule FiniteMap
  ((plusFM :: Ord a => FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b) :: Ord a => FiniteMap (Maybe a) b  ->  FiniteMap (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

  addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b
addToFM fm key elt = addToFM_C addToFM0 fm key elt

  
addToFM0 old new = new

  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_r) new_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 vwy vwz EmptyFM) = (key,elt)
findMax (Branch key elt vxu vxv fm_r) = findMax fm_r

  findMin :: FiniteMap a b  ->  (a,b)
findMin (Branch key elt wz EmptyFM xu) = (key,elt)
findMin (Branch key elt xv fm_l xw) = 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 wy fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l

  mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBalBranch key elt fm_L fm_R 
 | size_l + size_r < 2 = 
mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l = 
mkBalBranch0 fm_L fm_R fm_R
 | size_l > sIZE_RATIO * size_r = 
mkBalBranch1 fm_L fm_R fm_L
 | otherwise = 
mkBranch 2 key elt fm_L fm_R where 
double_L fm_l (Branch key_r elt_r vvy (Branch key_rl elt_rl vvz fm_rll fm_rlr) fm_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 vuz fm_ll (Branch key_lr elt_lr vvu 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 vwu vwv vww 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 vvv vvw vvx 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 vwx fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l vuy fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l = sizeFM fm_L
size_r = sizeFM fm_R

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

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux) 
 | sIZE_RATIO * size_l < size_r = 
mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zx) vuw) vux
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
 | otherwise = 
mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux) where 
size_l = sizeFM (Branch yz zu zv zw zx)
size_r = sizeFM (Branch zz vuu vuv vuw vux)

  plusFM :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
plusFM EmptyFM fm2 = fm2
plusFM fm1 EmptyFM = fm1
plusFM fm1 (Branch split_key elt1 yx left right) = 
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right) where 
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key

  sIZE_RATIO :: Int
sIZE_RATIO = 5

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM = 0
sizeFM (Branch xz yu size yv yw) = size

  splitGT :: Ord a => FiniteMap a b  ->  a  ->  FiniteMap a b
splitGT EmptyFM split_key = emptyFM
splitGT (Branch key elt xy fm_l fm_r) split_key 
 | split_key > key = 
splitGT fm_r split_key
 | split_key < key = 
mkVBalBranch key elt (splitGT fm_l split_key) fm_r
 | otherwise = 
fm_r

  splitLT :: Ord a => FiniteMap a b  ->  a  ->  FiniteMap a b
splitLT EmptyFM split_key = emptyFM
splitLT (Branch key elt xx fm_l fm_r) split_key 
 | split_key < key = 
splitLT fm_l split_key
 | split_key > key = 
mkVBalBranch key elt fm_l (splitLT fm_r split_key)
 | otherwise = 
fm_l

  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
splitLT EmptyFM split_key = emptyFM
splitLT (Branch key elt xx fm_l fm_r) split_key
 | split_key < key
 = splitLT fm_l split_key
 | split_key > key
 = mkVBalBranch key elt fm_l (splitLT fm_r split_key)
 | otherwise
 = fm_l

is transformed to
splitLT EmptyFM split_key = splitLT4 EmptyFM split_key
splitLT (Branch key elt xx fm_l fm_r) split_key = splitLT3 (Branch key elt xx fm_l fm_r) split_key

splitLT2 key elt xx fm_l fm_r split_key True = splitLT fm_l split_key
splitLT2 key elt xx fm_l fm_r split_key False = splitLT1 key elt xx fm_l fm_r split_key (split_key > key)

splitLT1 key elt xx fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key)
splitLT1 key elt xx fm_l fm_r split_key False = splitLT0 key elt xx fm_l fm_r split_key otherwise

splitLT0 key elt xx fm_l fm_r split_key True = fm_l

splitLT3 (Branch key elt xx fm_l fm_r) split_key = splitLT2 key elt xx fm_l fm_r split_key (split_key < key)

splitLT4 EmptyFM split_key = emptyFM
splitLT4 wwv www = splitLT3 wwv www

The following Function with conditions
splitGT EmptyFM split_key = emptyFM
splitGT (Branch key elt xy fm_l fm_r) split_key
 | split_key > key
 = splitGT fm_r split_key
 | split_key < key
 = mkVBalBranch key elt (splitGT fm_l split_key) fm_r
 | otherwise
 = fm_r

is transformed to
splitGT EmptyFM split_key = splitGT4 EmptyFM split_key
splitGT (Branch key elt xy fm_l fm_r) split_key = splitGT3 (Branch key elt xy fm_l fm_r) split_key

splitGT2 key elt xy fm_l fm_r split_key True = splitGT fm_r split_key
splitGT2 key elt xy fm_l fm_r split_key False = splitGT1 key elt xy fm_l fm_r split_key (split_key < key)

splitGT0 key elt xy fm_l fm_r split_key True = fm_r

splitGT1 key elt xy fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r
splitGT1 key elt xy fm_l fm_r split_key False = splitGT0 key elt xy fm_l fm_r split_key otherwise

splitGT3 (Branch key elt xy fm_l fm_r) split_key = splitGT2 key elt xy fm_l fm_r split_key (split_key > key)

splitGT4 EmptyFM split_key = emptyFM
splitGT4 wwz wxu = splitGT3 wwz wxu

The following Function with conditions
mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)
 | sIZE_RATIO * size_l < size_r
 = mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zx) vuw) vux
 | sIZE_RATIO * size_r < size_l
 = mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
 | otherwise
 = mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)
where 
size_l  = sizeFM (Branch yz zu zv zw zx)
size_r  = sizeFM (Branch zz vuu vuv vuw vux)

is transformed to
mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux) = mkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

mkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux) = 
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * size_l < size_r)
where 
mkVBalBranch0 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)
mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch0 key elt yz zu zv zw zx zz vuu vuv vuw vux otherwise
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zx) vuw) vux
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * size_r < size_l)
size_l  = sizeFM (Branch yz zu zv zw zx)
size_r  = sizeFM (Branch zz vuu vuv vuw vux)

mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 wxy wxz wyu wyv = mkVBalBranch3 wxy wxz wyu wyv

mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 wyx wyy wyz wzu = mkVBalBranch4 wyx wyy wyz wzu

The following Function with conditions
mkBalBranch1 fm_L fm_R (Branch vvv vvw vvx 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 vvv vvw vvx fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)

mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise

mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = double_R fm_L fm_R

mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

The following Function with conditions
mkBalBranch0 fm_L fm_R (Branch vwu vwv vww 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 vwu vwv vww fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)

mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise

mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr True = double_L fm_L fm_R

mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vwu vwv vww 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 vvy (Branch key_rl elt_rl vvz fm_rll fm_rlr) fm_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 vuz fm_ll (Branch key_lr elt_lr vvu 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 vwu vwv vww 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 vvv vvw vvx 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 vwx fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l vuy fm_ll fm_lr) fm_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 vvy (Branch key_rl elt_rl vvz fm_rll fm_rlr) fm_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 vuz fm_ll (Branch key_lr elt_lr vvu 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 vwu vwv vww fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vvv vvw vvx 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 vwx fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l vuy fm_ll fm_lr) fm_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_r) new_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

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_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt

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

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

addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_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_r) new_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 wzz xuu xuv xuw = addToFM_C3 wzz xuu xuv xuw

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

is transformed to
compare x y = compare3 x y

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

gcd'1 True x xux = x
gcd'1 xuy xuz xvu = gcd'0 xuz xvu

gcd'2 x xux = gcd'1 (xux == 0) x xux
gcd'2 xvv xvw = gcd'0 xvv xvw

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 xvx xvy = gcd3 xvx xvy
gcd x y = gcd0 x y

gcd0 x y = 
gcd' (abs x) (abs y)
where 
gcd' x xux = gcd'2 x xux
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x xux = x
gcd'1 xuy xuz xvu = gcd'0 xuz xvu
gcd'2 x xux = gcd'1 (xux == 0) x xux
gcd'2 xvv xvw = gcd'0 xvv xvw

gcd1 True xvx xvy = error []
gcd1 xvz xwu xwv = gcd0 xwu xwv

gcd2 True xvx xvy = gcd1 (xvy == 0) xvx xvy
gcd2 xww xwx xwy = gcd0 xwx xwy

gcd3 xvx xvy = gcd2 (xvx == 0) xvx xvy
gcd3 xwz xxu = gcd0 xwz xxu

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

is transformed to
absReal x = absReal2 x

absReal0 x True = `negate` x

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

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

mainModule FiniteMap
  ((plusFM :: Ord a => FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b) :: Ord a => FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b)

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

  addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM fm key elt = addToFM_C addToFM0 fm key elt

  
addToFM0 old new = new

  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_r) new_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_r) new_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 wzz xuu xuv xuw = addToFM_C3 wzz xuu xuv xuw

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

  findMax :: FiniteMap a b  ->  (a,b)
findMax (Branch key elt vwy vwz EmptyFM) = (key,elt)
findMax (Branch key elt vxu vxv fm_r) = findMax fm_r

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

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

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

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

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

  
mkBalBranch6 key elt fm_L fm_R = 
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where 
double_L fm_l (Branch key_r elt_r vvy (Branch key_rl elt_rl vvz fm_rll fm_rlr) fm_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 vuz fm_ll (Branch key_lr elt_lr vvu 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 vwu vwv vww fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vvv vvw vvx 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 vwx fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l vuy fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l = sizeFM fm_L
size_r = sizeFM fm_R

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

  mkVBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux) = mkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

  
mkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux) = 
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * size_l < size_r) where 
mkVBalBranch0 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)
mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch0 key elt yz zu zv zw zx zz vuu vuv vuw vux otherwise
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zx) vuw) vux
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * size_r < size_l)
size_l = sizeFM (Branch yz zu zv zw zx)
size_r = sizeFM (Branch zz vuu vuv vuw vux)

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 wxy wxz wyu wyv = mkVBalBranch3 wxy wxz wyu wyv

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 wyx wyy wyz wzu = mkVBalBranch4 wyx wyy wyz wzu

  plusFM :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
plusFM EmptyFM fm2 = fm2
plusFM fm1 EmptyFM = fm1
plusFM fm1 (Branch split_key elt1 yx left right) = 
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right) where 
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key

  sIZE_RATIO :: Int
sIZE_RATIO = 5

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM = 0
sizeFM (Branch xz yu size yv yw) = size

  splitGT :: Ord b => FiniteMap b a  ->  b  ->  FiniteMap b a
splitGT EmptyFM split_key = splitGT4 EmptyFM split_key
splitGT (Branch key elt xy fm_l fm_r) split_key = splitGT3 (Branch key elt xy fm_l fm_r) split_key

  
splitGT0 key elt xy fm_l fm_r split_key True = fm_r

  
splitGT1 key elt xy fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r
splitGT1 key elt xy fm_l fm_r split_key False = splitGT0 key elt xy fm_l fm_r split_key otherwise

  
splitGT2 key elt xy fm_l fm_r split_key True = splitGT fm_r split_key
splitGT2 key elt xy fm_l fm_r split_key False = splitGT1 key elt xy fm_l fm_r split_key (split_key < key)

  
splitGT3 (Branch key elt xy fm_l fm_r) split_key = splitGT2 key elt xy fm_l fm_r split_key (split_key > key)

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 wwz wxu = splitGT3 wwz wxu

  splitLT :: Ord b => FiniteMap b a  ->  b  ->  FiniteMap b a
splitLT EmptyFM split_key = splitLT4 EmptyFM split_key
splitLT (Branch key elt xx fm_l fm_r) split_key = splitLT3 (Branch key elt xx fm_l fm_r) split_key

  
splitLT0 key elt xx fm_l fm_r split_key True = fm_l

  
splitLT1 key elt xx fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key)
splitLT1 key elt xx fm_l fm_r split_key False = splitLT0 key elt xx fm_l fm_r split_key otherwise

  
splitLT2 key elt xx fm_l fm_r split_key True = splitLT fm_l split_key
splitLT2 key elt xx fm_l fm_r split_key False = splitLT1 key elt xx fm_l fm_r split_key (split_key > key)

  
splitLT3 (Branch key elt xx fm_l fm_r) split_key = splitLT2 key elt xx fm_l fm_r split_key (split_key < key)

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wwv www = splitLT3 wwv www

  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
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2)
where 
double_L fm_l (Branch key_r elt_r vvy (Branch key_rl elt_rl vvz fm_rll fm_rlr) fm_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 vuz fm_ll (Branch key_lr elt_lr vvu 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 vwu vwv vww fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vvv vvw vvx 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 vwx fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l vuy fm_ll fm_lr) fm_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
mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 xxv xxw xxx xxy fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 xxv xxw xxx xxy key elt fm_L fm_R otherwise

mkBalBranch6MkBalBranch00 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr True = mkBalBranch6Double_L xxv xxw xxx xxy fm_L fm_R

mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr True = mkBalBranch6Single_R xxv xxw xxx xxy fm_L fm_R
mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr False = mkBalBranch6MkBalBranch10 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise

mkBalBranch6MkBalBranch5 xxv xxw xxx xxy key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 xxv xxw xxx xxy key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R (mkBalBranch6Size_r xxv xxw xxx xxy > sIZE_RATIO * mkBalBranch6Size_l xxv xxw xxx xxy)

mkBalBranch6MkBalBranch2 xxv xxw xxx xxy key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

mkBalBranch6MkBalBranch02 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr True = mkBalBranch6Single_L xxv xxw xxx xxy fm_L fm_R
mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr False = mkBalBranch6MkBalBranch00 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise

mkBalBranch6Size_r xxv xxw xxx xxy = sizeFM xxv

mkBalBranch6Single_L xxv xxw xxx xxy fm_l (Branch key_r elt_r vwx fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 xxw xxx fm_l fm_rl) fm_rr

mkBalBranch6MkBalBranch12 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

mkBalBranch6Size_l xxv xxw xxx xxy = sizeFM xxy

mkBalBranch6Double_L xxv xxw xxx xxy fm_l (Branch key_r elt_r vvy (Branch key_rl elt_rl vvz fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 xxw xxx fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

mkBalBranch6MkBalBranch1 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch6MkBalBranch12 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)

mkBalBranch6MkBalBranch0 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch6MkBalBranch02 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)

mkBalBranch6MkBalBranch10 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr True = mkBalBranch6Double_R xxv xxw xxx xxy fm_L fm_R

mkBalBranch6Single_R xxv xxw xxx xxy (Branch key_l elt_l vuy fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 xxw xxx fm_lr fm_r)

mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 xxv xxw xxx xxy fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R (mkBalBranch6Size_l xxv xxw xxx xxy > sIZE_RATIO * mkBalBranch6Size_r xxv xxw xxx xxy)

mkBalBranch6Double_R xxv xxw xxx xxy (Branch key_l elt_l vuz fm_ll (Branch key_lr elt_lr vvu fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 xxw xxx fm_lrr fm_r)

The bindings of the following Let/Where expression
let 
result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result
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
mkBranchLeft_ok xxz xyu xyv = mkBranchLeft_ok0 xxz xyu xyv xxz xyu xxz

mkBranchRight_ok0 xxz xyu xyv fm_r key EmptyFM = True
mkBranchRight_ok0 xxz xyu xyv fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

mkBranchRight_ok xxz xyu xyv = mkBranchRight_ok0 xxz xyu xyv xyv xyu xyv

mkBranchLeft_size xxz xyu xyv = sizeFM xxz

mkBranchUnbox xxz xyu xyv x = x

mkBranchLeft_ok0 xxz xyu xyv fm_l key EmptyFM = True
mkBranchLeft_ok0 xxz xyu xyv fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

mkBranchBalance_ok xxz xyu xyv = True

mkBranchRight_size xxz xyu xyv = sizeFM xyv

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 xyw xyx xyy xyz = Branch xyw xyx (mkBranchUnbox xyy xyw xyz (1 + mkBranchLeft_size xyy xyw xyz + mkBranchRight_size xyy xyw xyz)) xyy xyz

The bindings of the following Let/Where expression
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * size_l < size_r)
where 
mkVBalBranch0 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)
mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch0 key elt yz zu zv zw zx zz vuu vuv vuw vux otherwise
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zx) vuw) vux
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * size_r < size_l)
size_l  = sizeFM (Branch yz zu zv zw zx)
size_r  = sizeFM (Branch zz vuu vuv vuw vux)

are unpacked to the following functions on top level
mkVBalBranch3Size_r xzu xzv xzw xzx xzy xzz yuu yuv yuw yux = sizeFM (Branch xzu xzv xzw xzx xzy)

mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch3MkVBalBranch0 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux otherwise

mkVBalBranch3MkVBalBranch0 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

mkVBalBranch3Size_l xzu xzv xzw xzx xzy xzz yuu yuv yuw yux = sizeFM (Branch xzz yuu yuv yuw yux)

mkVBalBranch3MkVBalBranch2 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zx) vuw) vux
mkVBalBranch3MkVBalBranch2 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * mkVBalBranch3Size_r xzu xzv xzw xzx xzy xzz yuu yuv yuw yux < mkVBalBranch3Size_l xzu xzv xzw xzx xzy xzz yuu yuv yuw yux)

The bindings of the following Let/Where expression
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right)
where 
gts  = splitGT fm1 split_key
lts  = splitLT fm1 split_key

are unpacked to the following functions on top level
plusFMGts yuy yuz = splitGT yuy yuz

plusFMLts yuy yuz = splitLT yuy yuz

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 yvu = fst (findMin yvu)

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 yvv = fst (findMax yvv)

The bindings of the following Let/Where expression
reduce1 x y (y == 0)
where 
d  = gcd x y
reduce0 x y True = x `quot` d :% (y `quot` d)
reduce1 x y True = error []
reduce1 x y False = reduce0 x y otherwise

are unpacked to the following functions on top level
reduce2Reduce0 yvw yvx x y True = x `quot` reduce2D yvw yvx :% (y `quot` reduce2D yvw yvx)

reduce2Reduce1 yvw yvx x y True = error []
reduce2Reduce1 yvw yvx x y False = reduce2Reduce0 yvw yvx x y otherwise

reduce2D yvw yvx = gcd yvw yvx

The bindings of the following Let/Where expression
gcd' (abs x) (abs y)
where 
gcd' x xux = gcd'2 x xux
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x xux = x
gcd'1 xuy xuz xvu = gcd'0 xuz xvu
gcd'2 x xux = gcd'1 (xux == 0) x xux
gcd'2 xvv xvw = gcd'0 xvv xvw

are unpacked to the following functions on top level
gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y)

gcd0Gcd' x xux = gcd0Gcd'2 x xux
gcd0Gcd' x y = gcd0Gcd'0 x y

gcd0Gcd'1 True x xux = x
gcd0Gcd'1 xuy xuz xvu = gcd0Gcd'0 xuz xvu

gcd0Gcd'2 x xux = gcd0Gcd'1 (xux == 0) x xux
gcd0Gcd'2 xvv xvw = gcd0Gcd'0 xvv xvw



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

mainModule FiniteMap
  ((plusFM :: Ord a => FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) b) :: Ord a => FiniteMap (Maybe a) b  ->  FiniteMap (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

  addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM fm key elt = addToFM_C addToFM0 fm key elt

  
addToFM0 old new = new

  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_r) new_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_r) new_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 wzz xuu xuv xuw = addToFM_C3 wzz xuu xuv xuw

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vwy vwz EmptyFM) = (key,elt)
findMax (Branch key elt vxu vxv fm_r) = findMax fm_r

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

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

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

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

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

  
mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 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 xxv xxw xxx xxy fm_l (Branch key_r elt_r vvy (Branch key_rl elt_rl vvz fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 xxw xxx fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R xxv xxw xxx xxy (Branch key_l elt_l vuz fm_ll (Branch key_lr elt_lr vvu fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 xxw xxx fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch6MkBalBranch02 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr True = mkBalBranch6Double_L xxv xxw xxx xxy fm_L fm_R

  
mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr True = mkBalBranch6Single_L xxv xxw xxx xxy fm_L fm_R
mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr False = mkBalBranch6MkBalBranch00 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch6MkBalBranch12 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr True = mkBalBranch6Double_R xxv xxw xxx xxy fm_L fm_R

  
mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr True = mkBalBranch6Single_R xxv xxw xxx xxy fm_L fm_R
mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr False = mkBalBranch6MkBalBranch10 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 xxv xxw xxx xxy key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 xxv xxw xxx xxy fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 xxv xxw xxx xxy key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 xxv xxw xxx xxy fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R (mkBalBranch6Size_l xxv xxw xxx xxy > sIZE_RATIO * mkBalBranch6Size_r xxv xxw xxx xxy)

  
mkBalBranch6MkBalBranch5 xxv xxw xxx xxy key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 xxv xxw xxx xxy key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R (mkBalBranch6Size_r xxv xxw xxx xxy > sIZE_RATIO * mkBalBranch6Size_l xxv xxw xxx xxy)

  
mkBalBranch6Single_L xxv xxw xxx xxy fm_l (Branch key_r elt_r vwx fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 xxw xxx fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R xxv xxw xxx xxy (Branch key_l elt_l vuy fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 xxw xxx fm_lr fm_r)

  
mkBalBranch6Size_l xxv xxw xxx xxy = sizeFM xxy

  
mkBalBranch6Size_r xxv xxw xxx xxy = sizeFM xxv

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

  
mkBranchBalance_ok xxz xyu xyv = True

  
mkBranchLeft_ok xxz xyu xyv = mkBranchLeft_ok0 xxz xyu xyv xxz xyu xxz

  
mkBranchLeft_ok0 xxz xyu xyv fm_l key EmptyFM = True
mkBranchLeft_ok0 xxz xyu xyv fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key yvv = fst (findMax yvv)

  
mkBranchLeft_size xxz xyu xyv = sizeFM xxz

  
mkBranchResult xyw xyx xyy xyz = Branch xyw xyx (mkBranchUnbox xyy xyw xyz (1 + mkBranchLeft_size xyy xyw xyz + mkBranchRight_size xyy xyw xyz)) xyy xyz

  
mkBranchRight_ok xxz xyu xyv = mkBranchRight_ok0 xxz xyu xyv xyv xyu xyv

  
mkBranchRight_ok0 xxz xyu xyv fm_r key EmptyFM = True
mkBranchRight_ok0 xxz xyu xyv fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key yvu = fst (findMin yvu)

  
mkBranchRight_size xxz xyu xyv = sizeFM xyv

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)))
mkBranchUnbox xxz xyu xyv x = x

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux) = mkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

  
mkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux) = mkVBalBranch3MkVBalBranch2 zz vuu vuv vuw vux yz zu zv zw zx key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * mkVBalBranch3Size_l zz vuu vuv vuw vux yz zu zv zw zx < mkVBalBranch3Size_r zz vuu vuv vuw vux yz zu zv zw zx)

  
mkVBalBranch3MkVBalBranch0 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

  
mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch3MkVBalBranch0 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux otherwise

  
mkVBalBranch3MkVBalBranch2 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zx) vuw) vux
mkVBalBranch3MkVBalBranch2 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * mkVBalBranch3Size_r xzu xzv xzw xzx xzy xzz yuu yuv yuw yux < mkVBalBranch3Size_l xzu xzv xzw xzx xzy xzz yuu yuv yuw yux)

  
mkVBalBranch3Size_l xzu xzv xzw xzx xzy xzz yuu yuv yuw yux = sizeFM (Branch xzz yuu yuv yuw yux)

  
mkVBalBranch3Size_r xzu xzv xzw xzx xzy xzz yuu yuv yuw yux = sizeFM (Branch xzu xzv xzw xzx xzy)

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 wxy wxz wyu wyv = mkVBalBranch3 wxy wxz wyu wyv

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 wyx wyy wyz wzu = mkVBalBranch4 wyx wyy wyz wzu

  plusFM :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
plusFM EmptyFM fm2 = fm2
plusFM fm1 EmptyFM = fm1
plusFM fm1 (Branch split_key elt1 yx left right) = mkVBalBranch split_key elt1 (plusFM (plusFMLts fm1 split_key) left) (plusFM (plusFMGts fm1 split_key) right)

  
plusFMGts yuy yuz = splitGT yuy yuz

  
plusFMLts yuy yuz = splitLT yuy yuz

  sIZE_RATIO :: Int
sIZE_RATIO = 5

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM = 0
sizeFM (Branch xz yu size yv yw) = size

  splitGT :: Ord b => FiniteMap b a  ->  b  ->  FiniteMap b a
splitGT EmptyFM split_key = splitGT4 EmptyFM split_key
splitGT (Branch key elt xy fm_l fm_r) split_key = splitGT3 (Branch key elt xy fm_l fm_r) split_key

  
splitGT0 key elt xy fm_l fm_r split_key True = fm_r

  
splitGT1 key elt xy fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r
splitGT1 key elt xy fm_l fm_r split_key False = splitGT0 key elt xy fm_l fm_r split_key otherwise

  
splitGT2 key elt xy fm_l fm_r split_key True = splitGT fm_r split_key
splitGT2 key elt xy fm_l fm_r split_key False = splitGT1 key elt xy fm_l fm_r split_key (split_key < key)

  
splitGT3 (Branch key elt xy fm_l fm_r) split_key = splitGT2 key elt xy fm_l fm_r split_key (split_key > key)

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 wwz wxu = splitGT3 wwz wxu

  splitLT :: Ord b => FiniteMap b a  ->  b  ->  FiniteMap b a
splitLT EmptyFM split_key = splitLT4 EmptyFM split_key
splitLT (Branch key elt xx fm_l fm_r) split_key = splitLT3 (Branch key elt xx fm_l fm_r) split_key

  
splitLT0 key elt xx fm_l fm_r split_key True = fm_l

  
splitLT1 key elt xx fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key)
splitLT1 key elt xx fm_l fm_r split_key False = splitLT0 key elt xx fm_l fm_r split_key otherwise

  
splitLT2 key elt xx fm_l fm_r split_key True = splitLT fm_l split_key
splitLT2 key elt xx fm_l fm_r split_key False = splitLT1 key elt xx fm_l fm_r split_key (split_key > key)

  
splitLT3 (Branch key elt xx fm_l fm_r) split_key = splitLT2 key elt xx fm_l fm_r split_key (split_key < key)

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wwv www = splitLT3 wwv www

  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
  (plusFM :: Ord b => FiniteMap (Maybe b) a  ->  FiniteMap (Maybe b) a  ->  FiniteMap (Maybe b) a)

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

  addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM fm key elt = addToFM_C addToFM0 fm key elt

  
addToFM0 old new = new

  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_r) new_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_r) new_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 wzz xuu xuv xuw = addToFM_C3 wzz xuu xuv xuw

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

  findMax :: FiniteMap a b  ->  (a,b)
findMax (Branch key elt vwy vwz EmptyFM) = (key,elt)
findMax (Branch key elt vxu vxv fm_r) = findMax fm_r

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

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

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

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

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

  
mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 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 xxv xxw xxx xxy fm_l (Branch key_r elt_r vvy (Branch key_rl elt_rl vvz fm_rll fm_rlr) fm_rr) = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) key_rl elt_rl (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) xxw xxx fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R xxv xxw xxx xxy (Branch key_l elt_l vuz fm_ll (Branch key_lr elt_lr vvu 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))))))))))))) xxw xxx fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch6MkBalBranch02 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr True = mkBalBranch6Double_L xxv xxw xxx xxy fm_L fm_R

  
mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr True = mkBalBranch6Single_L xxv xxw xxx xxy fm_L fm_R
mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr False = mkBalBranch6MkBalBranch00 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch6MkBalBranch12 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr True = mkBalBranch6Double_R xxv xxw xxx xxy fm_L fm_R

  
mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr True = mkBalBranch6Single_R xxv xxw xxx xxy fm_L fm_R
mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr False = mkBalBranch6MkBalBranch10 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 xxv xxw xxx xxy key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 xxv xxw xxx xxy fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 xxv xxw xxx xxy key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 xxv xxw xxx xxy fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R (mkBalBranch6Size_l xxv xxw xxx xxy > sIZE_RATIO * mkBalBranch6Size_r xxv xxw xxx xxy)

  
mkBalBranch6MkBalBranch5 xxv xxw xxx xxy key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R
mkBalBranch6MkBalBranch5 xxv xxw xxx xxy key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R (mkBalBranch6Size_r xxv xxw xxx xxy > sIZE_RATIO * mkBalBranch6Size_l xxv xxw xxx xxy)

  
mkBalBranch6Single_L xxv xxw xxx xxy fm_l (Branch key_r elt_r vwx fm_rl fm_rr) = mkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) xxw xxx fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R xxv xxw xxx xxy (Branch key_l elt_l vuy fm_ll fm_lr) fm_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)))))))))) xxw xxx fm_lr fm_r)

  
mkBalBranch6Size_l xxv xxw xxx xxy = sizeFM xxy

  
mkBalBranch6Size_r xxv xxw xxx xxy = sizeFM xxv

  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_l fm_r

  
mkBranchBalance_ok xxz xyu xyv = True

  
mkBranchLeft_ok xxz xyu xyv = mkBranchLeft_ok0 xxz xyu xyv xxz xyu xxz

  
mkBranchLeft_ok0 xxz xyu xyv fm_l key EmptyFM = True
mkBranchLeft_ok0 xxz xyu xyv fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key yvv = fst (findMax yvv)

  
mkBranchLeft_size xxz xyu xyv = sizeFM xxz

  
mkBranchResult xyw xyx xyy xyz = Branch xyw xyx (mkBranchUnbox xyy xyw xyz (Pos (Succ Zero) + mkBranchLeft_size xyy xyw xyz + mkBranchRight_size xyy xyw xyz)) xyy xyz

  
mkBranchRight_ok xxz xyu xyv = mkBranchRight_ok0 xxz xyu xyv xyv xyu xyv

  
mkBranchRight_ok0 xxz xyu xyv fm_r key EmptyFM = True
mkBranchRight_ok0 xxz xyu xyv fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key yvu = fst (findMin yvu)

  
mkBranchRight_size xxz xyu xyv = sizeFM xyv

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)))
mkBranchUnbox xxz xyu xyv x = x

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux) = mkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

  
mkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux) = mkVBalBranch3MkVBalBranch2 zz vuu vuv vuw vux yz zu zv zw zx key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * mkVBalBranch3Size_l zz vuu vuv vuw vux yz zu zv zw zx < mkVBalBranch3Size_r zz vuu vuv vuw vux yz zu zv zw zx)

  
mkVBalBranch3MkVBalBranch0 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

  
mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch3MkVBalBranch0 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux otherwise

  
mkVBalBranch3MkVBalBranch2 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zx) vuw) vux
mkVBalBranch3MkVBalBranch2 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * mkVBalBranch3Size_r xzu xzv xzw xzx xzy xzz yuu yuv yuw yux < mkVBalBranch3Size_l xzu xzv xzw xzx xzy xzz yuu yuv yuw yux)

  
mkVBalBranch3Size_l xzu xzv xzw xzx xzy xzz yuu yuv yuw yux = sizeFM (Branch xzz yuu yuv yuw yux)

  
mkVBalBranch3Size_r xzu xzv xzw xzx xzy xzz yuu yuv yuw yux = sizeFM (Branch xzu xzv xzw xzx xzy)

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 wxy wxz wyu wyv = mkVBalBranch3 wxy wxz wyu wyv

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 wyx wyy wyz wzu = mkVBalBranch4 wyx wyy wyz wzu

  plusFM :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
plusFM EmptyFM fm2 = fm2
plusFM fm1 EmptyFM = fm1
plusFM fm1 (Branch split_key elt1 yx left right) = mkVBalBranch split_key elt1 (plusFM (plusFMLts fm1 split_key) left) (plusFM (plusFMGts fm1 split_key) right)

  
plusFMGts yuy yuz = splitGT yuy yuz

  
plusFMLts yuy yuz = splitLT yuy yuz

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

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM = Pos Zero
sizeFM (Branch xz yu size yv yw) = size

  splitGT :: Ord a => FiniteMap a b  ->  a  ->  FiniteMap a b
splitGT EmptyFM split_key = splitGT4 EmptyFM split_key
splitGT (Branch key elt xy fm_l fm_r) split_key = splitGT3 (Branch key elt xy fm_l fm_r) split_key

  
splitGT0 key elt xy fm_l fm_r split_key True = fm_r

  
splitGT1 key elt xy fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r
splitGT1 key elt xy fm_l fm_r split_key False = splitGT0 key elt xy fm_l fm_r split_key otherwise

  
splitGT2 key elt xy fm_l fm_r split_key True = splitGT fm_r split_key
splitGT2 key elt xy fm_l fm_r split_key False = splitGT1 key elt xy fm_l fm_r split_key (split_key < key)

  
splitGT3 (Branch key elt xy fm_l fm_r) split_key = splitGT2 key elt xy fm_l fm_r split_key (split_key > key)

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 wwz wxu = splitGT3 wwz wxu

  splitLT :: Ord a => FiniteMap a b  ->  a  ->  FiniteMap a b
splitLT EmptyFM split_key = splitLT4 EmptyFM split_key
splitLT (Branch key elt xx fm_l fm_r) split_key = splitLT3 (Branch key elt xx fm_l fm_r) split_key

  
splitLT0 key elt xx fm_l fm_r split_key True = fm_l

  
splitLT1 key elt xx fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key)
splitLT1 key elt xx fm_l fm_r split_key False = splitLT0 key elt xx fm_l fm_r split_key otherwise

  
splitLT2 key elt xx fm_l fm_r split_key True = splitLT fm_l split_key
splitLT2 key elt xx fm_l fm_r split_key False = splitLT1 key elt xx fm_l fm_r split_key (split_key > key)

  
splitLT3 (Branch key elt xx fm_l fm_r) split_key = splitLT2 key elt xx fm_l fm_r split_key (split_key < key)

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wwv www = splitLT3 wwv www

  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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primEqNat(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat(yvy40000, yvy30000)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primCmpNat(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat(yvy49000, yvy50000)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primMinusNat(Succ(yvy18900), Succ(yvy18800)) → new_primMinusNat(yvy18900, yvy18800)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primPlusNat(Succ(yvy15500), Succ(yvy3001000)) → new_primPlusNat(yvy15500, yvy3001000)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primMulNat(Succ(yvy400100), Succ(yvy300100)) → new_primMulNat(yvy400100, Succ(yvy300100))

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_esEs2(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs1(yvy4000, yvy3000, bcd, bce, bcf)
new_esEs3(:(yvy4000, yvy4001), :(yvy3000, yvy3001), app(app(ty_Either, bda), bdb)) → new_esEs(yvy4000, yvy3000, bda, bdb)
new_esEs3(:(yvy4000, yvy4001), :(yvy3000, yvy3001), app(app(ty_@2, bdc), bdd)) → new_esEs0(yvy4000, yvy3000, bdc, bdd)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), he, app(app(app(ty_@3, bab), bac), bad), ge) → new_esEs1(yvy4001, yvy3001, bab, bac, bad)
new_esEs3(:(yvy4000, yvy4001), :(yvy3000, yvy3001), app(ty_[], bea)) → new_esEs3(yvy4000, yvy3000, bea)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), he, gd, app(ty_[], bbg)) → new_esEs3(yvy4002, yvy3002, bbg)
new_esEs2(Just(yvy4000), Just(yvy3000), app(app(ty_Either, bbh), bca)) → new_esEs(yvy4000, yvy3000, bbh, bca)
new_esEs0(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), eg, app(app(app(ty_@3, fd), ff), fg)) → new_esEs1(yvy4001, yvy3001, fd, ff, fg)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), he, gd, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs1(yvy4002, yvy3002, bbc, bbd, bbe)
new_esEs(Right(yvy4000), Right(yvy3000), cb, app(app(ty_@2, ce), cf)) → new_esEs0(yvy4000, yvy3000, ce, cf)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), he, gd, app(app(ty_@2, bba), bbb)) → new_esEs0(yvy4002, yvy3002, bba, bbb)
new_esEs0(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), eg, app(ty_[], ga)) → new_esEs3(yvy4001, yvy3001, ga)
new_esEs2(Just(yvy4000), Just(yvy3000), app(ty_Maybe, bcg)) → new_esEs2(yvy4000, yvy3000, bcg)
new_esEs0(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), app(ty_[], ef), dg) → new_esEs3(yvy4000, yvy3000, ef)
new_esEs0(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), app(app(ty_Either, de), df), dg) → new_esEs(yvy4000, yvy3000, de, df)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), app(app(ty_@2, gf), gg), gd, ge) → new_esEs0(yvy4000, yvy3000, gf, gg)
new_esEs(Left(yvy4000), Left(yvy3000), app(ty_Maybe, bh), bb) → new_esEs2(yvy4000, yvy3000, bh)
new_esEs0(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), eg, app(app(ty_Either, eh), fa)) → new_esEs(yvy4001, yvy3001, eh, fa)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), app(ty_[], hd), gd, ge) → new_esEs3(yvy4000, yvy3000, hd)
new_esEs3(:(yvy4000, yvy4001), :(yvy3000, yvy3001), beb) → new_esEs3(yvy4001, yvy3001, beb)
new_esEs(Left(yvy4000), Left(yvy3000), app(ty_[], ca), bb) → new_esEs3(yvy4000, yvy3000, ca)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), he, app(ty_[], baf), ge) → new_esEs3(yvy4001, yvy3001, baf)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), app(app(app(ty_@3, gh), ha), hb), gd, ge) → new_esEs1(yvy4000, yvy3000, gh, ha, hb)
new_esEs(Right(yvy4000), Right(yvy3000), cb, app(app(app(ty_@3, cg), da), db)) → new_esEs1(yvy4000, yvy3000, cg, da, db)
new_esEs0(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), eg, app(ty_Maybe, fh)) → new_esEs2(yvy4001, yvy3001, fh)
new_esEs(Right(yvy4000), Right(yvy3000), cb, app(app(ty_Either, cc), cd)) → new_esEs(yvy4000, yvy3000, cc, cd)
new_esEs(Right(yvy4000), Right(yvy3000), cb, app(ty_[], dd)) → new_esEs3(yvy4000, yvy3000, dd)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), he, app(ty_Maybe, bae), ge) → new_esEs2(yvy4001, yvy3001, bae)
new_esEs(Left(yvy4000), Left(yvy3000), app(app(ty_@2, bc), bd), bb) → new_esEs0(yvy4000, yvy3000, bc, bd)
new_esEs0(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), app(ty_Maybe, ee), dg) → new_esEs2(yvy4000, yvy3000, ee)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), he, gd, app(app(ty_Either, bag), bah)) → new_esEs(yvy4002, yvy3002, bag, bah)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), he, gd, app(ty_Maybe, bbf)) → new_esEs2(yvy4002, yvy3002, bbf)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), he, app(app(ty_Either, hf), hg), ge) → new_esEs(yvy4001, yvy3001, hf, hg)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), app(app(ty_Either, gb), gc), gd, ge) → new_esEs(yvy4000, yvy3000, gb, gc)
new_esEs(Right(yvy4000), Right(yvy3000), cb, app(ty_Maybe, dc)) → new_esEs2(yvy4000, yvy3000, dc)
new_esEs0(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), app(app(ty_@2, dh), ea), dg) → new_esEs0(yvy4000, yvy3000, dh, ea)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), app(ty_Maybe, hc), gd, ge) → new_esEs2(yvy4000, yvy3000, hc)
new_esEs(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, be), bf), bg), bb) → new_esEs1(yvy4000, yvy3000, be, bf, bg)
new_esEs0(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), app(app(app(ty_@3, eb), ec), ed), dg) → new_esEs1(yvy4000, yvy3000, eb, ec, ed)
new_esEs1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), he, app(app(ty_@2, hh), baa), ge) → new_esEs0(yvy4001, yvy3001, hh, baa)
new_esEs0(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), eg, app(app(ty_@2, fb), fc)) → new_esEs0(yvy4001, yvy3001, fb, fc)
new_esEs3(:(yvy4000, yvy4001), :(yvy3000, yvy3001), app(ty_Maybe, bdh)) → new_esEs2(yvy4000, yvy3000, bdh)
new_esEs3(:(yvy4000, yvy4001), :(yvy3000, yvy3001), app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs1(yvy4000, yvy3000, bde, bdf, bdg)
new_esEs(Left(yvy4000), Left(yvy3000), app(app(ty_Either, h), ba), bb) → new_esEs(yvy4000, yvy3000, h, ba)
new_esEs2(Just(yvy4000), Just(yvy3000), app(app(ty_@2, bcb), bcc)) → new_esEs0(yvy4000, yvy3000, bcb, bcc)
new_esEs2(Just(yvy4000), Just(yvy3000), app(ty_[], bch)) → new_esEs3(yvy4000, yvy3000, bch)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_ltEs1(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), ef, app(app(ty_@2, fb), fc)) → new_ltEs1(yvy49001, yvy50001, fb, fc)
new_ltEs0(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, cg), da), db), cb) → new_ltEs2(yvy49000, yvy50000, cg, da, db)
new_compare2(Just(Left(yvy49000)), Just(Left(yvy50000)), False, app(app(ty_Either, app(app(ty_@2, ce), cf)), cb)) → new_ltEs1(yvy49000, yvy50000, ce, cf)
new_ltEs(Just(yvy49000), Just(yvy50000), app(app(ty_Either, ba), bb)) → new_ltEs0(yvy49000, yvy50000, ba, bb)
new_compare2(Just(Left(yvy49000)), Just(Left(yvy50000)), False, app(app(ty_Either, app(app(ty_Either, cc), cd)), cb)) → new_ltEs0(yvy49000, yvy50000, cc, cd)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), hc, app(app(app(ty_@3, bbd), bbe), bbf), bag) → new_lt2(yvy49001, yvy50001, bbd, bbe, bbf)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), hc, app(ty_[], bbg), bag) → new_lt3(yvy49001, yvy50001, bbg)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, hc), app(app(app(ty_@3, bbd), bbe), bbf)), bag)) → new_lt2(yvy49001, yvy50001, bbd, bbe, bbf)
new_compare2(Just(@2(yvy49000, yvy49001)), Just(@2(yvy50000, yvy50001)), False, app(app(ty_@2, ef), app(ty_[], fh))) → new_ltEs3(yvy49001, yvy50001, fh)
new_ltEs1(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), ef, app(ty_[], fh)) → new_ltEs3(yvy49001, yvy50001, fh)
new_ltEs3(:(yvy49000, yvy49001), :(yvy50000, yvy50001), bda) → new_compare(yvy49001, yvy50001, bda)
new_primCompAux(yvy49000, yvy50000, yvy202, app(ty_[], beb)) → new_compare(yvy49000, yvy50000, beb)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, hc), hd), app(ty_Maybe, he))) → new_ltEs(yvy49002, yvy50002, he)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), hc, hd, app(ty_Maybe, he)) → new_ltEs(yvy49002, yvy50002, he)
new_lt0(yvy49000, yvy50000, gc, gd) → new_compare20(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, gc, gd), gc, gd)
new_ltEs1(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), ef, app(ty_Maybe, eg)) → new_ltEs(yvy49001, yvy50001, eg)
new_compare2(Just(:(yvy49000, yvy49001)), Just(:(yvy50000, yvy50001)), False, app(ty_[], bda)) → new_primCompAux(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, bda), bda)
new_ltEs1(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), app(ty_[], hb), gb) → new_compare(yvy49000, yvy50000, hb)
new_compare2(Just(@2(yvy49000, yvy49001)), Just(@2(yvy50000, yvy50001)), False, app(app(ty_@2, ef), app(app(ty_@2, fb), fc))) → new_ltEs1(yvy49001, yvy50001, fb, fc)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), hc, hd, app(ty_[], bae)) → new_ltEs3(yvy49002, yvy50002, bae)
new_lt1(yvy49000, yvy50000, ge, gf) → new_compare21(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, ge, gf), ge, gf)
new_compare2(Just(@2(yvy49000, yvy49001)), Just(@2(yvy50000, yvy50001)), False, app(app(ty_@2, ef), app(ty_Maybe, eg))) → new_ltEs(yvy49001, yvy50001, eg)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), hc, hd, app(app(ty_@2, hh), baa)) → new_ltEs1(yvy49002, yvy50002, hh, baa)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, hc), hd), app(app(ty_@2, hh), baa))) → new_ltEs1(yvy49002, yvy50002, hh, baa)
new_ltEs0(Right(yvy49000), Right(yvy50000), dd, app(app(ty_Either, df), dg)) → new_ltEs0(yvy49000, yvy50000, df, dg)
new_ltEs0(Right(yvy49000), Right(yvy50000), dd, app(ty_[], ee)) → new_ltEs3(yvy49000, yvy50000, ee)
new_ltEs0(Right(yvy49000), Right(yvy50000), dd, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs2(yvy49000, yvy50000, eb, ec, ed)
new_ltEs1(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), ef, app(app(app(ty_@3, fd), ff), fg)) → new_ltEs2(yvy49001, yvy50001, fd, ff, fg)
new_ltEs(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, be), bf), bg)) → new_ltEs2(yvy49000, yvy50000, be, bf, bg)
new_primCompAux(yvy49000, yvy50000, yvy202, app(app(app(ty_@3, bdg), bdh), bea)) → new_compare5(yvy49000, yvy50000, bdg, bdh, bea)
new_ltEs0(Right(yvy49000), Right(yvy50000), dd, app(ty_Maybe, de)) → new_ltEs(yvy49000, yvy50000, de)
new_compare2(Just(Just(yvy49000)), Just(Just(yvy50000)), False, app(ty_Maybe, app(app(ty_Either, ba), bb))) → new_ltEs0(yvy49000, yvy50000, ba, bb)
new_primCompAux(yvy49000, yvy50000, yvy202, app(ty_Maybe, bdb)) → new_compare1(yvy49000, yvy50000, bdb)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, app(app(ty_Either, bca), bcb)), hd), bag)) → new_lt0(yvy49000, yvy50000, bca, bcb)
new_primCompAux(yvy49000, yvy50000, yvy202, app(app(ty_Either, bdc), bdd)) → new_compare3(yvy49000, yvy50000, bdc, bdd)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), hc, app(ty_Maybe, baf), bag) → new_lt(yvy49001, yvy50001, baf)
new_compare2(Just(Just(yvy49000)), Just(Just(yvy50000)), False, app(ty_Maybe, app(ty_Maybe, h))) → new_ltEs(yvy49000, yvy50000, h)
new_compare2(Just(Left(yvy49000)), Just(Left(yvy50000)), False, app(app(ty_Either, app(ty_[], dc)), cb)) → new_ltEs3(yvy49000, yvy50000, dc)
new_compare2(Just(:(yvy49000, yvy49001)), Just(:(yvy50000, yvy50001)), False, app(ty_[], bda)) → new_compare(yvy49001, yvy50001, bda)
new_ltEs1(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), ef, app(app(ty_Either, eh), fa)) → new_ltEs0(yvy49001, yvy50001, eh, fa)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, hc), app(app(ty_Either, bah), bba)), bag)) → new_lt0(yvy49001, yvy50001, bah, bba)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, hc), hd), app(app(app(ty_@3, bab), bac), bad))) → new_ltEs2(yvy49002, yvy50002, bab, bac, bad)
new_compare2(Just(Right(yvy49000)), Just(Right(yvy50000)), False, app(app(ty_Either, dd), app(app(ty_Either, df), dg))) → new_ltEs0(yvy49000, yvy50000, df, dg)
new_compare4(yvy49000, yvy50000, ge, gf) → new_compare21(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, ge, gf), ge, gf)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), hc, app(app(ty_Either, bah), bba), bag) → new_lt0(yvy49001, yvy50001, bah, bba)
new_compare22(yvy49000, yvy50000, False, gg, gh, ha) → new_ltEs2(yvy49000, yvy50000, gg, gh, ha)
new_compare2(Just(Right(yvy49000)), Just(Right(yvy50000)), False, app(app(ty_Either, dd), app(ty_Maybe, de))) → new_ltEs(yvy49000, yvy50000, de)
new_compare2(Just(Left(yvy49000)), Just(Left(yvy50000)), False, app(app(ty_Either, app(app(app(ty_@3, cg), da), db)), cb)) → new_ltEs2(yvy49000, yvy50000, cg, da, db)
new_compare2(Just(Left(yvy49000)), Just(Left(yvy50000)), False, app(app(ty_Either, app(ty_Maybe, ca)), cb)) → new_ltEs(yvy49000, yvy50000, ca)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, app(app(ty_@2, bcc), bcd)), hd), bag)) → new_lt1(yvy49000, yvy50000, bcc, bcd)
new_ltEs0(Left(yvy49000), Left(yvy50000), app(ty_[], dc), cb) → new_ltEs3(yvy49000, yvy50000, dc)
new_ltEs0(Left(yvy49000), Left(yvy50000), app(app(ty_@2, ce), cf), cb) → new_ltEs1(yvy49000, yvy50000, ce, cf)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, hc), app(ty_Maybe, baf)), bag)) → new_lt(yvy49001, yvy50001, baf)
new_compare2(Just(Just(yvy49000)), Just(Just(yvy50000)), False, app(ty_Maybe, app(app(ty_@2, bc), bd))) → new_ltEs1(yvy49000, yvy50000, bc, bd)
new_compare2(Just(Right(yvy49000)), Just(Right(yvy50000)), False, app(app(ty_Either, dd), app(app(app(ty_@3, eb), ec), ed))) → new_ltEs2(yvy49000, yvy50000, eb, ec, ed)
new_compare1(yvy49000, yvy50000, ga) → new_compare2(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, ga), ga)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), hc, hd, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs2(yvy49002, yvy50002, bab, bac, bad)
new_ltEs1(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), app(ty_Maybe, ga), gb) → new_compare2(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, ga), ga)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), app(app(ty_@2, bcc), bcd), hd, bag) → new_lt1(yvy49000, yvy50000, bcc, bcd)
new_compare5(yvy49000, yvy50000, gg, gh, ha) → new_compare22(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, gg, gh, ha), gg, gh, ha)
new_compare2(Just(Just(yvy49000)), Just(Just(yvy50000)), False, app(ty_Maybe, app(app(app(ty_@3, be), bf), bg))) → new_ltEs2(yvy49000, yvy50000, be, bf, bg)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), app(ty_[], bch), hd, bag) → new_lt3(yvy49000, yvy50000, bch)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, app(ty_[], bch)), hd), bag)) → new_lt3(yvy49000, yvy50000, bch)
new_compare3(yvy49000, yvy50000, gc, gd) → new_compare20(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, gc, gd), gc, gd)
new_ltEs1(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), app(app(ty_@2, ge), gf), gb) → new_compare21(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, ge, gf), ge, gf)
new_compare2(Just(@2(yvy49000, yvy49001)), Just(@2(yvy50000, yvy50001)), False, app(app(ty_@2, app(ty_[], hb)), gb)) → new_compare(yvy49000, yvy50000, hb)
new_ltEs0(Right(yvy49000), Right(yvy50000), dd, app(app(ty_@2, dh), ea)) → new_ltEs1(yvy49000, yvy50000, dh, ea)
new_compare2(Just(Right(yvy49000)), Just(Right(yvy50000)), False, app(app(ty_Either, dd), app(app(ty_@2, dh), ea))) → new_ltEs1(yvy49000, yvy50000, dh, ea)
new_ltEs0(Left(yvy49000), Left(yvy50000), app(app(ty_Either, cc), cd), cb) → new_ltEs0(yvy49000, yvy50000, cc, cd)
new_lt(yvy49000, yvy50000, ga) → new_compare2(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, ga), ga)
new_ltEs(Just(yvy49000), Just(yvy50000), app(ty_Maybe, h)) → new_ltEs(yvy49000, yvy50000, h)
new_compare2(Just(@2(yvy49000, yvy49001)), Just(@2(yvy50000, yvy50001)), False, app(app(ty_@2, ef), app(app(ty_Either, eh), fa))) → new_ltEs0(yvy49001, yvy50001, eh, fa)
new_compare2(Just(Just(yvy49000)), Just(Just(yvy50000)), False, app(ty_Maybe, app(ty_[], bh))) → new_ltEs3(yvy49000, yvy50000, bh)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, hc), app(ty_[], bbg)), bag)) → new_lt3(yvy49001, yvy50001, bbg)
new_compare2(Just(@2(yvy49000, yvy49001)), Just(@2(yvy50000, yvy50001)), False, app(app(ty_@2, ef), app(app(app(ty_@3, fd), ff), fg))) → new_ltEs2(yvy49001, yvy50001, fd, ff, fg)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, hc), app(app(ty_@2, bbb), bbc)), bag)) → new_lt1(yvy49001, yvy50001, bbb, bbc)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, app(app(app(ty_@3, bce), bcf), bcg)), hd), bag)) → new_lt2(yvy49000, yvy50000, bce, bcf, bcg)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, hc), hd), app(ty_[], bae))) → new_ltEs3(yvy49002, yvy50002, bae)
new_ltEs(Just(yvy49000), Just(yvy50000), app(ty_[], bh)) → new_ltEs3(yvy49000, yvy50000, bh)
new_compare2(Just(@2(yvy49000, yvy49001)), Just(@2(yvy50000, yvy50001)), False, app(app(ty_@2, app(app(ty_Either, gc), gd)), gb)) → new_compare20(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, gc, gd), gc, gd)
new_compare20(yvy49000, yvy50000, False, gc, gd) → new_ltEs0(yvy49000, yvy50000, gc, gd)
new_compare21(yvy49000, yvy50000, False, ge, gf) → new_ltEs1(yvy49000, yvy50000, ge, gf)
new_ltEs1(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), app(app(app(ty_@3, gg), gh), ha), gb) → new_compare22(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, gg, gh, ha), gg, gh, ha)
new_compare2(Just(Right(yvy49000)), Just(Right(yvy50000)), False, app(app(ty_Either, dd), app(ty_[], ee))) → new_ltEs3(yvy49000, yvy50000, ee)
new_ltEs0(Left(yvy49000), Left(yvy50000), app(ty_Maybe, ca), cb) → new_ltEs(yvy49000, yvy50000, ca)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), hc, app(app(ty_@2, bbb), bbc), bag) → new_lt1(yvy49001, yvy50001, bbb, bbc)
new_compare2(Just(@2(yvy49000, yvy49001)), Just(@2(yvy50000, yvy50001)), False, app(app(ty_@2, app(app(ty_@2, ge), gf)), gb)) → new_compare21(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, ge, gf), ge, gf)
new_compare2(Just(@2(yvy49000, yvy49001)), Just(@2(yvy50000, yvy50001)), False, app(app(ty_@2, app(ty_Maybe, ga)), gb)) → new_compare2(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, ga), ga)
new_ltEs1(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), app(app(ty_Either, gc), gd), gb) → new_compare20(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, gc, gd), gc, gd)
new_ltEs(Just(yvy49000), Just(yvy50000), app(app(ty_@2, bc), bd)) → new_ltEs1(yvy49000, yvy50000, bc, bd)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), app(app(ty_Either, bca), bcb), hd, bag) → new_lt0(yvy49000, yvy50000, bca, bcb)
new_compare(:(yvy49000, yvy49001), :(yvy50000, yvy50001), bda) → new_compare(yvy49001, yvy50001, bda)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), app(ty_Maybe, bbh), hd, bag) → new_lt(yvy49000, yvy50000, bbh)
new_lt3(yvy49000, yvy50000, hb) → new_compare(yvy49000, yvy50000, hb)
new_ltEs3(:(yvy49000, yvy49001), :(yvy50000, yvy50001), bda) → new_primCompAux(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, bda), bda)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, hc), hd), app(app(ty_Either, hf), hg))) → new_ltEs0(yvy49002, yvy50002, hf, hg)
new_compare(:(yvy49000, yvy49001), :(yvy50000, yvy50001), bda) → new_primCompAux(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, bda), bda)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), app(app(app(ty_@3, bce), bcf), bcg), hd, bag) → new_lt2(yvy49000, yvy50000, bce, bcf, bcg)
new_primCompAux(yvy49000, yvy50000, yvy202, app(app(ty_@2, bde), bdf)) → new_compare4(yvy49000, yvy50000, bde, bdf)
new_ltEs2(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), hc, hd, app(app(ty_Either, hf), hg)) → new_ltEs0(yvy49002, yvy50002, hf, hg)
new_compare2(Just(@2(yvy49000, yvy49001)), Just(@2(yvy50000, yvy50001)), False, app(app(ty_@2, app(app(app(ty_@3, gg), gh), ha)), gb)) → new_compare22(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, gg, gh, ha), gg, gh, ha)
new_lt2(yvy49000, yvy50000, gg, gh, ha) → new_compare22(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, gg, gh, ha), gg, gh, ha)
new_compare2(Just(@3(yvy49000, yvy49001, yvy49002)), Just(@3(yvy50000, yvy50001, yvy50002)), False, app(app(app(ty_@3, app(ty_Maybe, bbh)), hd), bag)) → new_lt(yvy49000, yvy50000, bbh)

The TRS R consists of the following rules:

new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, bfe)) → new_esEs4(yvy4000, yvy3000, bfe)
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, ef), gb)) → new_ltEs5(yvy4900, yvy5000, ef, gb)
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, cdc), cdd)) → new_esEs5(yvy4000, yvy3000, cdc, cdd)
new_esEs28(yvy4000, yvy3000, app(ty_[], dcc)) → new_esEs19(yvy4000, yvy3000, dcc)
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, bhb), bhc)) → new_esEs6(yvy4000, yvy3000, bhb, bhc)
new_primCmpNat2(Zero, yvy4900) → LT
new_ltEs8(False, True) → True
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, ce), cf), cb) → new_ltEs5(yvy49000, yvy50000, ce, cf)
new_esEs22(yvy4001, yvy3001, app(ty_[], cbc)) → new_esEs19(yvy4001, yvy3001, cbc)
new_ltEs18(EQ, GT) → True
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_ltEs10(Left(yvy49000), Right(yvy50000), dd, cb) → True
new_compare110(yvy49000, yvy50000, True, ge, gf) → LT
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, cbd), cbe)) → new_esEs5(yvy4002, yvy3002, cbd, cbe)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_compare24(yvy49000, yvy50000, False, gg, gh, ha) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, gg, gh, ha), gg, gh, ha)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cec)) → new_esEs4(yvy4000, yvy3000, cec)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, bfh)) → new_ltEs17(yvy49001, yvy50001, bfh)
new_esEs4(Just(yvy4000), Nothing, bed) → False
new_esEs4(Nothing, Just(yvy3000), bed) → False
new_ltEs9(Nothing, Just(yvy50000), bgc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], che), cgc) → new_esEs19(yvy4000, yvy3000, che)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_primMulNat0(Zero, Zero) → Zero
new_compare26(Just(yvy4900), Nothing, False, cfg) → GT
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, cfh)) → new_esEs10(yvy49000, yvy50000, cfh)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, dbf)) → new_esEs10(yvy4000, yvy3000, dbf)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, ga)) → new_esEs4(yvy49000, yvy50000, ga)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, cgc) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_[], bch)) → new_esEs19(yvy49000, yvy50000, bch)
new_compare16(@0, @0) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, ccd)) → new_esEs4(yvy4002, yvy3002, ccd)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_compare26(Nothing, Just(yvy5000), False, cfg) → LT
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), bda) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, bda), bda)
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, app(ty_[], ee)) → new_ltEs14(yvy49000, yvy50000, ee)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs7(yvy4000, yvy3000, bhe, bhf, bhg)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, cb) → new_ltEs12(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, bbh)) → new_esEs4(yvy49000, yvy50000, bbh)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, ge), gf)) → new_esEs6(yvy49000, yvy50000, ge, gf)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_compare18(yvy49000, yvy50000, ge, gf) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, ge, gf), ge, gf)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_pePe(False, yvy201) → yvy201
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_compare23(yvy49000, yvy50000, False, gc, gd) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, gc, gd), gc, gd)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_compare26(Nothing, Nothing, False, cfg) → LT
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cga)) → new_lt17(yvy49001, yvy50001, cga)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, cb) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, cg), da), db), cb) → new_ltEs13(yvy49000, yvy50000, cg, da, db)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, cc), cd), cb) → new_ltEs10(yvy49000, yvy50000, cc, cd)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fd), ff), fg)) → new_ltEs13(yvy49001, yvy50001, fd, ff, fg)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, baf)) → new_lt10(yvy49001, yvy50001, baf)
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, cgf), cgg), cgc) → new_esEs6(yvy4000, yvy3000, cgf, cgg)
new_esEs24(yvy4000, yvy3000, app(ty_[], ced)) → new_esEs19(yvy4000, yvy3000, ced)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, chd), cgc) → new_esEs4(yvy4000, yvy3000, chd)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, bc), bd)) → new_ltEs5(yvy49000, yvy50000, bc, bd)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, app(app(ty_@2, dh), ea)) → new_ltEs5(yvy49000, yvy50000, dh, ea)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, cca), ccb), ccc)) → new_esEs7(yvy4002, yvy3002, cca, ccb, ccc)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, bbd), bbe), bbf)) → new_esEs7(yvy49001, yvy50001, bbd, bbe, bbf)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, bce), bcf), bcg)) → new_lt14(yvy49000, yvy50000, bce, bcf, bcg)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cee), cef)) → new_esEs5(yvy4001, yvy3001, cee, cef)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, ceg), ceh)) → new_esEs6(yvy4001, yvy3001, ceg, ceh)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, eg)) → new_ltEs9(yvy49001, yvy50001, eg)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, bgd)) → new_ltEs17(yvy49000, yvy50000, bgd)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, dd), cb)) → new_ltEs10(yvy4900, yvy5000, dd, cb)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), ef, gb) → new_pePe(new_lt6(yvy49000, yvy50000, ef), new_asAs(new_esEs20(yvy49000, yvy50000, ef), new_ltEs6(yvy49001, yvy50001, gb)))
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, he)) → new_ltEs9(yvy49002, yvy50002, he)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, cde), cdf)) → new_esEs6(yvy4000, yvy3000, cde, cdf)
new_compare0([], [], bda) → EQ
new_pePe(True, yvy201) → True
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_primEqNat0(Zero, Zero) → True
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, cb) → new_ltEs11(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), chf, app(app(ty_@2, daa), dab)) → new_esEs6(yvy4000, yvy3000, daa, dab)
new_ltEs14(yvy4900, yvy5000, bda) → new_fsEs(new_compare0(yvy4900, yvy5000, bda))
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, eh), fa)) → new_ltEs10(yvy49001, yvy50001, eh, fa)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_ltEs18(EQ, EQ) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, cgc) → new_esEs9(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_esEs19([], [], dba) → True
new_compare110(yvy49000, yvy50000, False, ge, gf) → GT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, bfa)) → new_esEs10(yvy4000, yvy3000, bfa)
new_esEs25(yvy4001, yvy3001, app(ty_[], cff)) → new_esEs19(yvy4001, yvy3001, cff)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_compare12(yvy49000, yvy50000, False, gc, gd) → GT
new_primCmpNat1(Zero, Zero) → EQ
new_primCompAux0(yvy49000, yvy50000, yvy202, bda) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, bda))
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs18(LT, LT) → True
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, cgc) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, gg), gh), ha)) → new_esEs7(yvy49000, yvy50000, gg, gh, ha)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, gc), gd)) → new_lt11(yvy49000, yvy50000, gc, gd)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, bgc)) → new_ltEs9(yvy4900, yvy5000, bgc)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs19(:(yvy4000, yvy4001), [], dba) → False
new_esEs19([], :(yvy3000, yvy3001), dba) → False
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_ltEs18(GT, GT) → True
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(EQ, EQ) → True
new_compare24(yvy49000, yvy50000, True, gg, gh, ha) → EQ
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, cb) → new_ltEs18(yvy49000, yvy50000)
new_esEs15(True, True) → True
new_ltEs18(LT, GT) → True
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, bgb)) → new_ltEs17(yvy4900, yvy5000, bgb)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, cfa)) → new_esEs10(yvy4001, yvy3001, cfa)
new_ltEs8(True, True) → True
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs7(yvy49000, yvy50000, bce, bcf, bcg)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, dcb)) → new_esEs4(yvy4000, yvy3000, dcb)
new_ltEs18(GT, LT) → False
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, cha), chb), chc), cgc) → new_esEs7(yvy4000, yvy3000, cha, chb, chc)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_lt14(yvy49000, yvy50000, gg, gh, ha) → new_esEs9(new_compare14(yvy49000, yvy50000, gg, gh, ha), LT)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, bah), bba)) → new_esEs5(yvy49001, yvy50001, bah, bba)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cgb)) → new_ltEs17(yvy49002, yvy50002, cgb)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, ba), bb)) → new_ltEs10(yvy49000, yvy50000, ba, bb)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], bh)) → new_ltEs14(yvy49000, yvy50000, bh)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], caa)) → new_esEs19(yvy4000, yvy3000, caa)
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, hh), baa)) → new_ltEs5(yvy49002, yvy50002, hh, baa)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), chf, app(ty_[], dah)) → new_esEs19(yvy4000, yvy3000, dah)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, cbb)) → new_esEs4(yvy4001, yvy3001, cbb)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, cfe)) → new_esEs4(yvy4001, yvy3001, cfe)
new_compare112(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), cda, cdb) → new_asAs(new_esEs24(yvy4000, yvy3000, cda), new_esEs25(yvy4001, yvy3001, cdb))
new_lt19(yvy49001, yvy50001, app(app(ty_@2, bbb), bbc)) → new_lt12(yvy49001, yvy50001, bbb, bbc)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare12(yvy49000, yvy50000, True, gc, gd) → LT
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_esEs5(Right(yvy4000), Right(yvy3000), chf, app(app(ty_Either, chg), chh)) → new_esEs5(yvy4000, yvy3000, chg, chh)
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs13(yvy49000, yvy50000, eb, ec, ed)
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_ltEs19(yvy4900, yvy5000, app(ty_[], bda)) → new_ltEs14(yvy4900, yvy5000, bda)
new_esEs5(Right(yvy4000), Right(yvy3000), chf, app(ty_Ratio, dac)) → new_esEs10(yvy4000, yvy3000, dac)
new_compare111(yvy49000, yvy50000, True, gg, gh, ha) → LT
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_primCompAux00(yvy206, LT) → LT
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, app(app(ty_Either, df), dg)) → new_ltEs10(yvy49000, yvy50000, df, dg)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, cgc) → new_esEs14(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, cfh)) → new_lt17(yvy49000, yvy50000, cfh)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare13(yvy175, yvy176, True, bga) → LT
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs23(yvy4002, yvy3002, app(ty_[], cce)) → new_esEs19(yvy4002, yvy3002, cce)
new_lt15(yvy49000, yvy50000, hb) → new_esEs9(new_compare0(yvy49000, yvy50000, hb), LT)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, bfg)) → new_lt17(yvy49000, yvy50000, bfg)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, h)) → new_ltEs9(yvy49000, yvy50000, h)
new_compare14(yvy49000, yvy50000, gg, gh, ha) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, gg, gh, ha), gg, gh, ha)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, bee), bef)) → new_esEs5(yvy4000, yvy3000, bee, bef)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, gc), gd)) → new_esEs5(yvy49000, yvy50000, gc, gd)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_esEs5(Right(yvy4000), Right(yvy3000), chf, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_ltEs20(yvy49002, yvy50002, app(ty_[], bae)) → new_ltEs14(yvy49002, yvy50002, bae)
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dbb), dbc)) → new_esEs5(yvy4000, yvy3000, dbb, dbc)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, beg), beh)) → new_esEs6(yvy4000, yvy3000, beg, beh)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, cad), cae)) → new_esEs6(yvy4001, yvy3001, cad, cae)
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_compare28(yvy49000, yvy50000, app(ty_[], beb)) → new_compare0(yvy49000, yvy50000, beb)
new_ltEs9(Just(yvy49000), Nothing, bgc) → False
new_primCompAux00(yvy206, EQ) → yvy206
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, cgc) → new_esEs15(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, cbh)) → new_esEs10(yvy4002, yvy3002, cbh)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, cgc) → new_esEs8(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_compare26(Just(yvy4900), Just(yvy5000), False, cfg) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, cfg), cfg)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bdg), bdh), bea)) → new_compare14(yvy49000, yvy50000, bdg, bdh, bea)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, hc), hd), bag)) → new_ltEs13(yvy4900, yvy5000, hc, hd, bag)
new_compare26(yvy490, yvy500, True, cfg) → EQ
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs18(GT, EQ) → False
new_compare17(yvy49000, yvy50000, gc, gd) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, gc, gd), gc, gd)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, cb) → new_ltEs16(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, bfg)) → new_esEs10(yvy49000, yvy50000, bfg)
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, cbf), cbg)) → new_esEs6(yvy4002, yvy3002, cbf, cbg)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, bgc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, cgc) → new_esEs17(yvy4000, yvy3000)
new_esEs9(GT, GT) → True
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bdb)) → new_compare19(yvy49000, yvy50000, bdb)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, cb) → new_ltEs15(yvy49000, yvy50000)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs18(EQ, LT) → False
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_compare0(:(yvy49000, yvy49001), [], bda) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), chf, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_ltEs18(LT, EQ) → True
new_esEs5(Right(yvy4000), Right(yvy3000), chf, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, bca), bcb)) → new_esEs5(yvy49000, yvy50000, bca, bcb)
new_lt6(yvy49000, yvy50000, app(ty_[], hb)) → new_lt15(yvy49000, yvy50000, hb)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fh)) → new_ltEs14(yvy49001, yvy50001, fh)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, cag), cah), cba)) → new_esEs7(yvy4001, yvy3001, cag, cah, cba)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, bbd), bbe), bbf)) → new_lt14(yvy49001, yvy50001, bbd, bbe, bbf)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, ga)) → new_lt10(yvy49000, yvy50000, ga)
new_lt19(yvy49001, yvy50001, app(ty_[], bbg)) → new_lt15(yvy49001, yvy50001, bbg)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, dbg), dbh), dca)) → new_esEs7(yvy4000, yvy3000, dbg, dbh, dca)
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), bge, bgf, bgg) → new_asAs(new_esEs21(yvy4000, yvy3000, bge), new_asAs(new_esEs22(yvy4001, yvy3001, bgf), new_esEs23(yvy4002, yvy3002, bgg)))
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs5(Left(yvy4000), Right(yvy3000), chf, cgc) → False
new_esEs5(Right(yvy4000), Left(yvy3000), chf, cgc) → False
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, bbb), bbc)) → new_esEs6(yvy49001, yvy50001, bbb, bbc)
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bhd)) → new_esEs10(yvy4000, yvy3000, bhd)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_ltEs8(False, False) → True
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_compare19(yvy49000, yvy50000, ga) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, ga), ga)
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, app(app(ty_@2, bcc), bcd)) → new_lt12(yvy49000, yvy50000, bcc, bcd)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, be), bf), bg)) → new_ltEs13(yvy49000, yvy50000, be, bf, bg)
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_compare25(yvy49000, yvy50000, True, ge, gf) → EQ
new_lt19(yvy49001, yvy50001, app(app(ty_Either, bah), bba)) → new_lt11(yvy49001, yvy50001, bah, bba)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, bbh)) → new_lt10(yvy49000, yvy50000, bbh)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, bed) → True
new_compare111(yvy49000, yvy50000, False, gg, gh, ha) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_compare210(yvy49000, yvy50000, True) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, cb) → new_ltEs7(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, baf)) → new_esEs4(yvy49001, yvy50001, baf)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, hf), hg)) → new_ltEs10(yvy49002, yvy50002, hf, hg)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bdc), bdd)) → new_compare17(yvy49000, yvy50000, bdc, bdd)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, bca), bcb)) → new_lt11(yvy49000, yvy50000, bca, bcb)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cga)) → new_esEs10(yvy49001, yvy50001, cga)
new_compare13(yvy175, yvy176, False, bga) → GT
new_compare23(yvy49000, yvy50000, True, gc, gd) → EQ
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], dc), cb) → new_ltEs14(yvy49000, yvy50000, dc)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), chf, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, cgc) → new_esEs13(yvy4000, yvy3000)
new_lt17(yvy49000, yvy50000, bfg) → new_esEs9(new_compare8(yvy49000, yvy50000, bfg), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), chf, app(app(app(ty_@3, dad), dae), daf)) → new_esEs7(yvy4000, yvy3000, dad, dae, daf)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs13(yvy49002, yvy50002, bab, bac, bad)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, dbd), dbe)) → new_esEs6(yvy4000, yvy3000, dbd, dbe)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bhh)) → new_esEs4(yvy4000, yvy3000, bhh)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, fb), fc)) → new_ltEs5(yvy49001, yvy50001, fb, fc)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, ca), cb) → new_ltEs9(yvy49000, yvy50000, ca)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, gg), gh), ha)) → new_lt14(yvy49000, yvy50000, gg, gh, ha)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, cdh), cea), ceb)) → new_esEs7(yvy4000, yvy3000, cdh, cea, ceb)
new_lt20(yvy49000, yvy50000, app(ty_[], bch)) → new_lt15(yvy49000, yvy50000, bch)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt12(yvy49000, yvy50000, ge, gf) → new_esEs9(new_compare18(yvy49000, yvy50000, ge, gf), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bec) → new_asAs(new_esEs11(yvy4000, yvy3000, bec), new_esEs12(yvy4001, yvy3001, bec))
new_asAs(False, yvy182) → False
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, bgh), bha)) → new_esEs5(yvy4000, yvy3000, bgh, bha)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_lt10(yvy49000, yvy50000, ga) → new_esEs9(new_compare19(yvy49000, yvy50000, ga), LT)
new_compare25(yvy49000, yvy50000, False, ge, gf) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, ge, gf), ge, gf)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, cch)) → new_compare8(yvy49000, yvy50000, cch)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_esEs5(Right(yvy4000), Right(yvy3000), chf, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), hc, hd, bag) → new_pePe(new_lt20(yvy49000, yvy50000, hc), new_asAs(new_esEs26(yvy49000, yvy50000, hc), new_pePe(new_lt19(yvy49001, yvy50001, hd), new_asAs(new_esEs27(yvy49001, yvy50001, hd), new_ltEs20(yvy49002, yvy50002, bag)))))
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), chf, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cdg)) → new_esEs10(yvy4000, yvy3000, cdg)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, app(ty_Ratio, ccg)) → new_ltEs17(yvy49000, yvy50000, ccg)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, caf)) → new_esEs10(yvy4001, yvy3001, caf)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs7(yvy4001, yvy3001, cfb, cfc, cfd)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), chf, app(ty_Maybe, dag)) → new_esEs4(yvy4000, yvy3000, dag)
new_esEs5(Right(yvy4000), Right(yvy3000), chf, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare11(yvy49000, yvy50000, False) → GT
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Left(yvy50000), dd, cb) → False
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_compare11(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], bff)) → new_esEs19(yvy4000, yvy3000, bff)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, cgd), cge), cgc) → new_esEs5(yvy4000, yvy3000, cgd, cge)
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, app(ty_Maybe, de)) → new_ltEs9(yvy49000, yvy50000, de)
new_compare112(yvy49000, yvy50000, False) → GT
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(ty_[], hb)) → new_esEs19(yvy49000, yvy50000, hb)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), dd, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], bbg)) → new_esEs19(yvy49001, yvy50001, bbg)
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy50000, yvy50001), bda) → LT
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_asAs(True, yvy182) → yvy182
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_esEs18(@0, @0) → True
new_compare211(yvy49000, yvy50000, True) → EQ
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, bcc), bcd)) → new_esEs6(yvy49000, yvy50000, bcc, bcd)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), chf, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, bfb), bfc), bfd)) → new_esEs7(yvy4000, yvy3000, bfb, bfc, bfd)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, cgh), cgc) → new_esEs10(yvy4000, yvy3000, cgh)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, ccf), cb) → new_ltEs17(yvy49000, yvy50000, ccf)
new_lt11(yvy49000, yvy50000, gc, gd) → new_esEs9(new_compare17(yvy49000, yvy50000, gc, gd), LT)
new_esEs9(LT, LT) → True
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), dba) → new_asAs(new_esEs28(yvy4000, yvy3000, dba), new_esEs19(yvy4001, yvy3001, dba))
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, cab), cac)) → new_esEs5(yvy4001, yvy3001, cab, cac)
new_primCompAux00(yvy206, GT) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, cb) → new_ltEs8(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(yvy49000, yvy50000, app(app(ty_@2, ge), gf)) → new_lt12(yvy49000, yvy50000, ge, gf)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bde), bdf)) → new_compare18(yvy49000, yvy50000, bde, bdf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_ltEs17(yvy4900, yvy5000, bgb) → new_fsEs(new_compare8(yvy4900, yvy5000, bgb))
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_compare110(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_@0)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(@0, @0)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primCompAux0(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Nothing, x1)
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, False)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt6(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_compare9(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs15(True, True)
new_compare19(x0, x1, x2)
new_primCmpNat0(x0, Zero)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_lt6(x0, x1, ty_@0)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_@0)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt13(x0, x1)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_compare111(x0, x1, False, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_compare24(x0, x1, True, x2, x3, x4)
new_lt6(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_ltEs6(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs25(x0, x1, ty_Int)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_compare17(x0, x1, x2, x3)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_compare23(x0, x1, True, x2, x3)
new_primCmpNat1(Zero, Zero)
new_ltEs6(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Float)
new_ltEs17(x0, x1, x2)
new_lt20(x0, x1, ty_Bool)
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Char)
new_esEs4(Nothing, Nothing, x0)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_compare11(x0, x1, False)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, ty_Float)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Double)
new_compare29(x0, x1)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs4(Nothing, Just(x0), x1)
new_compare13(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_compare25(x0, x1, False, x2, x3)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt20(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19([], :(x0, x1), x2)
new_ltEs20(x0, x1, ty_Float)
new_ltEs9(Nothing, Just(x0), x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_compare0([], [], x0)
new_lt11(x0, x1, x2, x3)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs25(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_compare28(x0, x1, ty_Double)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_compare0([], :(x0, x1), x2)
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Double)
new_compare26(x0, x1, True, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs28(x0, x1, ty_Char)
new_ltEs7(x0, x1)
new_compare7(Float(x0, x1), Float(x2, x3))
new_compare18(x0, x1, x2, x3)
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs19(:(x0, x1), [], x2)
new_esEs24(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs16(x0, x1)
new_ltEs11(x0, x1)
new_lt5(x0, x1)
new_compare24(x0, x1, False, x2, x3, x4)
new_lt19(x0, x1, ty_Float)
new_ltEs14(x0, x1, x2)
new_compare28(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt6(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, ty_Char)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19([], [], x0)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, x2, x3)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Succ(x0))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare28(x0, x1, app(ty_Ratio, x2))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_lt6(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primCmpNat1(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(GT, GT)
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs8(False, False)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt10(x0, x1, x2)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_primCompAux00(x0, LT)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Just(x0), Nothing, False, x1)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_lt19(x0, x1, ty_Double)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(LT, LT)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_esEs28(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Nothing, x1)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_ltEs6(x0, x1, ty_Int)
new_compare26(Just(x0), Just(x1), False, x2)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt15(x0, x1, x2)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(x0, x1)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_esEs22(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Nothing, Just(x0), False, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_esEs24(x0, x1, ty_Double)
new_compare110(x0, x1, False, x2, x3)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, False, x2)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs6(x0, x1, ty_Double)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare23(x0, x1, False, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_primPlusNat1(Succ(x0), Zero)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare26(Nothing, Nothing, False, x0)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_primMulNat0(Zero, Succ(x0))
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Int)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_lt19(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_compare14(x0, x1, x2, x3, x4)
new_esEs8(Char(x0), Char(x1))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_compare25(x0, x1, True, x2, x3)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs18(GT, GT)
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_compare28(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_compare12(x0, x1, True, x2, x3)
new_compare0(:(x0, x1), [], x2)
new_ltEs19(x0, x1, ty_Integer)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_lt18(x0, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare27(Double(x0, x1), Double(x2, x3))
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_lt14(x0, x1, x2, x3, x4)
new_esEs23(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_[], x2))
new_compare112(x0, x1, True)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare28(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_compare12(x0, x1, False, x2, x3)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare11(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs9(Nothing, Nothing, x0)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_addToFM_C1(yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy54, Nothing, yvy41, h, ba)
new_addToFM_C20(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, False, h, ba) → new_addToFM_C10(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, new_gt0(yvy500, h), h, ba)
new_addToFM_C20(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy53, Nothing, yvy41, h, ba)
new_addToFM_C22(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, False, h, ba) → new_addToFM_C12(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_gt2(yvy400, yvy500, h), h, ba)
new_addToFM_C21(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, False, h, ba) → new_addToFM_C11(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_gt1(yvy400, h), h, ba)
new_addToFM_C22(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy53, Just(yvy400), yvy41, h, ba)
new_addToFM_C(Branch(Nothing, yvy51, yvy52, yvy53, yvy54), Nothing, yvy41, h, ba) → new_addToFM_C2(yvy51, yvy52, yvy53, yvy54, yvy41, new_esEs9(new_compare26(Nothing, Nothing, True, h), LT), h, ba)
new_addToFM_C2(yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy53, Nothing, yvy41, h, ba)
new_addToFM_C(Branch(Nothing, yvy51, yvy52, yvy53, yvy54), Just(yvy400), yvy41, h, ba) → new_addToFM_C21(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), LT), h, ba)
new_addToFM_C11(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy54, Just(yvy400), yvy41, h, ba)
new_addToFM_C2(yvy51, yvy52, yvy53, yvy54, yvy41, False, h, ba) → new_addToFM_C1(yvy51, yvy52, yvy53, yvy54, yvy41, new_gt(h), h, ba)
new_addToFM_C10(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy54, Nothing, yvy41, h, ba)
new_addToFM_C(Branch(Just(yvy500), yvy51, yvy52, yvy53, yvy54), Nothing, yvy41, h, ba) → new_addToFM_C20(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, new_esEs9(new_compare26(Nothing, Just(yvy500), False, h), LT), h, ba)
new_addToFM_C(Branch(Just(yvy500), yvy51, yvy52, yvy53, yvy54), Just(yvy400), yvy41, h, ba) → new_addToFM_C22(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_esEs9(new_compare26(Just(yvy400), Just(yvy500), new_esEs29(yvy400, yvy500, h), h), LT), h, ba)
new_addToFM_C12(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy54, Just(yvy400), yvy41, h, ba)
new_addToFM_C21(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy53, Just(yvy400), yvy41, h, ba)

The TRS R consists of the following rules:

new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, ce)) → new_esEs4(yvy4000, yvy3000, ce)
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, cg), da)) → new_ltEs5(yvy4900, yvy5000, cg, da)
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, cac), cad)) → new_esEs5(yvy4000, yvy3000, cac, cad)
new_esEs28(yvy4000, yvy3000, app(ty_[], dea)) → new_esEs19(yvy4000, yvy3000, dea)
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, baa), bab)) → new_esEs6(yvy4000, yvy3000, baa, bab)
new_primCmpNat2(Zero, yvy4900) → LT
new_ltEs8(False, True) → True
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, bea), beb), bde) → new_ltEs5(yvy49000, yvy50000, bea, beb)
new_esEs22(yvy4001, yvy3001, app(ty_[], bcb)) → new_esEs19(yvy4001, yvy3001, bcb)
new_ltEs18(EQ, GT) → True
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_esEs29(yvy400, yvy500, ty_Integer) → new_esEs13(yvy400, yvy500)
new_ltEs10(Left(yvy49000), Right(yvy50000), beh, bde) → True
new_compare110(yvy49000, yvy50000, True, de, df) → LT
new_esEs29(yvy400, yvy500, app(ty_[], cab)) → new_esEs19(yvy400, yvy500, cab)
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bcc), bcd)) → new_esEs5(yvy4002, yvy3002, bcc, bcd)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_compare24(yvy49000, yvy50000, False, dg, dh, ea) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, dg, dh, ea), dg, dh, ea)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cbc)) → new_esEs4(yvy4000, yvy3000, cbc)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, ff)) → new_ltEs17(yvy49001, yvy50001, ff)
new_esEs4(Just(yvy4000), Nothing, bd) → False
new_esEs4(Nothing, Just(yvy3000), bd) → False
new_ltEs9(Nothing, Just(yvy50000), ga) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], dab), bhg) → new_esEs19(yvy4000, yvy3000, dab)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_primMulNat0(Zero, Zero) → Zero
new_compare26(Just(yvy4900), Nothing, False, ccg) → GT
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, ced)) → new_esEs10(yvy49000, yvy50000, ced)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, ddd)) → new_esEs10(yvy4000, yvy3000, ddd)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, db)) → new_esEs4(yvy49000, yvy50000, db)
new_compare33(yvy20, yvy15, dbe) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, dbe), dbe)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, bhg) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_[], cec)) → new_esEs19(yvy49000, yvy50000, cec)
new_compare16(@0, @0) → EQ
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, bdc)) → new_esEs4(yvy4002, yvy3002, bdc)
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_compare26(Nothing, Just(yvy5000), False, ccg) → LT
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), bc) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, bc), bc)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_[], bga)) → new_ltEs14(yvy49000, yvy50000, bga)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, bad), bae), baf)) → new_esEs7(yvy4000, yvy3000, bad, bae, baf)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_esEs29(yvy400, yvy500, app(app(app(ty_@3, hd), he), hf)) → new_esEs7(yvy400, yvy500, hd, he, hf)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bde) → new_ltEs12(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cdc)) → new_esEs4(yvy49000, yvy50000, cdc)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, de), df)) → new_esEs6(yvy49000, yvy50000, de, df)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_compare18(yvy49000, yvy50000, de, df) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, de, df), de, df)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_pePe(False, yvy201) → yvy201
new_esEs29(yvy400, yvy500, ty_Double) → new_esEs16(yvy400, yvy500)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_compare23(yvy49000, yvy50000, False, dc, dd) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, dc, dd), dc, dd)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_compare26(Nothing, Nothing, False, ccg) → LT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bde) → new_ltEs4(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cff)) → new_lt17(yvy49001, yvy50001, cff)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bec), bed), bee), bde) → new_ltEs13(yvy49000, yvy50000, bec, bed, bee)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bdg), bdh), bde) → new_ltEs10(yvy49000, yvy50000, bdg, bdh)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fa), fb), fc)) → new_ltEs13(yvy49001, yvy50001, fa, fb, fc)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cee)) → new_lt10(yvy49001, yvy50001, cee)
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chc), chd), bhg) → new_esEs6(yvy4000, yvy3000, chc, chd)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbd)) → new_esEs19(yvy4000, yvy3000, cbd)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, daa), bhg) → new_esEs4(yvy4000, yvy3000, daa)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, ge), gf)) → new_ltEs5(yvy49000, yvy50000, ge, gf)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(ty_@2, bfd), bfe)) → new_ltEs5(yvy49000, yvy50000, bfd, bfe)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs7(yvy4002, yvy3002, bch, bda, bdb)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs7(yvy49001, yvy50001, cfb, cfc, cfd)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cdh), cea), ceb)) → new_lt14(yvy49000, yvy50000, cdh, cea, ceb)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbe), cbf)) → new_esEs5(yvy4001, yvy3001, cbe, cbf)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbg), cbh)) → new_esEs6(yvy4001, yvy3001, cbg, cbh)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ed)) → new_ltEs9(yvy49001, yvy50001, ed)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, hc)) → new_ltEs17(yvy49000, yvy50000, hc)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, beh), bde)) → new_ltEs10(yvy4900, yvy5000, beh, bde)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), cg, da) → new_pePe(new_lt6(yvy49000, yvy50000, cg), new_asAs(new_esEs20(yvy49000, yvy50000, cg), new_ltEs6(yvy49001, yvy50001, da)))
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfg)) → new_ltEs9(yvy49002, yvy50002, cfg)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, cae), caf)) → new_esEs6(yvy4000, yvy3000, cae, caf)
new_gt2(yvy35, yvy30, bgc) → new_esEs9(new_compare33(yvy35, yvy30, bgc), GT)
new_compare0([], [], bc) → EQ
new_pePe(True, yvy201) → True
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_primEqNat0(Zero, Zero) → True
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bde) → new_ltEs11(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(ty_@2, dae), daf)) → new_esEs6(yvy4000, yvy3000, dae, daf)
new_ltEs14(yvy4900, yvy5000, bc) → new_fsEs(new_compare0(yvy4900, yvy5000, bc))
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, ee), ef)) → new_ltEs10(yvy49001, yvy50001, ee, ef)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_esEs29(yvy400, yvy500, ty_Int) → new_esEs14(yvy400, yvy500)
new_ltEs18(EQ, EQ) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, bhg) → new_esEs9(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_esEs19([], [], cab) → True
new_compare110(yvy49000, yvy50000, False, de, df) → GT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, ca)) → new_esEs10(yvy4000, yvy3000, ca)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccf)) → new_esEs19(yvy4001, yvy3001, ccf)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_compare12(yvy49000, yvy50000, False, dc, dd) → GT
new_primCmpNat1(Zero, Zero) → EQ
new_primCompAux0(yvy49000, yvy50000, yvy202, bc) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, bc))
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs18(LT, LT) → True
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, bhg) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, dg), dh), ea)) → new_esEs7(yvy49000, yvy50000, dg, dh, ea)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, dc), dd)) → new_lt11(yvy49000, yvy50000, dc, dd)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, ga)) → new_ltEs9(yvy4900, yvy5000, ga)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs19(:(yvy4000, yvy4001), [], cab) → False
new_esEs19([], :(yvy3000, yvy3001), cab) → False
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_ltEs18(GT, GT) → True
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(EQ, EQ) → True
new_compare24(yvy49000, yvy50000, True, dg, dh, ea) → EQ
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bde) → new_ltEs18(yvy49000, yvy50000)
new_esEs15(True, True) → True
new_esEs30(yvy20, yvy15, app(ty_[], dcg)) → new_esEs19(yvy20, yvy15, dcg)
new_ltEs18(LT, GT) → True
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcf)) → new_esEs4(yvy20, yvy15, dcf)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, fh)) → new_ltEs17(yvy4900, yvy5000, fh)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, cca)) → new_esEs10(yvy4001, yvy3001, cca)
new_esEs29(yvy400, yvy500, app(app(ty_Either, bhf), bhg)) → new_esEs5(yvy400, yvy500, bhf, bhg)
new_ltEs8(True, True) → True
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cdh), cea), ceb)) → new_esEs7(yvy49000, yvy50000, cdh, cea, ceb)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, ddh)) → new_esEs4(yvy4000, yvy3000, ddh)
new_ltEs18(GT, LT) → False
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, chf), chg), chh), bhg) → new_esEs7(yvy4000, yvy3000, chf, chg, chh)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_lt14(yvy49000, yvy50000, dg, dh, ea) → new_esEs9(new_compare14(yvy49000, yvy50000, dg, dh, ea), LT)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, cef), ceg)) → new_esEs5(yvy49001, yvy50001, cef, ceg)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cgh)) → new_ltEs17(yvy49002, yvy50002, cgh)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs7(yvy20, yvy15, dcc, dcd, dce)
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, gc), gd)) → new_ltEs10(yvy49000, yvy50000, gc, gd)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], hb)) → new_ltEs14(yvy49000, yvy50000, hb)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bah)) → new_esEs19(yvy4000, yvy3000, bah)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cgb), cgc)) → new_ltEs5(yvy49002, yvy50002, cgb, cgc)
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_[], dbd)) → new_esEs19(yvy4000, yvy3000, dbd)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bca)) → new_esEs4(yvy4001, yvy3001, bca)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, cce)) → new_esEs4(yvy4001, yvy3001, cce)
new_compare112(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bhh, caa) → new_asAs(new_esEs24(yvy4000, yvy3000, bhh), new_esEs25(yvy4001, yvy3001, caa))
new_lt19(yvy49001, yvy50001, app(app(ty_@2, ceh), cfa)) → new_lt12(yvy49001, yvy50001, ceh, cfa)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare12(yvy49000, yvy50000, True, dc, dd) → LT
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(ty_Either, dac), dad)) → new_esEs5(yvy4000, yvy3000, dac, dad)
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(app(ty_@3, bff), bfg), bfh)) → new_ltEs13(yvy49000, yvy50000, bff, bfg, bfh)
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_ltEs19(yvy4900, yvy5000, app(ty_[], bc)) → new_ltEs14(yvy4900, yvy5000, bc)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_Ratio, dag)) → new_esEs10(yvy4000, yvy3000, dag)
new_compare111(yvy49000, yvy50000, True, dg, dh, ea) → LT
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_primCompAux00(yvy206, LT) → LT
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(ty_Either, bfb), bfc)) → new_ltEs10(yvy49000, yvy50000, bfb, bfc)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, bhg) → new_esEs14(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, ced)) → new_lt17(yvy49000, yvy50000, ced)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare13(yvy175, yvy176, True, fg) → LT
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs23(yvy4002, yvy3002, app(ty_[], bdd)) → new_esEs19(yvy4002, yvy3002, bdd)
new_lt15(yvy49000, yvy50000, eb) → new_esEs9(new_compare0(yvy49000, yvy50000, eb), LT)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ec)) → new_lt17(yvy49000, yvy50000, ec)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, gb)) → new_ltEs9(yvy49000, yvy50000, gb)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_compare14(yvy49000, yvy50000, dg, dh, ea) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, dg, dh, ea), dg, dh, ea)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, be), bf)) → new_esEs5(yvy4000, yvy3000, be, bf)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, dc), dd)) → new_esEs5(yvy49000, yvy50000, dc, dd)
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_ltEs20(yvy49002, yvy50002, app(ty_[], cgg)) → new_ltEs14(yvy49002, yvy50002, cgg)
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dch), dda)) → new_esEs5(yvy4000, yvy3000, dch, dda)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, bg), bh)) → new_esEs6(yvy4000, yvy3000, bg, bh)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bbc), bbd)) → new_esEs6(yvy4001, yvy3001, bbc, bbd)
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_compare28(yvy49000, yvy50000, app(ty_[], bhd)) → new_compare0(yvy49000, yvy50000, bhd)
new_ltEs9(Just(yvy49000), Nothing, ga) → False
new_primCompAux00(yvy206, EQ) → yvy206
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, bhg) → new_esEs15(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bcg)) → new_esEs10(yvy4002, yvy3002, bcg)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, bhg) → new_esEs8(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_compare26(Just(yvy4900), Just(yvy5000), False, ccg) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, ccg), ccg)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bha), bhb), bhc)) → new_compare14(yvy49000, yvy50000, bha, bhb, bhc)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, cch), cda), cdb)) → new_ltEs13(yvy4900, yvy5000, cch, cda, cdb)
new_compare26(yvy490, yvy500, True, ccg) → EQ
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs18(GT, EQ) → False
new_compare17(yvy49000, yvy50000, dc, dd) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, dc, dd), dc, dd)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcb)) → new_esEs10(yvy20, yvy15, dcb)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bde) → new_ltEs16(yvy49000, yvy50000)
new_esEs29(yvy400, yvy500, ty_@0) → new_esEs18(yvy400, yvy500)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ec)) → new_esEs10(yvy49000, yvy50000, ec)
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bce), bcf)) → new_esEs6(yvy4002, yvy3002, bce, bcf)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, ga) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, bhg) → new_esEs17(yvy4000, yvy3000)
new_esEs9(GT, GT) → True
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bgd)) → new_compare19(yvy49000, yvy50000, bgd)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bde) → new_ltEs15(yvy49000, yvy50000)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs18(EQ, LT) → False
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_compare0(:(yvy49000, yvy49001), [], bc) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_ltEs18(LT, EQ) → True
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cdd), cde)) → new_esEs5(yvy49000, yvy50000, cdd, cde)
new_lt6(yvy49000, yvy50000, app(ty_[], eb)) → new_lt15(yvy49000, yvy50000, eb)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fd)) → new_ltEs14(yvy49001, yvy50001, fd)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs7(yvy4001, yvy3001, bbf, bbg, bbh)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, db)) → new_lt10(yvy49000, yvy50000, db)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_lt14(yvy49001, yvy50001, cfb, cfc, cfd)
new_lt19(yvy49001, yvy50001, app(ty_[], cfe)) → new_lt15(yvy49001, yvy50001, cfe)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs7(yvy4000, yvy3000, dde, ddf, ddg)
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), hd, he, hf) → new_asAs(new_esEs21(yvy4000, yvy3000, hd), new_asAs(new_esEs22(yvy4001, yvy3001, he), new_esEs23(yvy4002, yvy3002, hf)))
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs5(Left(yvy4000), Right(yvy3000), bhf, bhg) → False
new_esEs5(Right(yvy4000), Left(yvy3000), bhf, bhg) → False
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, ceh), cfa)) → new_esEs6(yvy49001, yvy50001, ceh, cfa)
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs29(yvy400, yvy500, app(app(ty_@2, bhh), caa)) → new_esEs6(yvy400, yvy500, bhh, caa)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bac)) → new_esEs10(yvy4000, yvy3000, bac)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_ltEs8(False, False) → True
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_compare19(yvy49000, yvy50000, db) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, db), db)
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdf), cdg)) → new_lt12(yvy49000, yvy50000, cdf, cdg)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, gg), gh), ha)) → new_ltEs13(yvy49000, yvy50000, gg, gh, ha)
new_gt(h) → new_esEs9(new_compare30(h), GT)
new_compare25(yvy49000, yvy50000, True, de, df) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_lt19(yvy49001, yvy50001, app(app(ty_Either, cef), ceg)) → new_lt11(yvy49001, yvy50001, cef, ceg)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cdc)) → new_lt10(yvy49000, yvy50000, cdc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, bd) → True
new_compare111(yvy49000, yvy50000, False, dg, dh, ea) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_compare210(yvy49000, yvy50000, True) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bde) → new_ltEs7(yvy49000, yvy50000)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cee)) → new_esEs4(yvy49001, yvy50001, cee)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bge), bgf)) → new_compare17(yvy49000, yvy50000, bge, bgf)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cfh), cga)) → new_ltEs10(yvy49002, yvy50002, cfh, cga)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cdd), cde)) → new_lt11(yvy49000, yvy50000, cdd, cde)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cff)) → new_esEs10(yvy49001, yvy50001, cff)
new_compare13(yvy175, yvy176, False, fg) → GT
new_compare23(yvy49000, yvy50000, True, dc, dd) → EQ
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], bef), bde) → new_ltEs14(yvy49000, yvy50000, bef)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, bhg) → new_esEs13(yvy4000, yvy3000)
new_lt17(yvy49000, yvy50000, ec) → new_esEs9(new_compare8(yvy49000, yvy50000, ec), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs7(yvy4000, yvy3000, dah, dba, dbb)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cgd), cge), cgf)) → new_ltEs13(yvy49002, yvy50002, cgd, cge, cgf)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddb), ddc)) → new_esEs6(yvy4000, yvy3000, ddb, ddc)
new_gt0(yvy300, h) → new_esEs9(new_compare31(yvy300, h), GT)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bag)) → new_esEs4(yvy4000, yvy3000, bag)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, eg), eh)) → new_ltEs5(yvy49001, yvy50001, eg, eh)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bdf), bde) → new_ltEs9(yvy49000, yvy50000, bdf)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, dg), dh), ea)) → new_lt14(yvy49000, yvy50000, dg, dh, ea)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, cah), cba), cbb)) → new_esEs7(yvy4000, yvy3000, cah, cba, cbb)
new_lt20(yvy49000, yvy50000, app(ty_[], cec)) → new_lt15(yvy49000, yvy50000, cec)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt12(yvy49000, yvy50000, de, df) → new_esEs9(new_compare18(yvy49000, yvy50000, de, df), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs29(yvy400, yvy500, ty_Bool) → new_esEs15(yvy400, yvy500)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bb) → new_asAs(new_esEs11(yvy4000, yvy3000, bb), new_esEs12(yvy4001, yvy3001, bb))
new_asAs(False, yvy182) → False
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_gt1(yvy400, h) → new_esEs9(new_compare32(yvy400, h), GT)
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, hg), hh)) → new_esEs5(yvy4000, yvy3000, hg, hh)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_lt10(yvy49000, yvy50000, db) → new_esEs9(new_compare19(yvy49000, yvy50000, db), LT)
new_compare25(yvy49000, yvy50000, False, de, df) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, de, df), de, df)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, bhe)) → new_compare8(yvy49000, yvy50000, bhe)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), cch, cda, cdb) → new_pePe(new_lt20(yvy49000, yvy50000, cch), new_asAs(new_esEs26(yvy49000, yvy50000, cch), new_pePe(new_lt19(yvy49001, yvy50001, cda), new_asAs(new_esEs27(yvy49001, yvy50001, cda), new_ltEs20(yvy49002, yvy50002, cdb)))))
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_esEs29(yvy400, yvy500, app(ty_Ratio, bb)) → new_esEs10(yvy400, yvy500, bb)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cag)) → new_esEs10(yvy4000, yvy3000, cag)
new_esEs29(yvy400, yvy500, ty_Char) → new_esEs8(yvy400, yvy500)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbf), dbg)) → new_esEs5(yvy20, yvy15, dbf, dbg)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_Ratio, bgb)) → new_ltEs17(yvy49000, yvy50000, bgb)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bbe)) → new_esEs10(yvy4001, yvy3001, bbe)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, ccb), ccc), ccd)) → new_esEs7(yvy4001, yvy3001, ccb, ccc, ccd)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_Maybe, dbc)) → new_esEs4(yvy4000, yvy3000, dbc)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare11(yvy49000, yvy50000, False) → GT
new_esEs30(yvy20, yvy15, app(app(ty_@2, dbh), dca)) → new_esEs6(yvy20, yvy15, dbh, dca)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Left(yvy50000), beh, bde) → False
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_compare11(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], cf)) → new_esEs19(yvy4000, yvy3000, cf)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, cha), chb), bhg) → new_esEs5(yvy4000, yvy3000, cha, chb)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_Maybe, bfa)) → new_ltEs9(yvy49000, yvy50000, bfa)
new_compare112(yvy49000, yvy50000, False) → GT
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(ty_[], eb)) → new_esEs19(yvy49000, yvy50000, eb)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cfe)) → new_esEs19(yvy49001, yvy50001, cfe)
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy50000, yvy50001), bc) → LT
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_asAs(True, yvy182) → yvy182
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_esEs18(@0, @0) → True
new_compare211(yvy49000, yvy50000, True) → EQ
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdf), cdg)) → new_esEs6(yvy49000, yvy50000, cdf, cdg)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy400, yvy500, ty_Float) → new_esEs17(yvy400, yvy500)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cb), cc), cd)) → new_esEs7(yvy4000, yvy3000, cb, cc, cd)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, che), bhg) → new_esEs10(yvy4000, yvy3000, che)
new_esEs29(yvy400, yvy500, app(ty_Maybe, bd)) → new_esEs4(yvy400, yvy500, bd)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, beg), bde) → new_ltEs17(yvy49000, yvy50000, beg)
new_lt11(yvy49000, yvy50000, dc, dd) → new_esEs9(new_compare17(yvy49000, yvy50000, dc, dd), LT)
new_esEs9(LT, LT) → True
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), cab) → new_asAs(new_esEs28(yvy4000, yvy3000, cab), new_esEs19(yvy4001, yvy3001, cab))
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bba), bbb)) → new_esEs5(yvy4001, yvy3001, bba, bbb)
new_primCompAux00(yvy206, GT) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bde) → new_ltEs8(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(yvy49000, yvy50000, app(app(ty_@2, de), df)) → new_lt12(yvy49000, yvy50000, de, df)
new_esEs29(yvy400, yvy500, ty_Ordering) → new_esEs9(yvy400, yvy500)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bgg), bgh)) → new_compare18(yvy49000, yvy50000, bgg, bgh)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_ltEs17(yvy4900, yvy5000, fh) → new_fsEs(new_compare8(yvy4900, yvy5000, fh))
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs30(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs9(Nothing, Nothing, x0)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_compare25(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare12(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_gt2(x0, x1, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs15(True, True)
new_primCmpNat0(x0, Zero)
new_compare0([], [], x0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare33(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_ltEs6(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs6(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs14(x0, x1, x2)
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt12(x0, x1, x2, x3)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Float)
new_compare18(x0, x1, x2, x3)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, x2)
new_esEs27(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_compare28(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_esEs19([], :(x0, x1), x2)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(:(x0, x1), [], x2)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Zero)
new_ltEs9(Nothing, Just(x0), x1)
new_esEs25(x0, x1, ty_Char)
new_esEs19([], [], x0)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt15(x0, x1, x2)
new_compare110(x0, x1, False, x2, x3)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat1(Zero, Succ(x0))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_gt(x0)
new_esEs27(x0, x1, ty_Double)
new_esEs9(GT, GT)
new_ltEs8(False, False)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare32(x0, x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs8(False, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs8(True, False)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_gt0(x0, x1)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Nothing, Just(x0), x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare26(Just(x0), Just(x1), False, x2)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpNat2(Zero, x0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs14(x0, x1)
new_esEs29(x0, x1, ty_Char)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_ltEs12(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_compare26(x0, x1, True, x2)
new_compare23(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, True, x2)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs29(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, False, x2)
new_esEs20(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_compare210(x0, x1, True)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat1(Succ(x0), Zero)
new_esEs4(Nothing, Nothing, x0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_compare31(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(Char(x0), Char(x1))
new_compare17(x0, x1, x2, x3)
new_esEs29(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_compare26(Just(x0), Nothing, False, x1)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), [], x2)
new_compare25(x0, x1, False, x2, x3)
new_compare28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_compare26(Nothing, Nothing, False, x0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_compare28(x0, x1, ty_Integer)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_compare12(x0, x1, True, x2, x3)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare28(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_gt1(x0, x1)
new_compare26(Nothing, Just(x0), False, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, False, x2, x3, x4)
new_compare11(x0, x1, True)
new_ltEs17(x0, x1, x2)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare14(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)

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

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

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

new_addToFM_C(Branch(Nothing, yvy51, yvy52, yvy53, yvy54), Just(yvy400), yvy41, h, ba) → new_addToFM_C21(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), LT), h, ba)
new_addToFM_C11(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy54, Just(yvy400), yvy41, h, ba)
new_addToFM_C22(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, False, h, ba) → new_addToFM_C12(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_gt2(yvy400, yvy500, h), h, ba)
new_addToFM_C(Branch(Just(yvy500), yvy51, yvy52, yvy53, yvy54), Just(yvy400), yvy41, h, ba) → new_addToFM_C22(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_esEs9(new_compare26(Just(yvy400), Just(yvy500), new_esEs29(yvy400, yvy500, h), h), LT), h, ba)
new_addToFM_C12(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy54, Just(yvy400), yvy41, h, ba)
new_addToFM_C21(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy53, Just(yvy400), yvy41, h, ba)
new_addToFM_C21(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, False, h, ba) → new_addToFM_C11(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_gt1(yvy400, h), h, ba)
new_addToFM_C22(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy53, Just(yvy400), yvy41, h, ba)

The TRS R consists of the following rules:

new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, ce)) → new_esEs4(yvy4000, yvy3000, ce)
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, cg), da)) → new_ltEs5(yvy4900, yvy5000, cg, da)
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, cac), cad)) → new_esEs5(yvy4000, yvy3000, cac, cad)
new_esEs28(yvy4000, yvy3000, app(ty_[], dea)) → new_esEs19(yvy4000, yvy3000, dea)
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, baa), bab)) → new_esEs6(yvy4000, yvy3000, baa, bab)
new_primCmpNat2(Zero, yvy4900) → LT
new_ltEs8(False, True) → True
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, bea), beb), bde) → new_ltEs5(yvy49000, yvy50000, bea, beb)
new_esEs22(yvy4001, yvy3001, app(ty_[], bcb)) → new_esEs19(yvy4001, yvy3001, bcb)
new_ltEs18(EQ, GT) → True
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_esEs29(yvy400, yvy500, ty_Integer) → new_esEs13(yvy400, yvy500)
new_ltEs10(Left(yvy49000), Right(yvy50000), beh, bde) → True
new_compare110(yvy49000, yvy50000, True, de, df) → LT
new_esEs29(yvy400, yvy500, app(ty_[], cab)) → new_esEs19(yvy400, yvy500, cab)
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bcc), bcd)) → new_esEs5(yvy4002, yvy3002, bcc, bcd)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_compare24(yvy49000, yvy50000, False, dg, dh, ea) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, dg, dh, ea), dg, dh, ea)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cbc)) → new_esEs4(yvy4000, yvy3000, cbc)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, ff)) → new_ltEs17(yvy49001, yvy50001, ff)
new_esEs4(Just(yvy4000), Nothing, bd) → False
new_esEs4(Nothing, Just(yvy3000), bd) → False
new_ltEs9(Nothing, Just(yvy50000), ga) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], dab), bhg) → new_esEs19(yvy4000, yvy3000, dab)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_primMulNat0(Zero, Zero) → Zero
new_compare26(Just(yvy4900), Nothing, False, ccg) → GT
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, ced)) → new_esEs10(yvy49000, yvy50000, ced)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, ddd)) → new_esEs10(yvy4000, yvy3000, ddd)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, db)) → new_esEs4(yvy49000, yvy50000, db)
new_compare33(yvy20, yvy15, dbe) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, dbe), dbe)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, bhg) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_[], cec)) → new_esEs19(yvy49000, yvy50000, cec)
new_compare16(@0, @0) → EQ
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, bdc)) → new_esEs4(yvy4002, yvy3002, bdc)
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_compare26(Nothing, Just(yvy5000), False, ccg) → LT
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), bc) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, bc), bc)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_[], bga)) → new_ltEs14(yvy49000, yvy50000, bga)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, bad), bae), baf)) → new_esEs7(yvy4000, yvy3000, bad, bae, baf)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_esEs29(yvy400, yvy500, app(app(app(ty_@3, hd), he), hf)) → new_esEs7(yvy400, yvy500, hd, he, hf)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bde) → new_ltEs12(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cdc)) → new_esEs4(yvy49000, yvy50000, cdc)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, de), df)) → new_esEs6(yvy49000, yvy50000, de, df)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_compare18(yvy49000, yvy50000, de, df) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, de, df), de, df)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_pePe(False, yvy201) → yvy201
new_esEs29(yvy400, yvy500, ty_Double) → new_esEs16(yvy400, yvy500)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_compare23(yvy49000, yvy50000, False, dc, dd) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, dc, dd), dc, dd)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_compare26(Nothing, Nothing, False, ccg) → LT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bde) → new_ltEs4(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cff)) → new_lt17(yvy49001, yvy50001, cff)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bec), bed), bee), bde) → new_ltEs13(yvy49000, yvy50000, bec, bed, bee)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bdg), bdh), bde) → new_ltEs10(yvy49000, yvy50000, bdg, bdh)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fa), fb), fc)) → new_ltEs13(yvy49001, yvy50001, fa, fb, fc)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cee)) → new_lt10(yvy49001, yvy50001, cee)
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chc), chd), bhg) → new_esEs6(yvy4000, yvy3000, chc, chd)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbd)) → new_esEs19(yvy4000, yvy3000, cbd)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, daa), bhg) → new_esEs4(yvy4000, yvy3000, daa)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, ge), gf)) → new_ltEs5(yvy49000, yvy50000, ge, gf)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(ty_@2, bfd), bfe)) → new_ltEs5(yvy49000, yvy50000, bfd, bfe)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs7(yvy4002, yvy3002, bch, bda, bdb)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs7(yvy49001, yvy50001, cfb, cfc, cfd)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cdh), cea), ceb)) → new_lt14(yvy49000, yvy50000, cdh, cea, ceb)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbe), cbf)) → new_esEs5(yvy4001, yvy3001, cbe, cbf)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbg), cbh)) → new_esEs6(yvy4001, yvy3001, cbg, cbh)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ed)) → new_ltEs9(yvy49001, yvy50001, ed)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, hc)) → new_ltEs17(yvy49000, yvy50000, hc)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, beh), bde)) → new_ltEs10(yvy4900, yvy5000, beh, bde)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), cg, da) → new_pePe(new_lt6(yvy49000, yvy50000, cg), new_asAs(new_esEs20(yvy49000, yvy50000, cg), new_ltEs6(yvy49001, yvy50001, da)))
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfg)) → new_ltEs9(yvy49002, yvy50002, cfg)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, cae), caf)) → new_esEs6(yvy4000, yvy3000, cae, caf)
new_gt2(yvy35, yvy30, bgc) → new_esEs9(new_compare33(yvy35, yvy30, bgc), GT)
new_compare0([], [], bc) → EQ
new_pePe(True, yvy201) → True
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_primEqNat0(Zero, Zero) → True
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bde) → new_ltEs11(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(ty_@2, dae), daf)) → new_esEs6(yvy4000, yvy3000, dae, daf)
new_ltEs14(yvy4900, yvy5000, bc) → new_fsEs(new_compare0(yvy4900, yvy5000, bc))
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, ee), ef)) → new_ltEs10(yvy49001, yvy50001, ee, ef)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_esEs29(yvy400, yvy500, ty_Int) → new_esEs14(yvy400, yvy500)
new_ltEs18(EQ, EQ) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, bhg) → new_esEs9(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_esEs19([], [], cab) → True
new_compare110(yvy49000, yvy50000, False, de, df) → GT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, ca)) → new_esEs10(yvy4000, yvy3000, ca)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccf)) → new_esEs19(yvy4001, yvy3001, ccf)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_compare12(yvy49000, yvy50000, False, dc, dd) → GT
new_primCmpNat1(Zero, Zero) → EQ
new_primCompAux0(yvy49000, yvy50000, yvy202, bc) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, bc))
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs18(LT, LT) → True
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, bhg) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, dg), dh), ea)) → new_esEs7(yvy49000, yvy50000, dg, dh, ea)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, dc), dd)) → new_lt11(yvy49000, yvy50000, dc, dd)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, ga)) → new_ltEs9(yvy4900, yvy5000, ga)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs19(:(yvy4000, yvy4001), [], cab) → False
new_esEs19([], :(yvy3000, yvy3001), cab) → False
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_ltEs18(GT, GT) → True
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(EQ, EQ) → True
new_compare24(yvy49000, yvy50000, True, dg, dh, ea) → EQ
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bde) → new_ltEs18(yvy49000, yvy50000)
new_esEs15(True, True) → True
new_esEs30(yvy20, yvy15, app(ty_[], dcg)) → new_esEs19(yvy20, yvy15, dcg)
new_ltEs18(LT, GT) → True
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcf)) → new_esEs4(yvy20, yvy15, dcf)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, fh)) → new_ltEs17(yvy4900, yvy5000, fh)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, cca)) → new_esEs10(yvy4001, yvy3001, cca)
new_esEs29(yvy400, yvy500, app(app(ty_Either, bhf), bhg)) → new_esEs5(yvy400, yvy500, bhf, bhg)
new_ltEs8(True, True) → True
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cdh), cea), ceb)) → new_esEs7(yvy49000, yvy50000, cdh, cea, ceb)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, ddh)) → new_esEs4(yvy4000, yvy3000, ddh)
new_ltEs18(GT, LT) → False
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, chf), chg), chh), bhg) → new_esEs7(yvy4000, yvy3000, chf, chg, chh)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_lt14(yvy49000, yvy50000, dg, dh, ea) → new_esEs9(new_compare14(yvy49000, yvy50000, dg, dh, ea), LT)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, cef), ceg)) → new_esEs5(yvy49001, yvy50001, cef, ceg)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cgh)) → new_ltEs17(yvy49002, yvy50002, cgh)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs7(yvy20, yvy15, dcc, dcd, dce)
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, gc), gd)) → new_ltEs10(yvy49000, yvy50000, gc, gd)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], hb)) → new_ltEs14(yvy49000, yvy50000, hb)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bah)) → new_esEs19(yvy4000, yvy3000, bah)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cgb), cgc)) → new_ltEs5(yvy49002, yvy50002, cgb, cgc)
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_[], dbd)) → new_esEs19(yvy4000, yvy3000, dbd)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bca)) → new_esEs4(yvy4001, yvy3001, bca)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, cce)) → new_esEs4(yvy4001, yvy3001, cce)
new_compare112(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bhh, caa) → new_asAs(new_esEs24(yvy4000, yvy3000, bhh), new_esEs25(yvy4001, yvy3001, caa))
new_lt19(yvy49001, yvy50001, app(app(ty_@2, ceh), cfa)) → new_lt12(yvy49001, yvy50001, ceh, cfa)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare12(yvy49000, yvy50000, True, dc, dd) → LT
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(ty_Either, dac), dad)) → new_esEs5(yvy4000, yvy3000, dac, dad)
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(app(ty_@3, bff), bfg), bfh)) → new_ltEs13(yvy49000, yvy50000, bff, bfg, bfh)
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_ltEs19(yvy4900, yvy5000, app(ty_[], bc)) → new_ltEs14(yvy4900, yvy5000, bc)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_Ratio, dag)) → new_esEs10(yvy4000, yvy3000, dag)
new_compare111(yvy49000, yvy50000, True, dg, dh, ea) → LT
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_primCompAux00(yvy206, LT) → LT
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(ty_Either, bfb), bfc)) → new_ltEs10(yvy49000, yvy50000, bfb, bfc)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, bhg) → new_esEs14(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, ced)) → new_lt17(yvy49000, yvy50000, ced)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare13(yvy175, yvy176, True, fg) → LT
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs23(yvy4002, yvy3002, app(ty_[], bdd)) → new_esEs19(yvy4002, yvy3002, bdd)
new_lt15(yvy49000, yvy50000, eb) → new_esEs9(new_compare0(yvy49000, yvy50000, eb), LT)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ec)) → new_lt17(yvy49000, yvy50000, ec)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, gb)) → new_ltEs9(yvy49000, yvy50000, gb)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_compare14(yvy49000, yvy50000, dg, dh, ea) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, dg, dh, ea), dg, dh, ea)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, be), bf)) → new_esEs5(yvy4000, yvy3000, be, bf)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, dc), dd)) → new_esEs5(yvy49000, yvy50000, dc, dd)
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_ltEs20(yvy49002, yvy50002, app(ty_[], cgg)) → new_ltEs14(yvy49002, yvy50002, cgg)
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dch), dda)) → new_esEs5(yvy4000, yvy3000, dch, dda)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, bg), bh)) → new_esEs6(yvy4000, yvy3000, bg, bh)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bbc), bbd)) → new_esEs6(yvy4001, yvy3001, bbc, bbd)
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_compare28(yvy49000, yvy50000, app(ty_[], bhd)) → new_compare0(yvy49000, yvy50000, bhd)
new_ltEs9(Just(yvy49000), Nothing, ga) → False
new_primCompAux00(yvy206, EQ) → yvy206
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, bhg) → new_esEs15(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bcg)) → new_esEs10(yvy4002, yvy3002, bcg)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, bhg) → new_esEs8(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_compare26(Just(yvy4900), Just(yvy5000), False, ccg) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, ccg), ccg)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bha), bhb), bhc)) → new_compare14(yvy49000, yvy50000, bha, bhb, bhc)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, cch), cda), cdb)) → new_ltEs13(yvy4900, yvy5000, cch, cda, cdb)
new_compare26(yvy490, yvy500, True, ccg) → EQ
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs18(GT, EQ) → False
new_compare17(yvy49000, yvy50000, dc, dd) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, dc, dd), dc, dd)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcb)) → new_esEs10(yvy20, yvy15, dcb)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bde) → new_ltEs16(yvy49000, yvy50000)
new_esEs29(yvy400, yvy500, ty_@0) → new_esEs18(yvy400, yvy500)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ec)) → new_esEs10(yvy49000, yvy50000, ec)
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bce), bcf)) → new_esEs6(yvy4002, yvy3002, bce, bcf)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, ga) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, bhg) → new_esEs17(yvy4000, yvy3000)
new_esEs9(GT, GT) → True
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bgd)) → new_compare19(yvy49000, yvy50000, bgd)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bde) → new_ltEs15(yvy49000, yvy50000)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs18(EQ, LT) → False
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_compare0(:(yvy49000, yvy49001), [], bc) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_ltEs18(LT, EQ) → True
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cdd), cde)) → new_esEs5(yvy49000, yvy50000, cdd, cde)
new_lt6(yvy49000, yvy50000, app(ty_[], eb)) → new_lt15(yvy49000, yvy50000, eb)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fd)) → new_ltEs14(yvy49001, yvy50001, fd)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs7(yvy4001, yvy3001, bbf, bbg, bbh)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, db)) → new_lt10(yvy49000, yvy50000, db)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_lt14(yvy49001, yvy50001, cfb, cfc, cfd)
new_lt19(yvy49001, yvy50001, app(ty_[], cfe)) → new_lt15(yvy49001, yvy50001, cfe)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs7(yvy4000, yvy3000, dde, ddf, ddg)
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), hd, he, hf) → new_asAs(new_esEs21(yvy4000, yvy3000, hd), new_asAs(new_esEs22(yvy4001, yvy3001, he), new_esEs23(yvy4002, yvy3002, hf)))
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs5(Left(yvy4000), Right(yvy3000), bhf, bhg) → False
new_esEs5(Right(yvy4000), Left(yvy3000), bhf, bhg) → False
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, ceh), cfa)) → new_esEs6(yvy49001, yvy50001, ceh, cfa)
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs29(yvy400, yvy500, app(app(ty_@2, bhh), caa)) → new_esEs6(yvy400, yvy500, bhh, caa)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bac)) → new_esEs10(yvy4000, yvy3000, bac)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_ltEs8(False, False) → True
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_compare19(yvy49000, yvy50000, db) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, db), db)
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdf), cdg)) → new_lt12(yvy49000, yvy50000, cdf, cdg)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, gg), gh), ha)) → new_ltEs13(yvy49000, yvy50000, gg, gh, ha)
new_gt(h) → new_esEs9(new_compare30(h), GT)
new_compare25(yvy49000, yvy50000, True, de, df) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_lt19(yvy49001, yvy50001, app(app(ty_Either, cef), ceg)) → new_lt11(yvy49001, yvy50001, cef, ceg)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cdc)) → new_lt10(yvy49000, yvy50000, cdc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, bd) → True
new_compare111(yvy49000, yvy50000, False, dg, dh, ea) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_compare210(yvy49000, yvy50000, True) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bde) → new_ltEs7(yvy49000, yvy50000)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cee)) → new_esEs4(yvy49001, yvy50001, cee)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bge), bgf)) → new_compare17(yvy49000, yvy50000, bge, bgf)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cfh), cga)) → new_ltEs10(yvy49002, yvy50002, cfh, cga)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cdd), cde)) → new_lt11(yvy49000, yvy50000, cdd, cde)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cff)) → new_esEs10(yvy49001, yvy50001, cff)
new_compare13(yvy175, yvy176, False, fg) → GT
new_compare23(yvy49000, yvy50000, True, dc, dd) → EQ
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], bef), bde) → new_ltEs14(yvy49000, yvy50000, bef)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, bhg) → new_esEs13(yvy4000, yvy3000)
new_lt17(yvy49000, yvy50000, ec) → new_esEs9(new_compare8(yvy49000, yvy50000, ec), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs7(yvy4000, yvy3000, dah, dba, dbb)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cgd), cge), cgf)) → new_ltEs13(yvy49002, yvy50002, cgd, cge, cgf)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddb), ddc)) → new_esEs6(yvy4000, yvy3000, ddb, ddc)
new_gt0(yvy300, h) → new_esEs9(new_compare31(yvy300, h), GT)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bag)) → new_esEs4(yvy4000, yvy3000, bag)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, eg), eh)) → new_ltEs5(yvy49001, yvy50001, eg, eh)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bdf), bde) → new_ltEs9(yvy49000, yvy50000, bdf)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, dg), dh), ea)) → new_lt14(yvy49000, yvy50000, dg, dh, ea)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, cah), cba), cbb)) → new_esEs7(yvy4000, yvy3000, cah, cba, cbb)
new_lt20(yvy49000, yvy50000, app(ty_[], cec)) → new_lt15(yvy49000, yvy50000, cec)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt12(yvy49000, yvy50000, de, df) → new_esEs9(new_compare18(yvy49000, yvy50000, de, df), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs29(yvy400, yvy500, ty_Bool) → new_esEs15(yvy400, yvy500)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bb) → new_asAs(new_esEs11(yvy4000, yvy3000, bb), new_esEs12(yvy4001, yvy3001, bb))
new_asAs(False, yvy182) → False
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_gt1(yvy400, h) → new_esEs9(new_compare32(yvy400, h), GT)
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, hg), hh)) → new_esEs5(yvy4000, yvy3000, hg, hh)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_lt10(yvy49000, yvy50000, db) → new_esEs9(new_compare19(yvy49000, yvy50000, db), LT)
new_compare25(yvy49000, yvy50000, False, de, df) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, de, df), de, df)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, bhe)) → new_compare8(yvy49000, yvy50000, bhe)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), cch, cda, cdb) → new_pePe(new_lt20(yvy49000, yvy50000, cch), new_asAs(new_esEs26(yvy49000, yvy50000, cch), new_pePe(new_lt19(yvy49001, yvy50001, cda), new_asAs(new_esEs27(yvy49001, yvy50001, cda), new_ltEs20(yvy49002, yvy50002, cdb)))))
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_esEs29(yvy400, yvy500, app(ty_Ratio, bb)) → new_esEs10(yvy400, yvy500, bb)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cag)) → new_esEs10(yvy4000, yvy3000, cag)
new_esEs29(yvy400, yvy500, ty_Char) → new_esEs8(yvy400, yvy500)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbf), dbg)) → new_esEs5(yvy20, yvy15, dbf, dbg)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_Ratio, bgb)) → new_ltEs17(yvy49000, yvy50000, bgb)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bbe)) → new_esEs10(yvy4001, yvy3001, bbe)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, ccb), ccc), ccd)) → new_esEs7(yvy4001, yvy3001, ccb, ccc, ccd)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_Maybe, dbc)) → new_esEs4(yvy4000, yvy3000, dbc)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare11(yvy49000, yvy50000, False) → GT
new_esEs30(yvy20, yvy15, app(app(ty_@2, dbh), dca)) → new_esEs6(yvy20, yvy15, dbh, dca)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Left(yvy50000), beh, bde) → False
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_compare11(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], cf)) → new_esEs19(yvy4000, yvy3000, cf)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, cha), chb), bhg) → new_esEs5(yvy4000, yvy3000, cha, chb)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_Maybe, bfa)) → new_ltEs9(yvy49000, yvy50000, bfa)
new_compare112(yvy49000, yvy50000, False) → GT
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(ty_[], eb)) → new_esEs19(yvy49000, yvy50000, eb)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cfe)) → new_esEs19(yvy49001, yvy50001, cfe)
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy50000, yvy50001), bc) → LT
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_asAs(True, yvy182) → yvy182
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_esEs18(@0, @0) → True
new_compare211(yvy49000, yvy50000, True) → EQ
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdf), cdg)) → new_esEs6(yvy49000, yvy50000, cdf, cdg)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy400, yvy500, ty_Float) → new_esEs17(yvy400, yvy500)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cb), cc), cd)) → new_esEs7(yvy4000, yvy3000, cb, cc, cd)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, che), bhg) → new_esEs10(yvy4000, yvy3000, che)
new_esEs29(yvy400, yvy500, app(ty_Maybe, bd)) → new_esEs4(yvy400, yvy500, bd)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, beg), bde) → new_ltEs17(yvy49000, yvy50000, beg)
new_lt11(yvy49000, yvy50000, dc, dd) → new_esEs9(new_compare17(yvy49000, yvy50000, dc, dd), LT)
new_esEs9(LT, LT) → True
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), cab) → new_asAs(new_esEs28(yvy4000, yvy3000, cab), new_esEs19(yvy4001, yvy3001, cab))
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bba), bbb)) → new_esEs5(yvy4001, yvy3001, bba, bbb)
new_primCompAux00(yvy206, GT) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bde) → new_ltEs8(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(yvy49000, yvy50000, app(app(ty_@2, de), df)) → new_lt12(yvy49000, yvy50000, de, df)
new_esEs29(yvy400, yvy500, ty_Ordering) → new_esEs9(yvy400, yvy500)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bgg), bgh)) → new_compare18(yvy49000, yvy50000, bgg, bgh)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_ltEs17(yvy4900, yvy5000, fh) → new_fsEs(new_compare8(yvy4900, yvy5000, fh))
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs30(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs9(Nothing, Nothing, x0)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_compare25(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare12(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_gt2(x0, x1, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs15(True, True)
new_primCmpNat0(x0, Zero)
new_compare0([], [], x0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare33(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_ltEs6(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs6(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs14(x0, x1, x2)
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt12(x0, x1, x2, x3)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Float)
new_compare18(x0, x1, x2, x3)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, x2)
new_esEs27(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_compare28(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_esEs19([], :(x0, x1), x2)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(:(x0, x1), [], x2)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Zero)
new_ltEs9(Nothing, Just(x0), x1)
new_esEs25(x0, x1, ty_Char)
new_esEs19([], [], x0)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt15(x0, x1, x2)
new_compare110(x0, x1, False, x2, x3)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat1(Zero, Succ(x0))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_gt(x0)
new_esEs27(x0, x1, ty_Double)
new_esEs9(GT, GT)
new_ltEs8(False, False)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare32(x0, x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs8(False, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs8(True, False)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_gt0(x0, x1)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Nothing, Just(x0), x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare26(Just(x0), Just(x1), False, x2)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpNat2(Zero, x0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs14(x0, x1)
new_esEs29(x0, x1, ty_Char)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_ltEs12(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_compare26(x0, x1, True, x2)
new_compare23(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, True, x2)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs29(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, False, x2)
new_esEs20(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_compare210(x0, x1, True)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat1(Succ(x0), Zero)
new_esEs4(Nothing, Nothing, x0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_compare31(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(Char(x0), Char(x1))
new_compare17(x0, x1, x2, x3)
new_esEs29(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_compare26(Just(x0), Nothing, False, x1)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), [], x2)
new_compare25(x0, x1, False, x2, x3)
new_compare28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_compare26(Nothing, Nothing, False, x0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_compare28(x0, x1, ty_Integer)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_compare12(x0, x1, True, x2, x3)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare28(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_gt1(x0, x1)
new_compare26(Nothing, Just(x0), False, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, False, x2, x3, x4)
new_compare11(x0, x1, True)
new_ltEs17(x0, x1, x2)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare14(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)

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

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

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

new_addToFM_C(Branch(Nothing, yvy51, yvy52, yvy53, yvy54), Just(yvy400), yvy41, h, ba) → new_addToFM_C21(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), LT), h, ba)
new_addToFM_C11(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy54, Just(yvy400), yvy41, h, ba)
new_addToFM_C22(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, False, h, ba) → new_addToFM_C12(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_gt2(yvy400, yvy500, h), h, ba)
new_addToFM_C(Branch(Just(yvy500), yvy51, yvy52, yvy53, yvy54), Just(yvy400), yvy41, h, ba) → new_addToFM_C22(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_esEs9(new_compare26(Just(yvy400), Just(yvy500), new_esEs29(yvy400, yvy500, h), h), LT), h, ba)
new_addToFM_C12(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy54, Just(yvy400), yvy41, h, ba)
new_addToFM_C21(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy53, Just(yvy400), yvy41, h, ba)
new_addToFM_C21(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, False, h, ba) → new_addToFM_C11(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_gt1(yvy400, h), h, ba)
new_addToFM_C22(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy53, Just(yvy400), yvy41, h, ba)

The TRS R consists of the following rules:

new_compare26(Just(yvy4900), Nothing, False, ccg) → GT
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True
new_gt2(yvy35, yvy30, bgc) → new_esEs9(new_compare33(yvy35, yvy30, bgc), GT)
new_compare33(yvy20, yvy15, dbe) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, dbe), dbe)
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(ty_[], dcg)) → new_esEs19(yvy20, yvy15, dcg)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcf)) → new_esEs4(yvy20, yvy15, dcf)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs7(yvy20, yvy15, dcc, dcd, dce)
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcb)) → new_esEs10(yvy20, yvy15, dcb)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbf), dbg)) → new_esEs5(yvy20, yvy15, dbf, dbg)
new_esEs30(yvy20, yvy15, app(app(ty_@2, dbh), dca)) → new_esEs6(yvy20, yvy15, dbh, dca)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_compare26(Just(yvy4900), Just(yvy5000), False, ccg) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, ccg), ccg)
new_compare26(yvy490, yvy500, True, ccg) → EQ
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, cg), da)) → new_ltEs5(yvy4900, yvy5000, cg, da)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, beh), bde)) → new_ltEs10(yvy4900, yvy5000, beh, bde)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, ga)) → new_ltEs9(yvy4900, yvy5000, ga)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, fh)) → new_ltEs17(yvy4900, yvy5000, fh)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(ty_[], bc)) → new_ltEs14(yvy4900, yvy5000, bc)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, cch), cda), cdb)) → new_ltEs13(yvy4900, yvy5000, cch, cda, cdb)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare13(yvy175, yvy176, True, fg) → LT
new_compare13(yvy175, yvy176, False, fg) → GT
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_compare16(@0, @0) → EQ
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_not(False) → True
new_not(True) → False
new_ltEs18(EQ, GT) → True
new_ltEs18(EQ, EQ) → True
new_ltEs18(LT, LT) → True
new_ltEs18(GT, GT) → True
new_ltEs18(LT, GT) → True
new_ltEs18(GT, LT) → False
new_ltEs18(GT, EQ) → False
new_ltEs18(EQ, LT) → False
new_ltEs18(LT, EQ) → True
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), cch, cda, cdb) → new_pePe(new_lt20(yvy49000, yvy50000, cch), new_asAs(new_esEs26(yvy49000, yvy50000, cch), new_pePe(new_lt19(yvy49001, yvy50001, cda), new_asAs(new_esEs27(yvy49001, yvy50001, cda), new_ltEs20(yvy49002, yvy50002, cdb)))))
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cdh), cea), ceb)) → new_lt14(yvy49000, yvy50000, cdh, cea, ceb)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, ced)) → new_lt17(yvy49000, yvy50000, ced)
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdf), cdg)) → new_lt12(yvy49000, yvy50000, cdf, cdg)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cdc)) → new_lt10(yvy49000, yvy50000, cdc)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cdd), cde)) → new_lt11(yvy49000, yvy50000, cdd, cde)
new_lt20(yvy49000, yvy50000, app(ty_[], cec)) → new_lt15(yvy49000, yvy50000, cec)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, ced)) → new_esEs10(yvy49000, yvy50000, ced)
new_esEs26(yvy49000, yvy50000, app(ty_[], cec)) → new_esEs19(yvy49000, yvy50000, cec)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cdc)) → new_esEs4(yvy49000, yvy50000, cdc)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cdh), cea), ceb)) → new_esEs7(yvy49000, yvy50000, cdh, cea, ceb)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cdd), cde)) → new_esEs5(yvy49000, yvy50000, cdd, cde)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdf), cdg)) → new_esEs6(yvy49000, yvy50000, cdf, cdg)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cff)) → new_lt17(yvy49001, yvy50001, cff)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cee)) → new_lt10(yvy49001, yvy50001, cee)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, app(app(ty_@2, ceh), cfa)) → new_lt12(yvy49001, yvy50001, ceh, cfa)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_lt14(yvy49001, yvy50001, cfb, cfc, cfd)
new_lt19(yvy49001, yvy50001, app(ty_[], cfe)) → new_lt15(yvy49001, yvy50001, cfe)
new_lt19(yvy49001, yvy50001, app(app(ty_Either, cef), ceg)) → new_lt11(yvy49001, yvy50001, cef, ceg)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs7(yvy49001, yvy50001, cfb, cfc, cfd)
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, cef), ceg)) → new_esEs5(yvy49001, yvy50001, cef, ceg)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, ceh), cfa)) → new_esEs6(yvy49001, yvy50001, ceh, cfa)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cee)) → new_esEs4(yvy49001, yvy50001, cee)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cff)) → new_esEs10(yvy49001, yvy50001, cff)
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cfe)) → new_esEs19(yvy49001, yvy50001, cfe)
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfg)) → new_ltEs9(yvy49002, yvy50002, cfg)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cgh)) → new_ltEs17(yvy49002, yvy50002, cgh)
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cgb), cgc)) → new_ltEs5(yvy49002, yvy50002, cgb, cgc)
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(ty_[], cgg)) → new_ltEs14(yvy49002, yvy50002, cgg)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cfh), cga)) → new_ltEs10(yvy49002, yvy50002, cfh, cga)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cgd), cge), cgf)) → new_ltEs13(yvy49002, yvy50002, cgd, cge, cgf)
new_asAs(False, yvy182) → False
new_asAs(True, yvy182) → yvy182
new_pePe(False, yvy201) → yvy201
new_pePe(True, yvy201) → True
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, bea), beb), bde) → new_ltEs5(yvy49000, yvy50000, bea, beb)
new_ltEs10(Left(yvy49000), Right(yvy50000), beh, bde) → True
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_[], bga)) → new_ltEs14(yvy49000, yvy50000, bga)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bde) → new_ltEs12(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bde) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bec), bed), bee), bde) → new_ltEs13(yvy49000, yvy50000, bec, bed, bee)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(ty_@2, bfd), bfe)) → new_ltEs5(yvy49000, yvy50000, bfd, bfe)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bde) → new_ltEs11(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bde) → new_ltEs18(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(app(ty_@3, bff), bfg), bfh)) → new_ltEs13(yvy49000, yvy50000, bff, bfg, bfh)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, gb)) → new_ltEs9(yvy49000, yvy50000, gb)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bdf), bde) → new_ltEs9(yvy49000, yvy50000, bdf)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bdg), bdh), bde) → new_ltEs10(yvy49000, yvy50000, bdg, bdh)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_Maybe, bfa)) → new_ltEs9(yvy49000, yvy50000, bfa)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(ty_Either, bfb), bfc)) → new_ltEs10(yvy49000, yvy50000, bfb, bfc)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, gc), gd)) → new_ltEs10(yvy49000, yvy50000, gc, gd)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bde) → new_ltEs16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bde) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bde) → new_ltEs7(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], bef), bde) → new_ltEs14(yvy49000, yvy50000, bef)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_Ratio, bgb)) → new_ltEs17(yvy49000, yvy50000, bgb)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Left(yvy50000), beh, bde) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, beg), bde) → new_ltEs17(yvy49000, yvy50000, beg)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bde) → new_ltEs8(yvy49000, yvy50000)
new_ltEs8(False, True) → True
new_ltEs8(True, True) → True
new_ltEs8(True, False) → False
new_ltEs8(False, False) → True
new_ltEs17(yvy4900, yvy5000, fh) → new_fsEs(new_compare8(yvy4900, yvy5000, fh))
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs14(yvy4900, yvy5000, bc) → new_fsEs(new_compare0(yvy4900, yvy5000, bc))
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), bc) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, bc), bc)
new_compare0([], [], bc) → EQ
new_compare0(:(yvy49000, yvy49001), [], bc) → GT
new_compare0([], :(yvy50000, yvy50001), bc) → LT
new_primCompAux0(yvy49000, yvy50000, yvy202, bc) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, bc))
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(ty_[], bhd)) → new_compare0(yvy49000, yvy50000, bhd)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bha), bhb), bhc)) → new_compare14(yvy49000, yvy50000, bha, bhb, bhc)
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bgd)) → new_compare19(yvy49000, yvy50000, bgd)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bge), bgf)) → new_compare17(yvy49000, yvy50000, bge, bgf)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, bhe)) → new_compare8(yvy49000, yvy50000, bhe)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bgg), bgh)) → new_compare18(yvy49000, yvy50000, bgg, bgh)
new_primCompAux00(yvy206, LT) → LT
new_primCompAux00(yvy206, EQ) → yvy206
new_primCompAux00(yvy206, GT) → GT
new_compare18(yvy49000, yvy50000, de, df) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, de, df), de, df)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bhh, caa) → new_asAs(new_esEs24(yvy4000, yvy3000, bhh), new_esEs25(yvy4001, yvy3001, caa))
new_compare25(yvy49000, yvy50000, True, de, df) → EQ
new_compare25(yvy49000, yvy50000, False, de, df) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, de, df), de, df)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), cg, da) → new_pePe(new_lt6(yvy49000, yvy50000, cg), new_asAs(new_esEs20(yvy49000, yvy50000, cg), new_ltEs6(yvy49001, yvy50001, da)))
new_compare110(yvy49000, yvy50000, True, de, df) → LT
new_compare110(yvy49000, yvy50000, False, de, df) → GT
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, dc), dd)) → new_lt11(yvy49000, yvy50000, dc, dd)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ec)) → new_lt17(yvy49000, yvy50000, ec)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_[], eb)) → new_lt15(yvy49000, yvy50000, eb)
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, db)) → new_lt10(yvy49000, yvy50000, db)
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, dg), dh), ea)) → new_lt14(yvy49000, yvy50000, dg, dh, ea)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(ty_@2, de), df)) → new_lt12(yvy49000, yvy50000, de, df)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, db)) → new_esEs4(yvy49000, yvy50000, db)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, de), df)) → new_esEs6(yvy49000, yvy50000, de, df)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, dg), dh), ea)) → new_esEs7(yvy49000, yvy50000, dg, dh, ea)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, dc), dd)) → new_esEs5(yvy49000, yvy50000, dc, dd)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ec)) → new_esEs10(yvy49000, yvy50000, ec)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_[], eb)) → new_esEs19(yvy49000, yvy50000, eb)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, ff)) → new_ltEs17(yvy49001, yvy50001, ff)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fa), fb), fc)) → new_ltEs13(yvy49001, yvy50001, fa, fb, fc)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ed)) → new_ltEs9(yvy49001, yvy50001, ed)
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, ee), ef)) → new_ltEs10(yvy49001, yvy50001, ee, ef)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fd)) → new_ltEs14(yvy49001, yvy50001, fd)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, eg), eh)) → new_ltEs5(yvy49001, yvy50001, eg, eh)
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs9(Nothing, Just(yvy50000), ga) → True
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, ge), gf)) → new_ltEs5(yvy49000, yvy50000, ge, gf)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, hc)) → new_ltEs17(yvy49000, yvy50000, hc)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], hb)) → new_ltEs14(yvy49000, yvy50000, hb)
new_ltEs9(Just(yvy49000), Nothing, ga) → False
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, ga) → True
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, gg), gh), ha)) → new_ltEs13(yvy49000, yvy50000, gg, gh, ha)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs19([], [], cab) → True
new_esEs19(:(yvy4000, yvy4001), [], cab) → False
new_esEs19([], :(yvy3000, yvy3001), cab) → False
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), cab) → new_asAs(new_esEs28(yvy4000, yvy3000, cab), new_esEs19(yvy4001, yvy3001, cab))
new_esEs28(yvy4000, yvy3000, app(ty_[], dea)) → new_esEs19(yvy4000, yvy3000, dea)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, ddd)) → new_esEs10(yvy4000, yvy3000, ddd)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, ddh)) → new_esEs4(yvy4000, yvy3000, ddh)
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dch), dda)) → new_esEs5(yvy4000, yvy3000, dch, dda)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs7(yvy4000, yvy3000, dde, ddf, ddg)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddb), ddc)) → new_esEs6(yvy4000, yvy3000, ddb, ddc)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_esEs15(True, True) → True
new_esEs15(False, False) → True
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), hd, he, hf) → new_asAs(new_esEs21(yvy4000, yvy3000, hd), new_asAs(new_esEs22(yvy4001, yvy3001, he), new_esEs23(yvy4002, yvy3002, hf)))
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, baa), bab)) → new_esEs6(yvy4000, yvy3000, baa, bab)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, bad), bae), baf)) → new_esEs7(yvy4000, yvy3000, bad, bae, baf)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bah)) → new_esEs19(yvy4000, yvy3000, bah)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bac)) → new_esEs10(yvy4000, yvy3000, bac)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bag)) → new_esEs4(yvy4000, yvy3000, bag)
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, hg), hh)) → new_esEs5(yvy4000, yvy3000, hg, hh)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, app(ty_[], bcb)) → new_esEs19(yvy4001, yvy3001, bcb)
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bca)) → new_esEs4(yvy4001, yvy3001, bca)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bbc), bbd)) → new_esEs6(yvy4001, yvy3001, bbc, bbd)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs7(yvy4001, yvy3001, bbf, bbg, bbh)
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bbe)) → new_esEs10(yvy4001, yvy3001, bbe)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bba), bbb)) → new_esEs5(yvy4001, yvy3001, bba, bbb)
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bcc), bcd)) → new_esEs5(yvy4002, yvy3002, bcc, bcd)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, bdc)) → new_esEs4(yvy4002, yvy3002, bdc)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs7(yvy4002, yvy3002, bch, bda, bdb)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_[], bdd)) → new_esEs19(yvy4002, yvy3002, bdd)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bcg)) → new_esEs10(yvy4002, yvy3002, bcg)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bce), bcf)) → new_esEs6(yvy4002, yvy3002, bce, bcf)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(LT, EQ) → False
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bb) → new_asAs(new_esEs11(yvy4000, yvy3000, bb), new_esEs12(yvy4001, yvy3001, bb))
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs18(@0, @0) → True
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Nothing, bd) → False
new_esEs4(Nothing, Just(yvy3000), bd) → False
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, ca)) → new_esEs10(yvy4000, yvy3000, ca)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_Maybe, dbc)) → new_esEs4(yvy4000, yvy3000, dbc)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, daa), bhg) → new_esEs4(yvy4000, yvy3000, daa)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, ce)) → new_esEs4(yvy4000, yvy3000, ce)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(ty_Either, dac), dad)) → new_esEs5(yvy4000, yvy3000, dac, dad)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, cha), chb), bhg) → new_esEs5(yvy4000, yvy3000, cha, chb)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, be), bf)) → new_esEs5(yvy4000, yvy3000, be, bf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, bg), bh)) → new_esEs6(yvy4000, yvy3000, bg, bh)
new_esEs4(Nothing, Nothing, bd) → True
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], cf)) → new_esEs19(yvy4000, yvy3000, cf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cb), cc), cd)) → new_esEs7(yvy4000, yvy3000, cb, cc, cd)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], dab), bhg) → new_esEs19(yvy4000, yvy3000, dab)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, bhg) → new_esEs18(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chc), chd), bhg) → new_esEs6(yvy4000, yvy3000, chc, chd)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(ty_@2, dae), daf)) → new_esEs6(yvy4000, yvy3000, dae, daf)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, bhg) → new_esEs9(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, bhg) → new_esEs16(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, chf), chg), chh), bhg) → new_esEs7(yvy4000, yvy3000, chf, chg, chh)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_[], dbd)) → new_esEs19(yvy4000, yvy3000, dbd)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_Ratio, dag)) → new_esEs10(yvy4000, yvy3000, dag)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, bhg) → new_esEs14(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, bhg) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, bhg) → new_esEs8(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, bhg) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Right(yvy3000), bhf, bhg) → False
new_esEs5(Right(yvy4000), Left(yvy3000), bhf, bhg) → False
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, bhg) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs7(yvy4000, yvy3000, dah, dba, dbb)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, che), bhg) → new_esEs10(yvy4000, yvy3000, che)
new_lt12(yvy49000, yvy50000, de, df) → new_esEs9(new_compare18(yvy49000, yvy50000, de, df), LT)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_lt14(yvy49000, yvy50000, dg, dh, ea) → new_esEs9(new_compare14(yvy49000, yvy50000, dg, dh, ea), LT)
new_compare14(yvy49000, yvy50000, dg, dh, ea) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, dg, dh, ea), dg, dh, ea)
new_compare24(yvy49000, yvy50000, False, dg, dh, ea) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, dg, dh, ea), dg, dh, ea)
new_compare24(yvy49000, yvy50000, True, dg, dh, ea) → EQ
new_compare111(yvy49000, yvy50000, True, dg, dh, ea) → LT
new_compare111(yvy49000, yvy50000, False, dg, dh, ea) → GT
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_compare211(yvy49000, yvy50000, True) → EQ
new_compare112(yvy49000, yvy50000, True) → LT
new_compare112(yvy49000, yvy50000, False) → GT
new_lt10(yvy49000, yvy50000, db) → new_esEs9(new_compare19(yvy49000, yvy50000, db), LT)
new_compare19(yvy49000, yvy50000, db) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, db), db)
new_compare26(Nothing, Just(yvy5000), False, ccg) → LT
new_compare26(Nothing, Nothing, False, ccg) → LT
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_lt15(yvy49000, yvy50000, eb) → new_esEs9(new_compare0(yvy49000, yvy50000, eb), LT)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_lt17(yvy49000, yvy50000, ec) → new_esEs9(new_compare8(yvy49000, yvy50000, ec), LT)
new_lt11(yvy49000, yvy50000, dc, dd) → new_esEs9(new_compare17(yvy49000, yvy50000, dc, dd), LT)
new_compare17(yvy49000, yvy50000, dc, dd) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, dc, dd), dc, dd)
new_compare23(yvy49000, yvy50000, False, dc, dd) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, dc, dd), dc, dd)
new_compare23(yvy49000, yvy50000, True, dc, dd) → EQ
new_compare12(yvy49000, yvy50000, False, dc, dd) → GT
new_compare12(yvy49000, yvy50000, True, dc, dd) → LT
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_compare210(yvy49000, yvy50000, True) → EQ
new_compare11(yvy49000, yvy50000, False) → GT
new_compare11(yvy49000, yvy50000, True) → LT
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, cac), cad)) → new_esEs5(yvy4000, yvy3000, cac, cad)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cbc)) → new_esEs4(yvy4000, yvy3000, cbc)
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbd)) → new_esEs19(yvy4000, yvy3000, cbd)
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, cae), caf)) → new_esEs6(yvy4000, yvy3000, cae, caf)
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, cah), cba), cbb)) → new_esEs7(yvy4000, yvy3000, cah, cba, cbb)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cag)) → new_esEs10(yvy4000, yvy3000, cag)
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbe), cbf)) → new_esEs5(yvy4001, yvy3001, cbe, cbf)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbg), cbh)) → new_esEs6(yvy4001, yvy3001, cbg, cbh)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccf)) → new_esEs19(yvy4001, yvy3001, ccf)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, cca)) → new_esEs10(yvy4001, yvy3001, cca)
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, cce)) → new_esEs4(yvy4001, yvy3001, cce)
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, ccb), ccc), ccd)) → new_esEs7(yvy4001, yvy3001, ccb, ccc, ccd)
new_esEs29(yvy400, yvy500, ty_Integer) → new_esEs13(yvy400, yvy500)
new_esEs29(yvy400, yvy500, app(ty_[], cab)) → new_esEs19(yvy400, yvy500, cab)
new_esEs29(yvy400, yvy500, app(app(app(ty_@3, hd), he), hf)) → new_esEs7(yvy400, yvy500, hd, he, hf)
new_esEs29(yvy400, yvy500, ty_Double) → new_esEs16(yvy400, yvy500)
new_esEs29(yvy400, yvy500, ty_Int) → new_esEs14(yvy400, yvy500)
new_esEs29(yvy400, yvy500, app(app(ty_Either, bhf), bhg)) → new_esEs5(yvy400, yvy500, bhf, bhg)
new_esEs29(yvy400, yvy500, ty_@0) → new_esEs18(yvy400, yvy500)
new_esEs29(yvy400, yvy500, app(app(ty_@2, bhh), caa)) → new_esEs6(yvy400, yvy500, bhh, caa)
new_esEs29(yvy400, yvy500, ty_Bool) → new_esEs15(yvy400, yvy500)
new_esEs29(yvy400, yvy500, app(ty_Ratio, bb)) → new_esEs10(yvy400, yvy500, bb)
new_esEs29(yvy400, yvy500, ty_Char) → new_esEs8(yvy400, yvy500)
new_esEs29(yvy400, yvy500, ty_Float) → new_esEs17(yvy400, yvy500)
new_esEs29(yvy400, yvy500, app(ty_Maybe, bd)) → new_esEs4(yvy400, yvy500, bd)
new_esEs29(yvy400, yvy500, ty_Ordering) → new_esEs9(yvy400, yvy500)
new_gt1(yvy400, h) → new_esEs9(new_compare32(yvy400, h), GT)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs30(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs9(Nothing, Nothing, x0)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_compare25(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare12(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_gt2(x0, x1, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs15(True, True)
new_primCmpNat0(x0, Zero)
new_compare0([], [], x0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare33(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_ltEs6(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs6(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs14(x0, x1, x2)
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt12(x0, x1, x2, x3)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Float)
new_compare18(x0, x1, x2, x3)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, x2)
new_esEs27(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_compare28(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_esEs19([], :(x0, x1), x2)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(:(x0, x1), [], x2)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Zero)
new_ltEs9(Nothing, Just(x0), x1)
new_esEs25(x0, x1, ty_Char)
new_esEs19([], [], x0)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt15(x0, x1, x2)
new_compare110(x0, x1, False, x2, x3)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat1(Zero, Succ(x0))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_gt(x0)
new_esEs27(x0, x1, ty_Double)
new_esEs9(GT, GT)
new_ltEs8(False, False)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare32(x0, x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs8(False, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs8(True, False)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_gt0(x0, x1)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Nothing, Just(x0), x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare26(Just(x0), Just(x1), False, x2)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpNat2(Zero, x0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs14(x0, x1)
new_esEs29(x0, x1, ty_Char)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_ltEs12(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_compare26(x0, x1, True, x2)
new_compare23(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, True, x2)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs29(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, False, x2)
new_esEs20(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_compare210(x0, x1, True)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat1(Succ(x0), Zero)
new_esEs4(Nothing, Nothing, x0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_compare31(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(Char(x0), Char(x1))
new_compare17(x0, x1, x2, x3)
new_esEs29(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_compare26(Just(x0), Nothing, False, x1)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), [], x2)
new_compare25(x0, x1, False, x2, x3)
new_compare28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_compare26(Nothing, Nothing, False, x0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_compare28(x0, x1, ty_Integer)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_compare12(x0, x1, True, x2, x3)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare28(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_gt1(x0, x1)
new_compare26(Nothing, Just(x0), False, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, False, x2, x3, x4)
new_compare11(x0, x1, True)
new_ltEs17(x0, x1, x2)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare14(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)

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_gt(x0)
new_gt0(x0, x1)
new_compare31(x0, x1)
new_compare30(x0)



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

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

new_addToFM_C(Branch(Nothing, yvy51, yvy52, yvy53, yvy54), Just(yvy400), yvy41, h, ba) → new_addToFM_C21(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), LT), h, ba)
new_addToFM_C11(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy54, Just(yvy400), yvy41, h, ba)
new_addToFM_C22(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, False, h, ba) → new_addToFM_C12(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_gt2(yvy400, yvy500, h), h, ba)
new_addToFM_C(Branch(Just(yvy500), yvy51, yvy52, yvy53, yvy54), Just(yvy400), yvy41, h, ba) → new_addToFM_C22(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_esEs9(new_compare26(Just(yvy400), Just(yvy500), new_esEs29(yvy400, yvy500, h), h), LT), h, ba)
new_addToFM_C12(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy54, Just(yvy400), yvy41, h, ba)
new_addToFM_C21(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, False, h, ba) → new_addToFM_C11(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_gt1(yvy400, h), h, ba)
new_addToFM_C21(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy53, Just(yvy400), yvy41, h, ba)
new_addToFM_C22(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_addToFM_C(yvy53, Just(yvy400), yvy41, h, ba)

The TRS R consists of the following rules:

new_compare26(Just(yvy4900), Nothing, False, ccg) → GT
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True
new_gt2(yvy35, yvy30, bgc) → new_esEs9(new_compare33(yvy35, yvy30, bgc), GT)
new_compare33(yvy20, yvy15, dbe) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, dbe), dbe)
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(ty_[], dcg)) → new_esEs19(yvy20, yvy15, dcg)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcf)) → new_esEs4(yvy20, yvy15, dcf)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs7(yvy20, yvy15, dcc, dcd, dce)
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcb)) → new_esEs10(yvy20, yvy15, dcb)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbf), dbg)) → new_esEs5(yvy20, yvy15, dbf, dbg)
new_esEs30(yvy20, yvy15, app(app(ty_@2, dbh), dca)) → new_esEs6(yvy20, yvy15, dbh, dca)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_compare26(Just(yvy4900), Just(yvy5000), False, ccg) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, ccg), ccg)
new_compare26(yvy490, yvy500, True, ccg) → EQ
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, cg), da)) → new_ltEs5(yvy4900, yvy5000, cg, da)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, beh), bde)) → new_ltEs10(yvy4900, yvy5000, beh, bde)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, ga)) → new_ltEs9(yvy4900, yvy5000, ga)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, fh)) → new_ltEs17(yvy4900, yvy5000, fh)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(ty_[], bc)) → new_ltEs14(yvy4900, yvy5000, bc)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, cch), cda), cdb)) → new_ltEs13(yvy4900, yvy5000, cch, cda, cdb)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare13(yvy175, yvy176, True, fg) → LT
new_compare13(yvy175, yvy176, False, fg) → GT
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_compare16(@0, @0) → EQ
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_not(False) → True
new_not(True) → False
new_ltEs18(EQ, GT) → True
new_ltEs18(EQ, EQ) → True
new_ltEs18(LT, LT) → True
new_ltEs18(GT, GT) → True
new_ltEs18(LT, GT) → True
new_ltEs18(GT, LT) → False
new_ltEs18(GT, EQ) → False
new_ltEs18(EQ, LT) → False
new_ltEs18(LT, EQ) → True
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), cch, cda, cdb) → new_pePe(new_lt20(yvy49000, yvy50000, cch), new_asAs(new_esEs26(yvy49000, yvy50000, cch), new_pePe(new_lt19(yvy49001, yvy50001, cda), new_asAs(new_esEs27(yvy49001, yvy50001, cda), new_ltEs20(yvy49002, yvy50002, cdb)))))
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cdh), cea), ceb)) → new_lt14(yvy49000, yvy50000, cdh, cea, ceb)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, ced)) → new_lt17(yvy49000, yvy50000, ced)
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdf), cdg)) → new_lt12(yvy49000, yvy50000, cdf, cdg)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cdc)) → new_lt10(yvy49000, yvy50000, cdc)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cdd), cde)) → new_lt11(yvy49000, yvy50000, cdd, cde)
new_lt20(yvy49000, yvy50000, app(ty_[], cec)) → new_lt15(yvy49000, yvy50000, cec)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, ced)) → new_esEs10(yvy49000, yvy50000, ced)
new_esEs26(yvy49000, yvy50000, app(ty_[], cec)) → new_esEs19(yvy49000, yvy50000, cec)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cdc)) → new_esEs4(yvy49000, yvy50000, cdc)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cdh), cea), ceb)) → new_esEs7(yvy49000, yvy50000, cdh, cea, ceb)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cdd), cde)) → new_esEs5(yvy49000, yvy50000, cdd, cde)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdf), cdg)) → new_esEs6(yvy49000, yvy50000, cdf, cdg)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cff)) → new_lt17(yvy49001, yvy50001, cff)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cee)) → new_lt10(yvy49001, yvy50001, cee)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, app(app(ty_@2, ceh), cfa)) → new_lt12(yvy49001, yvy50001, ceh, cfa)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_lt14(yvy49001, yvy50001, cfb, cfc, cfd)
new_lt19(yvy49001, yvy50001, app(ty_[], cfe)) → new_lt15(yvy49001, yvy50001, cfe)
new_lt19(yvy49001, yvy50001, app(app(ty_Either, cef), ceg)) → new_lt11(yvy49001, yvy50001, cef, ceg)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs7(yvy49001, yvy50001, cfb, cfc, cfd)
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, cef), ceg)) → new_esEs5(yvy49001, yvy50001, cef, ceg)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, ceh), cfa)) → new_esEs6(yvy49001, yvy50001, ceh, cfa)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cee)) → new_esEs4(yvy49001, yvy50001, cee)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cff)) → new_esEs10(yvy49001, yvy50001, cff)
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cfe)) → new_esEs19(yvy49001, yvy50001, cfe)
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfg)) → new_ltEs9(yvy49002, yvy50002, cfg)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cgh)) → new_ltEs17(yvy49002, yvy50002, cgh)
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cgb), cgc)) → new_ltEs5(yvy49002, yvy50002, cgb, cgc)
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(ty_[], cgg)) → new_ltEs14(yvy49002, yvy50002, cgg)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cfh), cga)) → new_ltEs10(yvy49002, yvy50002, cfh, cga)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cgd), cge), cgf)) → new_ltEs13(yvy49002, yvy50002, cgd, cge, cgf)
new_asAs(False, yvy182) → False
new_asAs(True, yvy182) → yvy182
new_pePe(False, yvy201) → yvy201
new_pePe(True, yvy201) → True
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, bea), beb), bde) → new_ltEs5(yvy49000, yvy50000, bea, beb)
new_ltEs10(Left(yvy49000), Right(yvy50000), beh, bde) → True
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_[], bga)) → new_ltEs14(yvy49000, yvy50000, bga)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bde) → new_ltEs12(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bde) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bec), bed), bee), bde) → new_ltEs13(yvy49000, yvy50000, bec, bed, bee)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(ty_@2, bfd), bfe)) → new_ltEs5(yvy49000, yvy50000, bfd, bfe)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bde) → new_ltEs11(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bde) → new_ltEs18(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(app(ty_@3, bff), bfg), bfh)) → new_ltEs13(yvy49000, yvy50000, bff, bfg, bfh)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, gb)) → new_ltEs9(yvy49000, yvy50000, gb)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bdf), bde) → new_ltEs9(yvy49000, yvy50000, bdf)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bdg), bdh), bde) → new_ltEs10(yvy49000, yvy50000, bdg, bdh)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_Maybe, bfa)) → new_ltEs9(yvy49000, yvy50000, bfa)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(ty_Either, bfb), bfc)) → new_ltEs10(yvy49000, yvy50000, bfb, bfc)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, gc), gd)) → new_ltEs10(yvy49000, yvy50000, gc, gd)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bde) → new_ltEs16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bde) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bde) → new_ltEs7(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], bef), bde) → new_ltEs14(yvy49000, yvy50000, bef)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_Ratio, bgb)) → new_ltEs17(yvy49000, yvy50000, bgb)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Left(yvy50000), beh, bde) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, beg), bde) → new_ltEs17(yvy49000, yvy50000, beg)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bde) → new_ltEs8(yvy49000, yvy50000)
new_ltEs8(False, True) → True
new_ltEs8(True, True) → True
new_ltEs8(True, False) → False
new_ltEs8(False, False) → True
new_ltEs17(yvy4900, yvy5000, fh) → new_fsEs(new_compare8(yvy4900, yvy5000, fh))
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs14(yvy4900, yvy5000, bc) → new_fsEs(new_compare0(yvy4900, yvy5000, bc))
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), bc) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, bc), bc)
new_compare0([], [], bc) → EQ
new_compare0(:(yvy49000, yvy49001), [], bc) → GT
new_compare0([], :(yvy50000, yvy50001), bc) → LT
new_primCompAux0(yvy49000, yvy50000, yvy202, bc) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, bc))
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(ty_[], bhd)) → new_compare0(yvy49000, yvy50000, bhd)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bha), bhb), bhc)) → new_compare14(yvy49000, yvy50000, bha, bhb, bhc)
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bgd)) → new_compare19(yvy49000, yvy50000, bgd)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bge), bgf)) → new_compare17(yvy49000, yvy50000, bge, bgf)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, bhe)) → new_compare8(yvy49000, yvy50000, bhe)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bgg), bgh)) → new_compare18(yvy49000, yvy50000, bgg, bgh)
new_primCompAux00(yvy206, LT) → LT
new_primCompAux00(yvy206, EQ) → yvy206
new_primCompAux00(yvy206, GT) → GT
new_compare18(yvy49000, yvy50000, de, df) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, de, df), de, df)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bhh, caa) → new_asAs(new_esEs24(yvy4000, yvy3000, bhh), new_esEs25(yvy4001, yvy3001, caa))
new_compare25(yvy49000, yvy50000, True, de, df) → EQ
new_compare25(yvy49000, yvy50000, False, de, df) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, de, df), de, df)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), cg, da) → new_pePe(new_lt6(yvy49000, yvy50000, cg), new_asAs(new_esEs20(yvy49000, yvy50000, cg), new_ltEs6(yvy49001, yvy50001, da)))
new_compare110(yvy49000, yvy50000, True, de, df) → LT
new_compare110(yvy49000, yvy50000, False, de, df) → GT
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, dc), dd)) → new_lt11(yvy49000, yvy50000, dc, dd)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ec)) → new_lt17(yvy49000, yvy50000, ec)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_[], eb)) → new_lt15(yvy49000, yvy50000, eb)
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, db)) → new_lt10(yvy49000, yvy50000, db)
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, dg), dh), ea)) → new_lt14(yvy49000, yvy50000, dg, dh, ea)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(ty_@2, de), df)) → new_lt12(yvy49000, yvy50000, de, df)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, db)) → new_esEs4(yvy49000, yvy50000, db)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, de), df)) → new_esEs6(yvy49000, yvy50000, de, df)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, dg), dh), ea)) → new_esEs7(yvy49000, yvy50000, dg, dh, ea)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, dc), dd)) → new_esEs5(yvy49000, yvy50000, dc, dd)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ec)) → new_esEs10(yvy49000, yvy50000, ec)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_[], eb)) → new_esEs19(yvy49000, yvy50000, eb)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, ff)) → new_ltEs17(yvy49001, yvy50001, ff)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fa), fb), fc)) → new_ltEs13(yvy49001, yvy50001, fa, fb, fc)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ed)) → new_ltEs9(yvy49001, yvy50001, ed)
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, ee), ef)) → new_ltEs10(yvy49001, yvy50001, ee, ef)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fd)) → new_ltEs14(yvy49001, yvy50001, fd)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, eg), eh)) → new_ltEs5(yvy49001, yvy50001, eg, eh)
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs9(Nothing, Just(yvy50000), ga) → True
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, ge), gf)) → new_ltEs5(yvy49000, yvy50000, ge, gf)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, hc)) → new_ltEs17(yvy49000, yvy50000, hc)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], hb)) → new_ltEs14(yvy49000, yvy50000, hb)
new_ltEs9(Just(yvy49000), Nothing, ga) → False
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, ga) → True
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, gg), gh), ha)) → new_ltEs13(yvy49000, yvy50000, gg, gh, ha)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs19([], [], cab) → True
new_esEs19(:(yvy4000, yvy4001), [], cab) → False
new_esEs19([], :(yvy3000, yvy3001), cab) → False
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), cab) → new_asAs(new_esEs28(yvy4000, yvy3000, cab), new_esEs19(yvy4001, yvy3001, cab))
new_esEs28(yvy4000, yvy3000, app(ty_[], dea)) → new_esEs19(yvy4000, yvy3000, dea)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, ddd)) → new_esEs10(yvy4000, yvy3000, ddd)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, ddh)) → new_esEs4(yvy4000, yvy3000, ddh)
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dch), dda)) → new_esEs5(yvy4000, yvy3000, dch, dda)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs7(yvy4000, yvy3000, dde, ddf, ddg)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddb), ddc)) → new_esEs6(yvy4000, yvy3000, ddb, ddc)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_esEs15(True, True) → True
new_esEs15(False, False) → True
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), hd, he, hf) → new_asAs(new_esEs21(yvy4000, yvy3000, hd), new_asAs(new_esEs22(yvy4001, yvy3001, he), new_esEs23(yvy4002, yvy3002, hf)))
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, baa), bab)) → new_esEs6(yvy4000, yvy3000, baa, bab)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, bad), bae), baf)) → new_esEs7(yvy4000, yvy3000, bad, bae, baf)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bah)) → new_esEs19(yvy4000, yvy3000, bah)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bac)) → new_esEs10(yvy4000, yvy3000, bac)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bag)) → new_esEs4(yvy4000, yvy3000, bag)
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, hg), hh)) → new_esEs5(yvy4000, yvy3000, hg, hh)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, app(ty_[], bcb)) → new_esEs19(yvy4001, yvy3001, bcb)
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bca)) → new_esEs4(yvy4001, yvy3001, bca)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bbc), bbd)) → new_esEs6(yvy4001, yvy3001, bbc, bbd)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs7(yvy4001, yvy3001, bbf, bbg, bbh)
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bbe)) → new_esEs10(yvy4001, yvy3001, bbe)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bba), bbb)) → new_esEs5(yvy4001, yvy3001, bba, bbb)
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bcc), bcd)) → new_esEs5(yvy4002, yvy3002, bcc, bcd)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, bdc)) → new_esEs4(yvy4002, yvy3002, bdc)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs7(yvy4002, yvy3002, bch, bda, bdb)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_[], bdd)) → new_esEs19(yvy4002, yvy3002, bdd)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bcg)) → new_esEs10(yvy4002, yvy3002, bcg)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bce), bcf)) → new_esEs6(yvy4002, yvy3002, bce, bcf)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(LT, EQ) → False
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bb) → new_asAs(new_esEs11(yvy4000, yvy3000, bb), new_esEs12(yvy4001, yvy3001, bb))
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs18(@0, @0) → True
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Nothing, bd) → False
new_esEs4(Nothing, Just(yvy3000), bd) → False
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, ca)) → new_esEs10(yvy4000, yvy3000, ca)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_Maybe, dbc)) → new_esEs4(yvy4000, yvy3000, dbc)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, daa), bhg) → new_esEs4(yvy4000, yvy3000, daa)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, ce)) → new_esEs4(yvy4000, yvy3000, ce)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(ty_Either, dac), dad)) → new_esEs5(yvy4000, yvy3000, dac, dad)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, cha), chb), bhg) → new_esEs5(yvy4000, yvy3000, cha, chb)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, be), bf)) → new_esEs5(yvy4000, yvy3000, be, bf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, bg), bh)) → new_esEs6(yvy4000, yvy3000, bg, bh)
new_esEs4(Nothing, Nothing, bd) → True
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], cf)) → new_esEs19(yvy4000, yvy3000, cf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cb), cc), cd)) → new_esEs7(yvy4000, yvy3000, cb, cc, cd)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], dab), bhg) → new_esEs19(yvy4000, yvy3000, dab)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, bhg) → new_esEs18(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chc), chd), bhg) → new_esEs6(yvy4000, yvy3000, chc, chd)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(ty_@2, dae), daf)) → new_esEs6(yvy4000, yvy3000, dae, daf)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, bhg) → new_esEs9(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, bhg) → new_esEs16(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, chf), chg), chh), bhg) → new_esEs7(yvy4000, yvy3000, chf, chg, chh)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_[], dbd)) → new_esEs19(yvy4000, yvy3000, dbd)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_Ratio, dag)) → new_esEs10(yvy4000, yvy3000, dag)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, bhg) → new_esEs14(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, bhg) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, bhg) → new_esEs8(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, bhg) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Right(yvy3000), bhf, bhg) → False
new_esEs5(Right(yvy4000), Left(yvy3000), bhf, bhg) → False
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, bhg) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs7(yvy4000, yvy3000, dah, dba, dbb)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, che), bhg) → new_esEs10(yvy4000, yvy3000, che)
new_lt12(yvy49000, yvy50000, de, df) → new_esEs9(new_compare18(yvy49000, yvy50000, de, df), LT)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_lt14(yvy49000, yvy50000, dg, dh, ea) → new_esEs9(new_compare14(yvy49000, yvy50000, dg, dh, ea), LT)
new_compare14(yvy49000, yvy50000, dg, dh, ea) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, dg, dh, ea), dg, dh, ea)
new_compare24(yvy49000, yvy50000, False, dg, dh, ea) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, dg, dh, ea), dg, dh, ea)
new_compare24(yvy49000, yvy50000, True, dg, dh, ea) → EQ
new_compare111(yvy49000, yvy50000, True, dg, dh, ea) → LT
new_compare111(yvy49000, yvy50000, False, dg, dh, ea) → GT
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_compare211(yvy49000, yvy50000, True) → EQ
new_compare112(yvy49000, yvy50000, True) → LT
new_compare112(yvy49000, yvy50000, False) → GT
new_lt10(yvy49000, yvy50000, db) → new_esEs9(new_compare19(yvy49000, yvy50000, db), LT)
new_compare19(yvy49000, yvy50000, db) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, db), db)
new_compare26(Nothing, Just(yvy5000), False, ccg) → LT
new_compare26(Nothing, Nothing, False, ccg) → LT
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_lt15(yvy49000, yvy50000, eb) → new_esEs9(new_compare0(yvy49000, yvy50000, eb), LT)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_lt17(yvy49000, yvy50000, ec) → new_esEs9(new_compare8(yvy49000, yvy50000, ec), LT)
new_lt11(yvy49000, yvy50000, dc, dd) → new_esEs9(new_compare17(yvy49000, yvy50000, dc, dd), LT)
new_compare17(yvy49000, yvy50000, dc, dd) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, dc, dd), dc, dd)
new_compare23(yvy49000, yvy50000, False, dc, dd) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, dc, dd), dc, dd)
new_compare23(yvy49000, yvy50000, True, dc, dd) → EQ
new_compare12(yvy49000, yvy50000, False, dc, dd) → GT
new_compare12(yvy49000, yvy50000, True, dc, dd) → LT
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_compare210(yvy49000, yvy50000, True) → EQ
new_compare11(yvy49000, yvy50000, False) → GT
new_compare11(yvy49000, yvy50000, True) → LT
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, cac), cad)) → new_esEs5(yvy4000, yvy3000, cac, cad)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cbc)) → new_esEs4(yvy4000, yvy3000, cbc)
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbd)) → new_esEs19(yvy4000, yvy3000, cbd)
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, cae), caf)) → new_esEs6(yvy4000, yvy3000, cae, caf)
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, cah), cba), cbb)) → new_esEs7(yvy4000, yvy3000, cah, cba, cbb)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cag)) → new_esEs10(yvy4000, yvy3000, cag)
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbe), cbf)) → new_esEs5(yvy4001, yvy3001, cbe, cbf)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbg), cbh)) → new_esEs6(yvy4001, yvy3001, cbg, cbh)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccf)) → new_esEs19(yvy4001, yvy3001, ccf)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, cca)) → new_esEs10(yvy4001, yvy3001, cca)
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, cce)) → new_esEs4(yvy4001, yvy3001, cce)
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, ccb), ccc), ccd)) → new_esEs7(yvy4001, yvy3001, ccb, ccc, ccd)
new_esEs29(yvy400, yvy500, ty_Integer) → new_esEs13(yvy400, yvy500)
new_esEs29(yvy400, yvy500, app(ty_[], cab)) → new_esEs19(yvy400, yvy500, cab)
new_esEs29(yvy400, yvy500, app(app(app(ty_@3, hd), he), hf)) → new_esEs7(yvy400, yvy500, hd, he, hf)
new_esEs29(yvy400, yvy500, ty_Double) → new_esEs16(yvy400, yvy500)
new_esEs29(yvy400, yvy500, ty_Int) → new_esEs14(yvy400, yvy500)
new_esEs29(yvy400, yvy500, app(app(ty_Either, bhf), bhg)) → new_esEs5(yvy400, yvy500, bhf, bhg)
new_esEs29(yvy400, yvy500, ty_@0) → new_esEs18(yvy400, yvy500)
new_esEs29(yvy400, yvy500, app(app(ty_@2, bhh), caa)) → new_esEs6(yvy400, yvy500, bhh, caa)
new_esEs29(yvy400, yvy500, ty_Bool) → new_esEs15(yvy400, yvy500)
new_esEs29(yvy400, yvy500, app(ty_Ratio, bb)) → new_esEs10(yvy400, yvy500, bb)
new_esEs29(yvy400, yvy500, ty_Char) → new_esEs8(yvy400, yvy500)
new_esEs29(yvy400, yvy500, ty_Float) → new_esEs17(yvy400, yvy500)
new_esEs29(yvy400, yvy500, app(ty_Maybe, bd)) → new_esEs4(yvy400, yvy500, bd)
new_esEs29(yvy400, yvy500, ty_Ordering) → new_esEs9(yvy400, yvy500)
new_gt1(yvy400, h) → new_esEs9(new_compare32(yvy400, h), GT)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs30(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs9(Nothing, Nothing, x0)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_compare25(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare12(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_gt2(x0, x1, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs15(True, True)
new_primCmpNat0(x0, Zero)
new_compare0([], [], x0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare33(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_ltEs6(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs6(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs14(x0, x1, x2)
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt12(x0, x1, x2, x3)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Float)
new_compare18(x0, x1, x2, x3)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, x2)
new_esEs27(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_compare28(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_esEs19([], :(x0, x1), x2)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(:(x0, x1), [], x2)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Zero)
new_ltEs9(Nothing, Just(x0), x1)
new_esEs25(x0, x1, ty_Char)
new_esEs19([], [], x0)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt15(x0, x1, x2)
new_compare110(x0, x1, False, x2, x3)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat1(Zero, Succ(x0))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Double)
new_esEs9(GT, GT)
new_ltEs8(False, False)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare32(x0, x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs8(False, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs8(True, False)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Nothing, Just(x0), x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare26(Just(x0), Just(x1), False, x2)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpNat2(Zero, x0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs14(x0, x1)
new_esEs29(x0, x1, ty_Char)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_ltEs12(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_compare26(x0, x1, True, x2)
new_compare23(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, True, x2)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs29(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, False, x2)
new_esEs20(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_compare210(x0, x1, True)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat1(Succ(x0), Zero)
new_esEs4(Nothing, Nothing, x0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(Char(x0), Char(x1))
new_compare17(x0, x1, x2, x3)
new_esEs29(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_compare26(Just(x0), Nothing, False, x1)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), [], x2)
new_compare25(x0, x1, False, x2, x3)
new_compare28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_compare26(Nothing, Nothing, False, x0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_compare28(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_compare12(x0, x1, True, x2, x3)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare28(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_gt1(x0, x1)
new_compare26(Nothing, Just(x0), False, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, False, x2, x3, x4)
new_compare11(x0, x1, True)
new_ltEs17(x0, x1, x2)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare14(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_addToFM_C1(yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy54, Nothing, yvy41, h, ba)
new_addToFM_C20(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, False, h, ba) → new_addToFM_C10(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, new_gt0(yvy500, h), h, ba)
new_addToFM_C2(yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy53, Nothing, yvy41, h, ba)
new_addToFM_C20(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy53, Nothing, yvy41, h, ba)
new_addToFM_C2(yvy51, yvy52, yvy53, yvy54, yvy41, False, h, ba) → new_addToFM_C1(yvy51, yvy52, yvy53, yvy54, yvy41, new_gt(h), h, ba)
new_addToFM_C10(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy54, Nothing, yvy41, h, ba)
new_addToFM_C(Branch(Just(yvy500), yvy51, yvy52, yvy53, yvy54), Nothing, yvy41, h, ba) → new_addToFM_C20(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, new_esEs9(new_compare26(Nothing, Just(yvy500), False, h), LT), h, ba)
new_addToFM_C(Branch(Nothing, yvy51, yvy52, yvy53, yvy54), Nothing, yvy41, h, ba) → new_addToFM_C2(yvy51, yvy52, yvy53, yvy54, yvy41, new_esEs9(new_compare26(Nothing, Nothing, True, h), LT), h, ba)

The TRS R consists of the following rules:

new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, ce)) → new_esEs4(yvy4000, yvy3000, ce)
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, cg), da)) → new_ltEs5(yvy4900, yvy5000, cg, da)
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, cac), cad)) → new_esEs5(yvy4000, yvy3000, cac, cad)
new_esEs28(yvy4000, yvy3000, app(ty_[], dea)) → new_esEs19(yvy4000, yvy3000, dea)
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, baa), bab)) → new_esEs6(yvy4000, yvy3000, baa, bab)
new_primCmpNat2(Zero, yvy4900) → LT
new_ltEs8(False, True) → True
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, bea), beb), bde) → new_ltEs5(yvy49000, yvy50000, bea, beb)
new_esEs22(yvy4001, yvy3001, app(ty_[], bcb)) → new_esEs19(yvy4001, yvy3001, bcb)
new_ltEs18(EQ, GT) → True
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_esEs29(yvy400, yvy500, ty_Integer) → new_esEs13(yvy400, yvy500)
new_ltEs10(Left(yvy49000), Right(yvy50000), beh, bde) → True
new_compare110(yvy49000, yvy50000, True, de, df) → LT
new_esEs29(yvy400, yvy500, app(ty_[], cab)) → new_esEs19(yvy400, yvy500, cab)
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bcc), bcd)) → new_esEs5(yvy4002, yvy3002, bcc, bcd)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_compare24(yvy49000, yvy50000, False, dg, dh, ea) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, dg, dh, ea), dg, dh, ea)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cbc)) → new_esEs4(yvy4000, yvy3000, cbc)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, ff)) → new_ltEs17(yvy49001, yvy50001, ff)
new_esEs4(Just(yvy4000), Nothing, bd) → False
new_esEs4(Nothing, Just(yvy3000), bd) → False
new_ltEs9(Nothing, Just(yvy50000), ga) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], dab), bhg) → new_esEs19(yvy4000, yvy3000, dab)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_primMulNat0(Zero, Zero) → Zero
new_compare26(Just(yvy4900), Nothing, False, ccg) → GT
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, ced)) → new_esEs10(yvy49000, yvy50000, ced)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, ddd)) → new_esEs10(yvy4000, yvy3000, ddd)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, db)) → new_esEs4(yvy49000, yvy50000, db)
new_compare33(yvy20, yvy15, dbe) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, dbe), dbe)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, bhg) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_[], cec)) → new_esEs19(yvy49000, yvy50000, cec)
new_compare16(@0, @0) → EQ
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, bdc)) → new_esEs4(yvy4002, yvy3002, bdc)
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_compare26(Nothing, Just(yvy5000), False, ccg) → LT
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), bc) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, bc), bc)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_[], bga)) → new_ltEs14(yvy49000, yvy50000, bga)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, bad), bae), baf)) → new_esEs7(yvy4000, yvy3000, bad, bae, baf)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_esEs29(yvy400, yvy500, app(app(app(ty_@3, hd), he), hf)) → new_esEs7(yvy400, yvy500, hd, he, hf)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bde) → new_ltEs12(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cdc)) → new_esEs4(yvy49000, yvy50000, cdc)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, de), df)) → new_esEs6(yvy49000, yvy50000, de, df)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_compare18(yvy49000, yvy50000, de, df) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, de, df), de, df)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_pePe(False, yvy201) → yvy201
new_esEs29(yvy400, yvy500, ty_Double) → new_esEs16(yvy400, yvy500)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_compare23(yvy49000, yvy50000, False, dc, dd) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, dc, dd), dc, dd)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_compare26(Nothing, Nothing, False, ccg) → LT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bde) → new_ltEs4(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cff)) → new_lt17(yvy49001, yvy50001, cff)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bec), bed), bee), bde) → new_ltEs13(yvy49000, yvy50000, bec, bed, bee)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bdg), bdh), bde) → new_ltEs10(yvy49000, yvy50000, bdg, bdh)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fa), fb), fc)) → new_ltEs13(yvy49001, yvy50001, fa, fb, fc)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cee)) → new_lt10(yvy49001, yvy50001, cee)
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chc), chd), bhg) → new_esEs6(yvy4000, yvy3000, chc, chd)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbd)) → new_esEs19(yvy4000, yvy3000, cbd)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, daa), bhg) → new_esEs4(yvy4000, yvy3000, daa)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, ge), gf)) → new_ltEs5(yvy49000, yvy50000, ge, gf)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(ty_@2, bfd), bfe)) → new_ltEs5(yvy49000, yvy50000, bfd, bfe)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs7(yvy4002, yvy3002, bch, bda, bdb)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs7(yvy49001, yvy50001, cfb, cfc, cfd)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cdh), cea), ceb)) → new_lt14(yvy49000, yvy50000, cdh, cea, ceb)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbe), cbf)) → new_esEs5(yvy4001, yvy3001, cbe, cbf)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbg), cbh)) → new_esEs6(yvy4001, yvy3001, cbg, cbh)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ed)) → new_ltEs9(yvy49001, yvy50001, ed)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, hc)) → new_ltEs17(yvy49000, yvy50000, hc)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, beh), bde)) → new_ltEs10(yvy4900, yvy5000, beh, bde)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), cg, da) → new_pePe(new_lt6(yvy49000, yvy50000, cg), new_asAs(new_esEs20(yvy49000, yvy50000, cg), new_ltEs6(yvy49001, yvy50001, da)))
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfg)) → new_ltEs9(yvy49002, yvy50002, cfg)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, cae), caf)) → new_esEs6(yvy4000, yvy3000, cae, caf)
new_gt2(yvy35, yvy30, bgc) → new_esEs9(new_compare33(yvy35, yvy30, bgc), GT)
new_compare0([], [], bc) → EQ
new_pePe(True, yvy201) → True
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_primEqNat0(Zero, Zero) → True
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bde) → new_ltEs11(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(ty_@2, dae), daf)) → new_esEs6(yvy4000, yvy3000, dae, daf)
new_ltEs14(yvy4900, yvy5000, bc) → new_fsEs(new_compare0(yvy4900, yvy5000, bc))
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, ee), ef)) → new_ltEs10(yvy49001, yvy50001, ee, ef)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_esEs29(yvy400, yvy500, ty_Int) → new_esEs14(yvy400, yvy500)
new_ltEs18(EQ, EQ) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, bhg) → new_esEs9(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_esEs19([], [], cab) → True
new_compare110(yvy49000, yvy50000, False, de, df) → GT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, ca)) → new_esEs10(yvy4000, yvy3000, ca)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccf)) → new_esEs19(yvy4001, yvy3001, ccf)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_compare12(yvy49000, yvy50000, False, dc, dd) → GT
new_primCmpNat1(Zero, Zero) → EQ
new_primCompAux0(yvy49000, yvy50000, yvy202, bc) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, bc))
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs18(LT, LT) → True
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, bhg) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, dg), dh), ea)) → new_esEs7(yvy49000, yvy50000, dg, dh, ea)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, dc), dd)) → new_lt11(yvy49000, yvy50000, dc, dd)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, ga)) → new_ltEs9(yvy4900, yvy5000, ga)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs19(:(yvy4000, yvy4001), [], cab) → False
new_esEs19([], :(yvy3000, yvy3001), cab) → False
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_ltEs18(GT, GT) → True
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(EQ, EQ) → True
new_compare24(yvy49000, yvy50000, True, dg, dh, ea) → EQ
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bde) → new_ltEs18(yvy49000, yvy50000)
new_esEs15(True, True) → True
new_esEs30(yvy20, yvy15, app(ty_[], dcg)) → new_esEs19(yvy20, yvy15, dcg)
new_ltEs18(LT, GT) → True
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcf)) → new_esEs4(yvy20, yvy15, dcf)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, fh)) → new_ltEs17(yvy4900, yvy5000, fh)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, cca)) → new_esEs10(yvy4001, yvy3001, cca)
new_esEs29(yvy400, yvy500, app(app(ty_Either, bhf), bhg)) → new_esEs5(yvy400, yvy500, bhf, bhg)
new_ltEs8(True, True) → True
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cdh), cea), ceb)) → new_esEs7(yvy49000, yvy50000, cdh, cea, ceb)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, ddh)) → new_esEs4(yvy4000, yvy3000, ddh)
new_ltEs18(GT, LT) → False
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, chf), chg), chh), bhg) → new_esEs7(yvy4000, yvy3000, chf, chg, chh)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_lt14(yvy49000, yvy50000, dg, dh, ea) → new_esEs9(new_compare14(yvy49000, yvy50000, dg, dh, ea), LT)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, cef), ceg)) → new_esEs5(yvy49001, yvy50001, cef, ceg)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cgh)) → new_ltEs17(yvy49002, yvy50002, cgh)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs7(yvy20, yvy15, dcc, dcd, dce)
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, gc), gd)) → new_ltEs10(yvy49000, yvy50000, gc, gd)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], hb)) → new_ltEs14(yvy49000, yvy50000, hb)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bah)) → new_esEs19(yvy4000, yvy3000, bah)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cgb), cgc)) → new_ltEs5(yvy49002, yvy50002, cgb, cgc)
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_[], dbd)) → new_esEs19(yvy4000, yvy3000, dbd)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bca)) → new_esEs4(yvy4001, yvy3001, bca)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, cce)) → new_esEs4(yvy4001, yvy3001, cce)
new_compare112(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bhh, caa) → new_asAs(new_esEs24(yvy4000, yvy3000, bhh), new_esEs25(yvy4001, yvy3001, caa))
new_lt19(yvy49001, yvy50001, app(app(ty_@2, ceh), cfa)) → new_lt12(yvy49001, yvy50001, ceh, cfa)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare12(yvy49000, yvy50000, True, dc, dd) → LT
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(ty_Either, dac), dad)) → new_esEs5(yvy4000, yvy3000, dac, dad)
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(app(ty_@3, bff), bfg), bfh)) → new_ltEs13(yvy49000, yvy50000, bff, bfg, bfh)
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_ltEs19(yvy4900, yvy5000, app(ty_[], bc)) → new_ltEs14(yvy4900, yvy5000, bc)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_Ratio, dag)) → new_esEs10(yvy4000, yvy3000, dag)
new_compare111(yvy49000, yvy50000, True, dg, dh, ea) → LT
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_primCompAux00(yvy206, LT) → LT
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(app(ty_Either, bfb), bfc)) → new_ltEs10(yvy49000, yvy50000, bfb, bfc)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, bhg) → new_esEs14(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, ced)) → new_lt17(yvy49000, yvy50000, ced)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare13(yvy175, yvy176, True, fg) → LT
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs23(yvy4002, yvy3002, app(ty_[], bdd)) → new_esEs19(yvy4002, yvy3002, bdd)
new_lt15(yvy49000, yvy50000, eb) → new_esEs9(new_compare0(yvy49000, yvy50000, eb), LT)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ec)) → new_lt17(yvy49000, yvy50000, ec)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, gb)) → new_ltEs9(yvy49000, yvy50000, gb)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_compare14(yvy49000, yvy50000, dg, dh, ea) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, dg, dh, ea), dg, dh, ea)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, be), bf)) → new_esEs5(yvy4000, yvy3000, be, bf)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, dc), dd)) → new_esEs5(yvy49000, yvy50000, dc, dd)
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_ltEs20(yvy49002, yvy50002, app(ty_[], cgg)) → new_ltEs14(yvy49002, yvy50002, cgg)
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dch), dda)) → new_esEs5(yvy4000, yvy3000, dch, dda)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, bg), bh)) → new_esEs6(yvy4000, yvy3000, bg, bh)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bbc), bbd)) → new_esEs6(yvy4001, yvy3001, bbc, bbd)
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_compare28(yvy49000, yvy50000, app(ty_[], bhd)) → new_compare0(yvy49000, yvy50000, bhd)
new_ltEs9(Just(yvy49000), Nothing, ga) → False
new_primCompAux00(yvy206, EQ) → yvy206
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, bhg) → new_esEs15(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bcg)) → new_esEs10(yvy4002, yvy3002, bcg)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, bhg) → new_esEs8(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_compare26(Just(yvy4900), Just(yvy5000), False, ccg) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, ccg), ccg)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bha), bhb), bhc)) → new_compare14(yvy49000, yvy50000, bha, bhb, bhc)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, cch), cda), cdb)) → new_ltEs13(yvy4900, yvy5000, cch, cda, cdb)
new_compare26(yvy490, yvy500, True, ccg) → EQ
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs18(GT, EQ) → False
new_compare17(yvy49000, yvy50000, dc, dd) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, dc, dd), dc, dd)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcb)) → new_esEs10(yvy20, yvy15, dcb)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bde) → new_ltEs16(yvy49000, yvy50000)
new_esEs29(yvy400, yvy500, ty_@0) → new_esEs18(yvy400, yvy500)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ec)) → new_esEs10(yvy49000, yvy50000, ec)
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bce), bcf)) → new_esEs6(yvy4002, yvy3002, bce, bcf)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, ga) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, bhg) → new_esEs17(yvy4000, yvy3000)
new_esEs9(GT, GT) → True
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bgd)) → new_compare19(yvy49000, yvy50000, bgd)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bde) → new_ltEs15(yvy49000, yvy50000)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs18(EQ, LT) → False
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_compare0(:(yvy49000, yvy49001), [], bc) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_ltEs18(LT, EQ) → True
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cdd), cde)) → new_esEs5(yvy49000, yvy50000, cdd, cde)
new_lt6(yvy49000, yvy50000, app(ty_[], eb)) → new_lt15(yvy49000, yvy50000, eb)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fd)) → new_ltEs14(yvy49001, yvy50001, fd)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs7(yvy4001, yvy3001, bbf, bbg, bbh)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, db)) → new_lt10(yvy49000, yvy50000, db)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_lt14(yvy49001, yvy50001, cfb, cfc, cfd)
new_lt19(yvy49001, yvy50001, app(ty_[], cfe)) → new_lt15(yvy49001, yvy50001, cfe)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs7(yvy4000, yvy3000, dde, ddf, ddg)
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), hd, he, hf) → new_asAs(new_esEs21(yvy4000, yvy3000, hd), new_asAs(new_esEs22(yvy4001, yvy3001, he), new_esEs23(yvy4002, yvy3002, hf)))
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs5(Left(yvy4000), Right(yvy3000), bhf, bhg) → False
new_esEs5(Right(yvy4000), Left(yvy3000), bhf, bhg) → False
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, ceh), cfa)) → new_esEs6(yvy49001, yvy50001, ceh, cfa)
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs29(yvy400, yvy500, app(app(ty_@2, bhh), caa)) → new_esEs6(yvy400, yvy500, bhh, caa)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bac)) → new_esEs10(yvy4000, yvy3000, bac)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_ltEs8(False, False) → True
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_compare19(yvy49000, yvy50000, db) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, db), db)
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdf), cdg)) → new_lt12(yvy49000, yvy50000, cdf, cdg)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, gg), gh), ha)) → new_ltEs13(yvy49000, yvy50000, gg, gh, ha)
new_gt(h) → new_esEs9(new_compare30(h), GT)
new_compare25(yvy49000, yvy50000, True, de, df) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_lt19(yvy49001, yvy50001, app(app(ty_Either, cef), ceg)) → new_lt11(yvy49001, yvy50001, cef, ceg)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cdc)) → new_lt10(yvy49000, yvy50000, cdc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, bd) → True
new_compare111(yvy49000, yvy50000, False, dg, dh, ea) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_compare210(yvy49000, yvy50000, True) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bde) → new_ltEs7(yvy49000, yvy50000)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cee)) → new_esEs4(yvy49001, yvy50001, cee)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bge), bgf)) → new_compare17(yvy49000, yvy50000, bge, bgf)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cfh), cga)) → new_ltEs10(yvy49002, yvy50002, cfh, cga)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cdd), cde)) → new_lt11(yvy49000, yvy50000, cdd, cde)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cff)) → new_esEs10(yvy49001, yvy50001, cff)
new_compare13(yvy175, yvy176, False, fg) → GT
new_compare23(yvy49000, yvy50000, True, dc, dd) → EQ
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], bef), bde) → new_ltEs14(yvy49000, yvy50000, bef)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, bhg) → new_esEs13(yvy4000, yvy3000)
new_lt17(yvy49000, yvy50000, ec) → new_esEs9(new_compare8(yvy49000, yvy50000, ec), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs7(yvy4000, yvy3000, dah, dba, dbb)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cgd), cge), cgf)) → new_ltEs13(yvy49002, yvy50002, cgd, cge, cgf)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddb), ddc)) → new_esEs6(yvy4000, yvy3000, ddb, ddc)
new_gt0(yvy300, h) → new_esEs9(new_compare31(yvy300, h), GT)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bag)) → new_esEs4(yvy4000, yvy3000, bag)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, eg), eh)) → new_ltEs5(yvy49001, yvy50001, eg, eh)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bdf), bde) → new_ltEs9(yvy49000, yvy50000, bdf)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, dg), dh), ea)) → new_lt14(yvy49000, yvy50000, dg, dh, ea)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, cah), cba), cbb)) → new_esEs7(yvy4000, yvy3000, cah, cba, cbb)
new_lt20(yvy49000, yvy50000, app(ty_[], cec)) → new_lt15(yvy49000, yvy50000, cec)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt12(yvy49000, yvy50000, de, df) → new_esEs9(new_compare18(yvy49000, yvy50000, de, df), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs29(yvy400, yvy500, ty_Bool) → new_esEs15(yvy400, yvy500)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bb) → new_asAs(new_esEs11(yvy4000, yvy3000, bb), new_esEs12(yvy4001, yvy3001, bb))
new_asAs(False, yvy182) → False
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_gt1(yvy400, h) → new_esEs9(new_compare32(yvy400, h), GT)
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, hg), hh)) → new_esEs5(yvy4000, yvy3000, hg, hh)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_lt10(yvy49000, yvy50000, db) → new_esEs9(new_compare19(yvy49000, yvy50000, db), LT)
new_compare25(yvy49000, yvy50000, False, de, df) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, de, df), de, df)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, bhe)) → new_compare8(yvy49000, yvy50000, bhe)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), cch, cda, cdb) → new_pePe(new_lt20(yvy49000, yvy50000, cch), new_asAs(new_esEs26(yvy49000, yvy50000, cch), new_pePe(new_lt19(yvy49001, yvy50001, cda), new_asAs(new_esEs27(yvy49001, yvy50001, cda), new_ltEs20(yvy49002, yvy50002, cdb)))))
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_esEs29(yvy400, yvy500, app(ty_Ratio, bb)) → new_esEs10(yvy400, yvy500, bb)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cag)) → new_esEs10(yvy4000, yvy3000, cag)
new_esEs29(yvy400, yvy500, ty_Char) → new_esEs8(yvy400, yvy500)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbf), dbg)) → new_esEs5(yvy20, yvy15, dbf, dbg)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_Ratio, bgb)) → new_ltEs17(yvy49000, yvy50000, bgb)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bbe)) → new_esEs10(yvy4001, yvy3001, bbe)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, ccb), ccc), ccd)) → new_esEs7(yvy4001, yvy3001, ccb, ccc, ccd)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, app(ty_Maybe, dbc)) → new_esEs4(yvy4000, yvy3000, dbc)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare11(yvy49000, yvy50000, False) → GT
new_esEs30(yvy20, yvy15, app(app(ty_@2, dbh), dca)) → new_esEs6(yvy20, yvy15, dbh, dca)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Left(yvy50000), beh, bde) → False
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_compare11(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], cf)) → new_esEs19(yvy4000, yvy3000, cf)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, cha), chb), bhg) → new_esEs5(yvy4000, yvy3000, cha, chb)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, app(ty_Maybe, bfa)) → new_ltEs9(yvy49000, yvy50000, bfa)
new_compare112(yvy49000, yvy50000, False) → GT
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(ty_[], eb)) → new_esEs19(yvy49000, yvy50000, eb)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), beh, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cfe)) → new_esEs19(yvy49001, yvy50001, cfe)
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy50000, yvy50001), bc) → LT
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_asAs(True, yvy182) → yvy182
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_esEs18(@0, @0) → True
new_compare211(yvy49000, yvy50000, True) → EQ
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdf), cdg)) → new_esEs6(yvy49000, yvy50000, cdf, cdg)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bhf, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy400, yvy500, ty_Float) → new_esEs17(yvy400, yvy500)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cb), cc), cd)) → new_esEs7(yvy4000, yvy3000, cb, cc, cd)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, che), bhg) → new_esEs10(yvy4000, yvy3000, che)
new_esEs29(yvy400, yvy500, app(ty_Maybe, bd)) → new_esEs4(yvy400, yvy500, bd)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, beg), bde) → new_ltEs17(yvy49000, yvy50000, beg)
new_lt11(yvy49000, yvy50000, dc, dd) → new_esEs9(new_compare17(yvy49000, yvy50000, dc, dd), LT)
new_esEs9(LT, LT) → True
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), cab) → new_asAs(new_esEs28(yvy4000, yvy3000, cab), new_esEs19(yvy4001, yvy3001, cab))
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bba), bbb)) → new_esEs5(yvy4001, yvy3001, bba, bbb)
new_primCompAux00(yvy206, GT) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bde) → new_ltEs8(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(yvy49000, yvy50000, app(app(ty_@2, de), df)) → new_lt12(yvy49000, yvy50000, de, df)
new_esEs29(yvy400, yvy500, ty_Ordering) → new_esEs9(yvy400, yvy500)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bgg), bgh)) → new_compare18(yvy49000, yvy50000, bgg, bgh)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_ltEs17(yvy4900, yvy5000, fh) → new_fsEs(new_compare8(yvy4900, yvy5000, fh))
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs30(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs9(Nothing, Nothing, x0)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_compare25(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare12(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_gt2(x0, x1, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs15(True, True)
new_primCmpNat0(x0, Zero)
new_compare0([], [], x0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare33(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_ltEs6(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs6(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs14(x0, x1, x2)
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt12(x0, x1, x2, x3)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Float)
new_compare18(x0, x1, x2, x3)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, x2)
new_esEs27(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_compare28(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_esEs19([], :(x0, x1), x2)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(:(x0, x1), [], x2)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Zero)
new_ltEs9(Nothing, Just(x0), x1)
new_esEs25(x0, x1, ty_Char)
new_esEs19([], [], x0)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt15(x0, x1, x2)
new_compare110(x0, x1, False, x2, x3)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat1(Zero, Succ(x0))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_gt(x0)
new_esEs27(x0, x1, ty_Double)
new_esEs9(GT, GT)
new_ltEs8(False, False)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare32(x0, x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs8(False, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs8(True, False)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_gt0(x0, x1)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Nothing, Just(x0), x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare26(Just(x0), Just(x1), False, x2)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpNat2(Zero, x0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs14(x0, x1)
new_esEs29(x0, x1, ty_Char)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_ltEs12(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_compare26(x0, x1, True, x2)
new_compare23(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, True, x2)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs29(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, False, x2)
new_esEs20(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_compare210(x0, x1, True)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat1(Succ(x0), Zero)
new_esEs4(Nothing, Nothing, x0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_compare31(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(Char(x0), Char(x1))
new_compare17(x0, x1, x2, x3)
new_esEs29(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_compare26(Just(x0), Nothing, False, x1)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), [], x2)
new_compare25(x0, x1, False, x2, x3)
new_compare28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_compare26(Nothing, Nothing, False, x0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_compare28(x0, x1, ty_Integer)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_compare12(x0, x1, True, x2, x3)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare28(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_gt1(x0, x1)
new_compare26(Nothing, Just(x0), False, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, False, x2, x3, x4)
new_compare11(x0, x1, True)
new_ltEs17(x0, x1, x2)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare14(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_addToFM_C1(yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy54, Nothing, yvy41, h, ba)
new_addToFM_C20(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, False, h, ba) → new_addToFM_C10(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, new_gt0(yvy500, h), h, ba)
new_addToFM_C2(yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy53, Nothing, yvy41, h, ba)
new_addToFM_C20(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy53, Nothing, yvy41, h, ba)
new_addToFM_C2(yvy51, yvy52, yvy53, yvy54, yvy41, False, h, ba) → new_addToFM_C1(yvy51, yvy52, yvy53, yvy54, yvy41, new_gt(h), h, ba)
new_addToFM_C10(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy54, Nothing, yvy41, h, ba)
new_addToFM_C(Branch(Just(yvy500), yvy51, yvy52, yvy53, yvy54), Nothing, yvy41, h, ba) → new_addToFM_C20(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, new_esEs9(new_compare26(Nothing, Just(yvy500), False, h), LT), h, ba)
new_addToFM_C(Branch(Nothing, yvy51, yvy52, yvy53, yvy54), Nothing, yvy41, h, ba) → new_addToFM_C2(yvy51, yvy52, yvy53, yvy54, yvy41, new_esEs9(new_compare26(Nothing, Nothing, True, h), LT), h, ba)

The TRS R consists of the following rules:

new_gt0(yvy300, h) → new_esEs9(new_compare31(yvy300, h), GT)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_compare26(Nothing, Just(yvy5000), False, ccg) → LT
new_compare26(yvy490, yvy500, True, ccg) → EQ
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True
new_gt(h) → new_esEs9(new_compare30(h), GT)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs30(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs9(Nothing, Nothing, x0)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_compare25(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare12(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_gt2(x0, x1, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs15(True, True)
new_primCmpNat0(x0, Zero)
new_compare0([], [], x0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare33(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_ltEs6(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs6(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs14(x0, x1, x2)
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt12(x0, x1, x2, x3)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Float)
new_compare18(x0, x1, x2, x3)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, x2)
new_esEs27(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_compare28(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_esEs19([], :(x0, x1), x2)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(:(x0, x1), [], x2)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Zero)
new_ltEs9(Nothing, Just(x0), x1)
new_esEs25(x0, x1, ty_Char)
new_esEs19([], [], x0)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt15(x0, x1, x2)
new_compare110(x0, x1, False, x2, x3)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat1(Zero, Succ(x0))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_gt(x0)
new_esEs27(x0, x1, ty_Double)
new_esEs9(GT, GT)
new_ltEs8(False, False)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare32(x0, x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs8(False, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs8(True, False)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_gt0(x0, x1)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Nothing, Just(x0), x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare26(Just(x0), Just(x1), False, x2)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpNat2(Zero, x0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs14(x0, x1)
new_esEs29(x0, x1, ty_Char)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_ltEs12(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_compare26(x0, x1, True, x2)
new_compare23(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, True, x2)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs29(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, False, x2)
new_esEs20(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_compare210(x0, x1, True)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat1(Succ(x0), Zero)
new_esEs4(Nothing, Nothing, x0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_compare31(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(Char(x0), Char(x1))
new_compare17(x0, x1, x2, x3)
new_esEs29(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_compare26(Just(x0), Nothing, False, x1)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), [], x2)
new_compare25(x0, x1, False, x2, x3)
new_compare28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_compare26(Nothing, Nothing, False, x0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_compare28(x0, x1, ty_Integer)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_compare12(x0, x1, True, x2, x3)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare28(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_gt1(x0, x1)
new_compare26(Nothing, Just(x0), False, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, False, x2, x3, x4)
new_compare11(x0, x1, True)
new_ltEs17(x0, x1, x2)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare14(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)

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_ltEs20(x0, x1, ty_Int)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs30(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs9(Nothing, Nothing, x0)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_compare25(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare12(x0, x1, False, x2, x3)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_gt2(x0, x1, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs15(True, True)
new_primCmpNat0(x0, Zero)
new_compare0([], [], x0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare33(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, True, x2, x3)
new_ltEs6(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_ltEs6(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_ltEs6(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs14(x0, x1, x2)
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt12(x0, x1, x2, x3)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_compare110(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Float)
new_compare18(x0, x1, x2, x3)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, x2)
new_esEs27(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_compare28(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_esEs19([], :(x0, x1), x2)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(:(x0, x1), [], x2)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_primPlusNat1(Zero, Zero)
new_ltEs9(Nothing, Just(x0), x1)
new_esEs25(x0, x1, ty_Char)
new_esEs19([], [], x0)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt15(x0, x1, x2)
new_compare110(x0, x1, False, x2, x3)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat1(Zero, Succ(x0))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_esEs27(x0, x1, ty_Double)
new_ltEs8(False, False)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare32(x0, x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_ltEs8(False, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs8(True, False)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Nothing, Just(x0), x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primCmpNat2(Zero, x0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs14(x0, x1)
new_esEs29(x0, x1, ty_Char)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_ltEs12(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_compare23(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Bool)
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, True, x2)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs29(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, False, x2)
new_esEs20(x0, x1, ty_Float)
new_primPlusNat0(Zero, x0)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_compare210(x0, x1, True)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat1(Succ(x0), Zero)
new_esEs4(Nothing, Nothing, x0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(Char(x0), Char(x1))
new_compare17(x0, x1, x2, x3)
new_esEs29(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(:(x0, x1), [], x2)
new_compare25(x0, x1, False, x2, x3)
new_compare28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1, x2, x3, x4)
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_compare28(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_compare12(x0, x1, True, x2, x3)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare28(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_gt1(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare24(x0, x1, False, x2, x3, x4)
new_compare11(x0, x1, True)
new_ltEs17(x0, x1, x2)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare14(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)



↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_addToFM_C1(yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy54, Nothing, yvy41, h, ba)
new_addToFM_C20(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, False, h, ba) → new_addToFM_C10(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, new_gt0(yvy500, h), h, ba)
new_addToFM_C2(yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy53, Nothing, yvy41, h, ba)
new_addToFM_C20(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy53, Nothing, yvy41, h, ba)
new_addToFM_C2(yvy51, yvy52, yvy53, yvy54, yvy41, False, h, ba) → new_addToFM_C1(yvy51, yvy52, yvy53, yvy54, yvy41, new_gt(h), h, ba)
new_addToFM_C10(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_addToFM_C(yvy54, Nothing, yvy41, h, ba)
new_addToFM_C(Branch(Just(yvy500), yvy51, yvy52, yvy53, yvy54), Nothing, yvy41, h, ba) → new_addToFM_C20(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, new_esEs9(new_compare26(Nothing, Just(yvy500), False, h), LT), h, ba)
new_addToFM_C(Branch(Nothing, yvy51, yvy52, yvy53, yvy54), Nothing, yvy41, h, ba) → new_addToFM_C2(yvy51, yvy52, yvy53, yvy54, yvy41, new_esEs9(new_compare26(Nothing, Nothing, True, h), LT), h, ba)

The TRS R consists of the following rules:

new_gt0(yvy300, h) → new_esEs9(new_compare31(yvy300, h), GT)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_compare26(Nothing, Just(yvy5000), False, ccg) → LT
new_compare26(yvy490, yvy500, True, ccg) → EQ
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True
new_gt(h) → new_esEs9(new_compare30(h), GT)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)

The set Q consists of the following terms:

new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_gt(x0)
new_esEs9(GT, GT)
new_esEs9(EQ, EQ)
new_gt0(x0, x1)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare26(x0, x1, True, x2)
new_compare31(x0, x1)
new_compare26(Just(x0), Nothing, False, x1)
new_compare26(Nothing, Nothing, False, x0)
new_compare30(x0)
new_compare26(Nothing, Just(x0), False, x1)
new_esEs9(LT, 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
                                    ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_lt5(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_lt5(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat2(Zero, yvy4900) → LT
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primPlusNat1(Zero, Zero) → Zero
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_sizeFM(EmptyFM, h, ba) → Pos(Zero)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_esEs9(EQ, EQ) → True
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_esEs9(GT, GT) → True
new_esEs9(LT, LT) → True
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_lt5(x0, x1)
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare9(x0, x1)
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_lt5(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_lt5(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_lt5(x0, x1)
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare9(x0, x1)
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_lt5(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), h, ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_compare9(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_lt5(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_compare9(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_lt5(x0, x1)
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare9(x0, x1)
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_lt5(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), h, ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_compare9(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_compare9(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_compare9(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_lt5(x0, x1)
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare9(x0, x1)
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_compare9(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_compare9(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_lt5(x0, x1)
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare9(x0, x1)
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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_lt5(x0, x1)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_compare9(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_compare9(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare9(x0, x1)
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_compare9(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_compare9(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare9(x0, x1)
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_compare9(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare9(x0, x1)
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare9(x0, x1)
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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_compare9(x0, x1)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_sr(x0, x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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_sr(x0, x1)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_sIZE_RATIO
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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_sIZE_RATIO



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(yvy620)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(yvy620)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(yvy620)), LT), h, ba)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(yvy620)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(yvy620)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(yvy620)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(yvy620)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_sizeFM(EmptyFM, x0, x1)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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_sizeFM(EmptyFM, x0, x1)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QDPOrderProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(yvy620)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(yvy620)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(yvy620)), LT), h, ba)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(yvy620)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x1 + x3 + x5   
POL(EQ) = 0   
POL(False) = 0   
POL(GT) = 0   
POL(LT) = 0   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 1   
POL(Succ(x1)) = 0   
POL(True) = 0   
POL(Zero) = 0   
POL(new_esEs9(x1, x2)) = 0   
POL(new_mkVBalBranch(x1, x2, x3, x4, x5, x6)) = x3 + x6   
POL(new_mkVBalBranch3MkVBalBranch1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x10 + x15   
POL(new_mkVBalBranch3MkVBalBranch10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x10 + x15   
POL(new_mkVBalBranch3MkVBalBranch2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x10 + x15 + x6   
POL(new_mkVBalBranch3MkVBalBranch20(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x10 + x15 + x6   
POL(new_mkVBalBranch3Size_r(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x1 + x12 + x2 + x3   
POL(new_mkVBalBranch3Size_r0(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 0   
POL(new_primCmpInt(x1, x2)) = 0   
POL(new_primCmpInt0(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x10 + x12 + x2 + x3 + x4 + x7 + x9   
POL(new_primCmpInt1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 0   
POL(new_primCmpInt2(x1, x2)) = 0   
POL(new_primCmpInt3(x1, x2)) = x2   
POL(new_primCmpNat0(x1, x2)) = 1   
POL(new_primCmpNat1(x1, x2)) = 0   
POL(new_primCmpNat2(x1, x2)) = 1   
POL(new_primMulInt(x1, x2)) = 0   
POL(new_primMulNat0(x1, x2)) = 0   
POL(new_primPlusNat0(x1, x2)) = 0   
POL(new_primPlusNat1(x1, x2)) = 1   
POL(new_sizeFM0(x1, x2, x3, x4, x5, x6, x7)) = 0   

The following usable rules [17] were oriented: none



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(yvy620)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs with 1 less node.

↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                              ↳ AND
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ UsableRulesProof
                                                                                                                                                ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                              ↳ AND
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ UsableRulesProof
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ QReductionProof
                                                                                                                                                ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(x0, x1)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                              ↳ AND
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ UsableRulesProof
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ QReductionProof
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ QDPSizeChangeProof
                                                                                                                                                ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                              ↳ AND
                                                                                                                                                ↳ QDP
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(yvy620)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                              ↳ AND
                                                                                                                                                ↳ QDP
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ UsableRulesProof
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ QReductionProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(yvy620)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt3(x0, x1)
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt3(x0, x1)
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                              ↳ AND
                                                                                                                                                ↳ QDP
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ UsableRulesProof
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ QReductionProof
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ QDPOrderProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(yvy620)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(yvy620)), LT), h, ba)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x5   
POL(EQ) = 0   
POL(False) = 0   
POL(GT) = 0   
POL(LT) = 0   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(True) = 0   
POL(Zero) = 0   
POL(new_esEs9(x1, x2)) = 0   
POL(new_mkVBalBranch(x1, x2, x3, x4, x5, x6)) = x3   
POL(new_mkVBalBranch3MkVBalBranch10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x10   
POL(new_mkVBalBranch3MkVBalBranch20(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x10   
POL(new_mkVBalBranch3Size_r0(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 0   
POL(new_primCmpInt(x1, x2)) = 0   
POL(new_primCmpInt1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 0   
POL(new_primCmpInt2(x1, x2)) = 0   
POL(new_primCmpNat0(x1, x2)) = 0   
POL(new_primCmpNat1(x1, x2)) = 0   
POL(new_primCmpNat2(x1, x2)) = 0   
POL(new_primMulInt(x1, x2)) = 0   
POL(new_primMulNat0(x1, x2)) = 0   
POL(new_primPlusNat0(x1, x2)) = 0   
POL(new_primPlusNat1(x1, x2)) = 0   
POL(new_sizeFM0(x1, x2, x3, x4, x5, x6, x7)) = 0   

The following usable rules [17] were oriented: none



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                              ↳ AND
                                                                                                                                                ↳ QDP
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ UsableRulesProof
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ QReductionProof
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ QDPOrderProof
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.

↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                              ↳ AND
                                                                                                                                                ↳ QDP
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ UsableRulesProof
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ QReductionProof
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ QDPOrderProof
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ DependencyGraphProof
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primMulNat0(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                              ↳ AND
                                                                                                                                                ↳ QDP
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ UsableRulesProof
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ QReductionProof
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ QDPOrderProof
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ DependencyGraphProof
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ UsableRulesProof
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ QReductionProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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_primMulNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Succ(x0), Zero)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulNat0(Succ(x0), Succ(x1))



↳ 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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ UsableRulesProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ QReductionProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ QDPOrderProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                              ↳ AND
                                                                                                                                                ↳ QDP
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ UsableRulesProof
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ QReductionProof
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ QDPOrderProof
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ DependencyGraphProof
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ UsableRulesProof
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ QReductionProof
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(GT, GT)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_primPlusNat1(Zero, Zero)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(x0, x1)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Zero, Zero)
new_primPlusNat0(Zero, x0)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat0(x0, Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat0(x0, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs9(LT, LT)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), x1)
new_primCmpNat2(Zero, x0)

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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP

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

new_splitLT12(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, True, bb, bc) → new_splitLT0(yvy34, yvy35, bb, bc)
new_splitLT3(Nothing, yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitLT20(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), LT), h, ba)
new_splitLT2(yvy300, yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, True, h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Nothing, h, ba)
new_splitLT1(yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitLT(yvy34, h, ba)
new_splitLT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitLT21(yvy300, yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Just(yvy300), new_esEs31(yvy400, yvy300, h), h), LT), h, ba)
new_splitLT20(yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, yvy400, True, h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Just(yvy400), h, ba)
new_splitLT21(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, True, bb, bc) → new_splitLT0(yvy33, yvy35, bb, bc)
new_splitLT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitLT2(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare26(Nothing, Just(yvy300), False, h), LT), h, ba)
new_splitLT(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Nothing, h, ba)
new_splitLT20(yvy31, yvy32, yvy33, yvy34, yvy400, False, h, ba) → new_splitLT11(yvy31, yvy32, yvy33, yvy34, yvy400, new_gt1(yvy400, h), h, ba)
new_splitLT2(yvy300, yvy31, yvy32, yvy33, yvy34, False, h, ba) → new_splitLT10(yvy300, yvy31, yvy32, yvy33, yvy34, new_gt0(yvy300, h), h, ba)
new_splitLT21(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, False, bb, bc) → new_splitLT12(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, new_gt2(yvy35, yvy30, bb), bb, bc)
new_splitLT0(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy400, h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Just(yvy400), h, ba)
new_splitLT10(yvy300, yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitLT(yvy34, h, ba)
new_splitLT3(Nothing, yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitLT1(yvy31, yvy32, yvy33, yvy34, new_gt(h), h, ba)
new_splitLT11(yvy31, yvy32, yvy33, yvy34, yvy400, True, h, ba) → new_splitLT0(yvy34, yvy400, h, ba)

The TRS R consists of the following rules:

new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, cg)) → new_esEs4(yvy4000, yvy3000, cg)
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, db), dc)) → new_ltEs5(yvy4900, yvy5000, db, dc)
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, caa), cab)) → new_esEs5(yvy4000, yvy3000, caa, cab)
new_esEs28(yvy4000, yvy3000, app(ty_[], deb)) → new_esEs19(yvy4000, yvy3000, deb)
new_esEs31(yvy400, yvy300, ty_Ordering) → new_esEs9(yvy400, yvy300)
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, bac), bad)) → new_esEs6(yvy4000, yvy3000, bac, bad)
new_primCmpNat2(Zero, yvy4900) → LT
new_ltEs8(False, True) → True
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, bec), bed), bdg) → new_ltEs5(yvy49000, yvy50000, bec, bed)
new_esEs22(yvy4001, yvy3001, app(ty_[], bcd)) → new_esEs19(yvy4001, yvy3001, bcd)
new_ltEs18(EQ, GT) → True
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_ltEs10(Left(yvy49000), Right(yvy50000), bfb, bdg) → True
new_compare110(yvy49000, yvy50000, True, dg, dh) → LT
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bce), bcf)) → new_esEs5(yvy4002, yvy3002, bce, bcf)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_compare24(yvy49000, yvy50000, False, ea, eb, ec) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cba)) → new_esEs4(yvy4000, yvy3000, cba)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, fh)) → new_ltEs17(yvy49001, yvy50001, fh)
new_esEs4(Just(yvy4000), Nothing, bf) → False
new_esEs4(Nothing, Just(yvy3000), bf) → False
new_ltEs9(Nothing, Just(yvy50000), gc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], daa), cgg) → new_esEs19(yvy4000, yvy3000, daa)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_primMulNat0(Zero, Zero) → Zero
new_compare26(Just(yvy4900), Nothing, False, cce) → GT
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, ceb)) → new_esEs10(yvy49000, yvy50000, ceb)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, dde)) → new_esEs10(yvy4000, yvy3000, dde)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_esEs4(yvy49000, yvy50000, dd)
new_compare33(yvy20, yvy15, dbf) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, dbf), dbf)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, cgg) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_[], cea)) → new_esEs19(yvy49000, yvy50000, cea)
new_compare16(@0, @0) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, bde)) → new_esEs4(yvy4002, yvy3002, bde)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_compare26(Nothing, Just(yvy5000), False, cce) → LT
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), be) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, be), be)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_[], bgc)) → new_ltEs14(yvy49000, yvy50000, bgc)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs7(yvy4000, yvy3000, baf, bag, bah)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bdg) → new_ltEs12(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cda)) → new_esEs4(yvy49000, yvy50000, cda)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_esEs6(yvy49000, yvy50000, dg, dh)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_compare18(yvy49000, yvy50000, dg, dh) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, dg, dh), dg, dh)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_pePe(False, yvy201) → yvy201
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs31(yvy400, yvy300, ty_Float) → new_esEs17(yvy400, yvy300)
new_compare23(yvy49000, yvy50000, False, de, df) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, de, df), de, df)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_compare26(Nothing, Nothing, False, cce) → LT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bdg) → new_ltEs4(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cfd)) → new_lt17(yvy49001, yvy50001, cfd)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bee), bef), beg), bdg) → new_ltEs13(yvy49000, yvy50000, bee, bef, beg)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bea), beb), bdg) → new_ltEs10(yvy49000, yvy50000, bea, beb)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs13(yvy49001, yvy50001, fc, fd, ff)
new_esEs31(yvy400, yvy300, ty_Bool) → new_esEs15(yvy400, yvy300)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cec)) → new_lt10(yvy49001, yvy50001, cec)
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chb), chc), cgg) → new_esEs6(yvy4000, yvy3000, chb, chc)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbb)) → new_esEs19(yvy4000, yvy3000, cbb)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, chh), cgg) → new_esEs4(yvy4000, yvy3000, chh)
new_esEs31(yvy400, yvy300, ty_Integer) → new_esEs13(yvy400, yvy300)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, gg), gh)) → new_ltEs5(yvy49000, yvy50000, gg, gh)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(ty_@2, bff), bfg)) → new_ltEs5(yvy49000, yvy50000, bff, bfg)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs7(yvy4002, yvy3002, bdb, bdc, bdd)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs7(yvy49001, yvy50001, ceh, cfa, cfb)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cdf), cdg), cdh)) → new_lt14(yvy49000, yvy50000, cdf, cdg, cdh)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbc), cbd)) → new_esEs5(yvy4001, yvy3001, cbc, cbd)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbe), cbf)) → new_esEs6(yvy4001, yvy3001, cbe, cbf)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ef)) → new_ltEs9(yvy49001, yvy50001, ef)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, he)) → new_ltEs17(yvy49000, yvy50000, he)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, bfb), bdg)) → new_ltEs10(yvy4900, yvy5000, bfb, bdg)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), db, dc) → new_pePe(new_lt6(yvy49000, yvy50000, db), new_asAs(new_esEs20(yvy49000, yvy50000, db), new_ltEs6(yvy49001, yvy50001, dc)))
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfe)) → new_ltEs9(yvy49002, yvy50002, cfe)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, cac), cad)) → new_esEs6(yvy4000, yvy3000, cac, cad)
new_gt2(yvy35, yvy30, bb) → new_esEs9(new_compare33(yvy35, yvy30, bb), GT)
new_compare0([], [], be) → EQ
new_pePe(True, yvy201) → True
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_primEqNat0(Zero, Zero) → True
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bdg) → new_ltEs11(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(ty_@2, dae), daf)) → new_esEs6(yvy4000, yvy3000, dae, daf)
new_ltEs14(yvy4900, yvy5000, be) → new_fsEs(new_compare0(yvy4900, yvy5000, be))
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, eg), eh)) → new_ltEs10(yvy49001, yvy50001, eg, eh)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_ltEs18(EQ, EQ) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, cgg) → new_esEs9(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_esEs19([], [], dbe) → True
new_compare110(yvy49000, yvy50000, False, dg, dh) → GT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, cc)) → new_esEs10(yvy4000, yvy3000, cc)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccd)) → new_esEs19(yvy4001, yvy3001, ccd)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_compare12(yvy49000, yvy50000, False, de, df) → GT
new_primCmpNat1(Zero, Zero) → EQ
new_primCompAux0(yvy49000, yvy50000, yvy202, be) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, be))
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs18(LT, LT) → True
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_esEs31(yvy400, yvy300, app(app(app(ty_@3, hf), hg), hh)) → new_esEs7(yvy400, yvy300, hf, hg, hh)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, cgg) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_esEs7(yvy49000, yvy50000, ea, eb, ec)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_lt11(yvy49000, yvy50000, de, df)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, gc)) → new_ltEs9(yvy4900, yvy5000, gc)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs19(:(yvy4000, yvy4001), [], dbe) → False
new_esEs19([], :(yvy3000, yvy3001), dbe) → False
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_ltEs18(GT, GT) → True
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(EQ, EQ) → True
new_compare24(yvy49000, yvy50000, True, ea, eb, ec) → EQ
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bdg) → new_ltEs18(yvy49000, yvy50000)
new_esEs15(True, True) → True
new_esEs30(yvy20, yvy15, app(ty_[], dch)) → new_esEs19(yvy20, yvy15, dch)
new_ltEs18(LT, GT) → True
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcg)) → new_esEs4(yvy20, yvy15, dcg)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, gb)) → new_ltEs17(yvy4900, yvy5000, gb)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, cbg)) → new_esEs10(yvy4001, yvy3001, cbg)
new_ltEs8(True, True) → True
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs7(yvy49000, yvy50000, cdf, cdg, cdh)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, dea)) → new_esEs4(yvy4000, yvy3000, dea)
new_esEs31(yvy400, yvy300, ty_Char) → new_esEs8(yvy400, yvy300)
new_ltEs18(GT, LT) → False
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, che), chf), chg), cgg) → new_esEs7(yvy4000, yvy3000, che, chf, chg)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_lt14(yvy49000, yvy50000, ea, eb, ec) → new_esEs9(new_compare14(yvy49000, yvy50000, ea, eb, ec), LT)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, ced), cee)) → new_esEs5(yvy49001, yvy50001, ced, cee)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cgf)) → new_ltEs17(yvy49002, yvy50002, cgf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcd), dce), dcf)) → new_esEs7(yvy20, yvy15, dcd, dce, dcf)
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, ge), gf)) → new_ltEs10(yvy49000, yvy50000, ge, gf)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], hd)) → new_ltEs14(yvy49000, yvy50000, hd)
new_esEs31(yvy400, yvy300, app(app(ty_Either, dab), cgg)) → new_esEs5(yvy400, yvy300, dab, cgg)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bbb)) → new_esEs19(yvy4000, yvy3000, bbb)
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cfh), cga)) → new_ltEs5(yvy49002, yvy50002, cfh, cga)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_[], dbd)) → new_esEs19(yvy4000, yvy3000, dbd)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bcc)) → new_esEs4(yvy4001, yvy3001, bcc)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, ccc)) → new_esEs4(yvy4001, yvy3001, ccc)
new_compare112(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bhg, bhh) → new_asAs(new_esEs24(yvy4000, yvy3000, bhg), new_esEs25(yvy4001, yvy3001, bhh))
new_lt19(yvy49001, yvy50001, app(app(ty_@2, cef), ceg)) → new_lt12(yvy49001, yvy50001, cef, ceg)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare12(yvy49000, yvy50000, True, de, df) → LT
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(ty_Either, dac), dad)) → new_esEs5(yvy4000, yvy3000, dac, dad)
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(app(ty_@3, bfh), bga), bgb)) → new_ltEs13(yvy49000, yvy50000, bfh, bga, bgb)
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_ltEs19(yvy4900, yvy5000, app(ty_[], be)) → new_ltEs14(yvy4900, yvy5000, be)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_Ratio, dag)) → new_esEs10(yvy4000, yvy3000, dag)
new_compare111(yvy49000, yvy50000, True, ea, eb, ec) → LT
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_primCompAux00(yvy206, LT) → LT
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(ty_Either, bfd), bfe)) → new_ltEs10(yvy49000, yvy50000, bfd, bfe)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, cgg) → new_esEs14(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, ceb)) → new_lt17(yvy49000, yvy50000, ceb)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare13(yvy175, yvy176, True, ga) → LT
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs23(yvy4002, yvy3002, app(ty_[], bdf)) → new_esEs19(yvy4002, yvy3002, bdf)
new_lt15(yvy49000, yvy50000, ed) → new_esEs9(new_compare0(yvy49000, yvy50000, ed), LT)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_lt17(yvy49000, yvy50000, ee)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, gd)) → new_ltEs9(yvy49000, yvy50000, gd)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_compare14(yvy49000, yvy50000, ea, eb, ec) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, bg), bh)) → new_esEs5(yvy4000, yvy3000, bg, bh)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_esEs5(yvy49000, yvy50000, de, df)
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs31(yvy400, yvy300, ty_Int) → new_esEs14(yvy400, yvy300)
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_esEs31(yvy400, yvy300, app(ty_Ratio, bd)) → new_esEs10(yvy400, yvy300, bd)
new_ltEs20(yvy49002, yvy50002, app(ty_[], cge)) → new_ltEs14(yvy49002, yvy50002, cge)
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dda), ddb)) → new_esEs5(yvy4000, yvy3000, dda, ddb)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, ca), cb)) → new_esEs6(yvy4000, yvy3000, ca, cb)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs31(yvy400, yvy300, app(ty_[], dbe)) → new_esEs19(yvy400, yvy300, dbe)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bbe), bbf)) → new_esEs6(yvy4001, yvy3001, bbe, bbf)
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_compare28(yvy49000, yvy50000, app(ty_[], bhe)) → new_compare0(yvy49000, yvy50000, bhe)
new_ltEs9(Just(yvy49000), Nothing, gc) → False
new_primCompAux00(yvy206, EQ) → yvy206
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, cgg) → new_esEs15(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bda)) → new_esEs10(yvy4002, yvy3002, bda)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, cgg) → new_esEs8(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_compare26(Just(yvy4900), Just(yvy5000), False, cce) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, cce), cce)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bhb), bhc), bhd)) → new_compare14(yvy49000, yvy50000, bhb, bhc, bhd)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, ccf), ccg), cch)) → new_ltEs13(yvy4900, yvy5000, ccf, ccg, cch)
new_compare26(yvy490, yvy500, True, cce) → EQ
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs18(GT, EQ) → False
new_compare17(yvy49000, yvy50000, de, df) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, de, df), de, df)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcc)) → new_esEs10(yvy20, yvy15, dcc)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bdg) → new_ltEs16(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_esEs10(yvy49000, yvy50000, ee)
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bcg), bch)) → new_esEs6(yvy4002, yvy3002, bcg, bch)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, gc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, cgg) → new_esEs17(yvy4000, yvy3000)
new_esEs9(GT, GT) → True
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bge)) → new_compare19(yvy49000, yvy50000, bge)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bdg) → new_ltEs15(yvy49000, yvy50000)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs18(EQ, LT) → False
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_compare0(:(yvy49000, yvy49001), [], be) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_ltEs18(LT, EQ) → True
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cdb), cdc)) → new_esEs5(yvy49000, yvy50000, cdb, cdc)
new_lt6(yvy49000, yvy50000, app(ty_[], ed)) → new_lt15(yvy49000, yvy50000, ed)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fg)) → new_ltEs14(yvy49001, yvy50001, fg)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs7(yvy4001, yvy3001, bbh, bca, bcb)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_lt10(yvy49000, yvy50000, dd)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, ceh), cfa), cfb)) → new_lt14(yvy49001, yvy50001, ceh, cfa, cfb)
new_lt19(yvy49001, yvy50001, app(ty_[], cfc)) → new_lt15(yvy49001, yvy50001, cfc)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, ddf), ddg), ddh)) → new_esEs7(yvy4000, yvy3000, ddf, ddg, ddh)
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), hf, hg, hh) → new_asAs(new_esEs21(yvy4000, yvy3000, hf), new_asAs(new_esEs22(yvy4001, yvy3001, hg), new_esEs23(yvy4002, yvy3002, hh)))
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs5(Left(yvy4000), Right(yvy3000), dab, cgg) → False
new_esEs5(Right(yvy4000), Left(yvy3000), dab, cgg) → False
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, cef), ceg)) → new_esEs6(yvy49001, yvy50001, cef, ceg)
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bae)) → new_esEs10(yvy4000, yvy3000, bae)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_ltEs8(False, False) → True
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_compare19(yvy49000, yvy50000, dd) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, dd), dd)
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdd), cde)) → new_lt12(yvy49000, yvy50000, cdd, cde)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, ha), hb), hc)) → new_ltEs13(yvy49000, yvy50000, ha, hb, hc)
new_gt(h) → new_esEs9(new_compare30(h), GT)
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_compare25(yvy49000, yvy50000, True, dg, dh) → EQ
new_lt19(yvy49001, yvy50001, app(app(ty_Either, ced), cee)) → new_lt11(yvy49001, yvy50001, ced, cee)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cda)) → new_lt10(yvy49000, yvy50000, cda)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, bf) → True
new_compare111(yvy49000, yvy50000, False, ea, eb, ec) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_compare210(yvy49000, yvy50000, True) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bdg) → new_ltEs7(yvy49000, yvy50000)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cec)) → new_esEs4(yvy49001, yvy50001, cec)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cff), cfg)) → new_ltEs10(yvy49002, yvy50002, cff, cfg)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bgf), bgg)) → new_compare17(yvy49000, yvy50000, bgf, bgg)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cdb), cdc)) → new_lt11(yvy49000, yvy50000, cdb, cdc)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cfd)) → new_esEs10(yvy49001, yvy50001, cfd)
new_compare13(yvy175, yvy176, False, ga) → GT
new_compare23(yvy49000, yvy50000, True, de, df) → EQ
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], beh), bdg) → new_ltEs14(yvy49000, yvy50000, beh)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, cgg) → new_esEs13(yvy4000, yvy3000)
new_lt17(yvy49000, yvy50000, ee) → new_esEs9(new_compare8(yvy49000, yvy50000, ee), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs7(yvy4000, yvy3000, dah, dba, dbb)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cgb), cgc), cgd)) → new_ltEs13(yvy49002, yvy50002, cgb, cgc, cgd)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddc), ddd)) → new_esEs6(yvy4000, yvy3000, ddc, ddd)
new_gt0(yvy300, h) → new_esEs9(new_compare31(yvy300, h), GT)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bba)) → new_esEs4(yvy4000, yvy3000, bba)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, fa), fb)) → new_ltEs5(yvy49001, yvy50001, fa, fb)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bdh), bdg) → new_ltEs9(yvy49000, yvy50000, bdh)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_lt14(yvy49000, yvy50000, ea, eb, ec)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, caf), cag), cah)) → new_esEs7(yvy4000, yvy3000, caf, cag, cah)
new_lt20(yvy49000, yvy50000, app(ty_[], cea)) → new_lt15(yvy49000, yvy50000, cea)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt12(yvy49000, yvy50000, dg, dh) → new_esEs9(new_compare18(yvy49000, yvy50000, dg, dh), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bd) → new_asAs(new_esEs11(yvy4000, yvy3000, bd), new_esEs12(yvy4001, yvy3001, bd))
new_asAs(False, yvy182) → False
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_gt1(yvy400, h) → new_esEs9(new_compare32(yvy400, h), GT)
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, baa), bab)) → new_esEs5(yvy4000, yvy3000, baa, bab)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_esEs31(yvy400, yvy300, ty_Double) → new_esEs16(yvy400, yvy300)
new_lt10(yvy49000, yvy50000, dd) → new_esEs9(new_compare19(yvy49000, yvy50000, dd), LT)
new_compare25(yvy49000, yvy50000, False, dg, dh) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, dg, dh), dg, dh)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, bhf)) → new_compare8(yvy49000, yvy50000, bhf)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), ccf, ccg, cch) → new_pePe(new_lt20(yvy49000, yvy50000, ccf), new_asAs(new_esEs26(yvy49000, yvy50000, ccf), new_pePe(new_lt19(yvy49001, yvy50001, ccg), new_asAs(new_esEs27(yvy49001, yvy50001, ccg), new_ltEs20(yvy49002, yvy50002, cch)))))
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cae)) → new_esEs10(yvy4000, yvy3000, cae)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbg), dbh)) → new_esEs5(yvy20, yvy15, dbg, dbh)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_Ratio, bgd)) → new_ltEs17(yvy49000, yvy50000, bgd)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bbg)) → new_esEs10(yvy4001, yvy3001, bbg)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs7(yvy4001, yvy3001, cbh, cca, ccb)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_Maybe, dbc)) → new_esEs4(yvy4000, yvy3000, dbc)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare11(yvy49000, yvy50000, False) → GT
new_esEs30(yvy20, yvy15, app(app(ty_@2, dca), dcb)) → new_esEs6(yvy20, yvy15, dca, dcb)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Left(yvy50000), bfb, bdg) → False
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_compare11(yvy49000, yvy50000, True) → LT
new_esEs31(yvy400, yvy300, app(ty_Maybe, bf)) → new_esEs4(yvy400, yvy300, bf)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], da)) → new_esEs19(yvy4000, yvy3000, da)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, cgh), cha), cgg) → new_esEs5(yvy4000, yvy3000, cgh, cha)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_Maybe, bfc)) → new_ltEs9(yvy49000, yvy50000, bfc)
new_compare112(yvy49000, yvy50000, False) → GT
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(ty_[], ed)) → new_esEs19(yvy49000, yvy50000, ed)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cfc)) → new_esEs19(yvy49001, yvy50001, cfc)
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_esEs31(yvy400, yvy300, ty_@0) → new_esEs18(yvy400, yvy300)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy50000, yvy50001), be) → LT
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_asAs(True, yvy182) → yvy182
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_esEs18(@0, @0) → True
new_compare211(yvy49000, yvy50000, True) → EQ
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdd), cde)) → new_esEs6(yvy49000, yvy50000, cdd, cde)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cd), ce), cf)) → new_esEs7(yvy4000, yvy3000, cd, ce, cf)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, chd), cgg) → new_esEs10(yvy4000, yvy3000, chd)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, bfa), bdg) → new_ltEs17(yvy49000, yvy50000, bfa)
new_lt11(yvy49000, yvy50000, de, df) → new_esEs9(new_compare17(yvy49000, yvy50000, de, df), LT)
new_esEs9(LT, LT) → True
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), dbe) → new_asAs(new_esEs28(yvy4000, yvy3000, dbe), new_esEs19(yvy4001, yvy3001, dbe))
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bbc), bbd)) → new_esEs5(yvy4001, yvy3001, bbc, bbd)
new_primCompAux00(yvy206, GT) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bdg) → new_ltEs8(yvy49000, yvy50000)
new_esEs31(yvy400, yvy300, app(app(ty_@2, bhg), bhh)) → new_esEs6(yvy400, yvy300, bhg, bhh)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_lt12(yvy49000, yvy50000, dg, dh)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bgh), bha)) → new_compare18(yvy49000, yvy50000, bgh, bha)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_ltEs17(yvy4900, yvy5000, gb) → new_fsEs(new_compare8(yvy4900, yvy5000, gb))
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Int)
new_esEs19(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_@0)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs9(Nothing, Nothing, x0)
new_esEs18(@0, @0)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_asAs(True, x0)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Char)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs31(x0, x1, ty_Float)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpNat0(x0, Zero)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_@0)
new_gt2(x0, x1, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs31(x0, x1, ty_Ordering)
new_compare26(Nothing, Nothing, False, x0)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs19([], :(x0, x1), x2)
new_compare6(Char(x0), Char(x1))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primCmpNat1(Zero, Zero)
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs31(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_@0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Nothing, Just(x0), x1)
new_esEs12(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, True, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_compare110(x0, x1, False, x2, x3)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_compare111(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Nothing, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs22(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare33(x0, x1, x2)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primPlusNat1(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs9(Just(x0), Nothing, x1)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_gt(x0)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs9(GT, GT)
new_ltEs8(False, False)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, x2, x3)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_compare32(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_esEs19([], [], x0)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Ordering)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_gt0(x0, x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_compare26(Nothing, Just(x0), False, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_ltEs6(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs12(x0, x1)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_esEs28(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_compare18(x0, x1, x2, x3)
new_compare31(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_lt19(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(Char(x0), Char(x1))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs17(x0, x1, x2)
new_esEs31(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_compare0([], :(x0, x1), x2)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_esEs31(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare27(Double(x0, x1), Double(x2, x3))
new_compare28(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare28(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_compare26(x0, x1, True, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare12(x0, x1, False, x2, x3)
new_gt1(x0, x1)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare13(x0, x1, False, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)

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

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

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

new_splitLT(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Nothing, h, ba)
new_splitLT2(yvy300, yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, True, h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Nothing, h, ba)
new_splitLT2(yvy300, yvy31, yvy32, yvy33, yvy34, False, h, ba) → new_splitLT10(yvy300, yvy31, yvy32, yvy33, yvy34, new_gt0(yvy300, h), h, ba)
new_splitLT1(yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitLT(yvy34, h, ba)
new_splitLT10(yvy300, yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitLT(yvy34, h, ba)
new_splitLT3(Nothing, yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitLT1(yvy31, yvy32, yvy33, yvy34, new_gt(h), h, ba)
new_splitLT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitLT2(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare26(Nothing, Just(yvy300), False, h), LT), h, ba)

The TRS R consists of the following rules:

new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, cg)) → new_esEs4(yvy4000, yvy3000, cg)
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, db), dc)) → new_ltEs5(yvy4900, yvy5000, db, dc)
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, caa), cab)) → new_esEs5(yvy4000, yvy3000, caa, cab)
new_esEs28(yvy4000, yvy3000, app(ty_[], deb)) → new_esEs19(yvy4000, yvy3000, deb)
new_esEs31(yvy400, yvy300, ty_Ordering) → new_esEs9(yvy400, yvy300)
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, bac), bad)) → new_esEs6(yvy4000, yvy3000, bac, bad)
new_primCmpNat2(Zero, yvy4900) → LT
new_ltEs8(False, True) → True
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, bec), bed), bdg) → new_ltEs5(yvy49000, yvy50000, bec, bed)
new_esEs22(yvy4001, yvy3001, app(ty_[], bcd)) → new_esEs19(yvy4001, yvy3001, bcd)
new_ltEs18(EQ, GT) → True
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_ltEs10(Left(yvy49000), Right(yvy50000), bfb, bdg) → True
new_compare110(yvy49000, yvy50000, True, dg, dh) → LT
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bce), bcf)) → new_esEs5(yvy4002, yvy3002, bce, bcf)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_compare24(yvy49000, yvy50000, False, ea, eb, ec) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cba)) → new_esEs4(yvy4000, yvy3000, cba)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, fh)) → new_ltEs17(yvy49001, yvy50001, fh)
new_esEs4(Just(yvy4000), Nothing, bf) → False
new_esEs4(Nothing, Just(yvy3000), bf) → False
new_ltEs9(Nothing, Just(yvy50000), gc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], daa), cgg) → new_esEs19(yvy4000, yvy3000, daa)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_primMulNat0(Zero, Zero) → Zero
new_compare26(Just(yvy4900), Nothing, False, cce) → GT
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, ceb)) → new_esEs10(yvy49000, yvy50000, ceb)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, dde)) → new_esEs10(yvy4000, yvy3000, dde)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_esEs4(yvy49000, yvy50000, dd)
new_compare33(yvy20, yvy15, dbf) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, dbf), dbf)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, cgg) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_[], cea)) → new_esEs19(yvy49000, yvy50000, cea)
new_compare16(@0, @0) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, bde)) → new_esEs4(yvy4002, yvy3002, bde)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_compare26(Nothing, Just(yvy5000), False, cce) → LT
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), be) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, be), be)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_[], bgc)) → new_ltEs14(yvy49000, yvy50000, bgc)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs7(yvy4000, yvy3000, baf, bag, bah)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bdg) → new_ltEs12(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cda)) → new_esEs4(yvy49000, yvy50000, cda)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_esEs6(yvy49000, yvy50000, dg, dh)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_compare18(yvy49000, yvy50000, dg, dh) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, dg, dh), dg, dh)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_pePe(False, yvy201) → yvy201
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs31(yvy400, yvy300, ty_Float) → new_esEs17(yvy400, yvy300)
new_compare23(yvy49000, yvy50000, False, de, df) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, de, df), de, df)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_compare26(Nothing, Nothing, False, cce) → LT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bdg) → new_ltEs4(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cfd)) → new_lt17(yvy49001, yvy50001, cfd)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bee), bef), beg), bdg) → new_ltEs13(yvy49000, yvy50000, bee, bef, beg)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bea), beb), bdg) → new_ltEs10(yvy49000, yvy50000, bea, beb)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs13(yvy49001, yvy50001, fc, fd, ff)
new_esEs31(yvy400, yvy300, ty_Bool) → new_esEs15(yvy400, yvy300)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cec)) → new_lt10(yvy49001, yvy50001, cec)
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chb), chc), cgg) → new_esEs6(yvy4000, yvy3000, chb, chc)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbb)) → new_esEs19(yvy4000, yvy3000, cbb)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, chh), cgg) → new_esEs4(yvy4000, yvy3000, chh)
new_esEs31(yvy400, yvy300, ty_Integer) → new_esEs13(yvy400, yvy300)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, gg), gh)) → new_ltEs5(yvy49000, yvy50000, gg, gh)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(ty_@2, bff), bfg)) → new_ltEs5(yvy49000, yvy50000, bff, bfg)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs7(yvy4002, yvy3002, bdb, bdc, bdd)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs7(yvy49001, yvy50001, ceh, cfa, cfb)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cdf), cdg), cdh)) → new_lt14(yvy49000, yvy50000, cdf, cdg, cdh)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbc), cbd)) → new_esEs5(yvy4001, yvy3001, cbc, cbd)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbe), cbf)) → new_esEs6(yvy4001, yvy3001, cbe, cbf)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ef)) → new_ltEs9(yvy49001, yvy50001, ef)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, he)) → new_ltEs17(yvy49000, yvy50000, he)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, bfb), bdg)) → new_ltEs10(yvy4900, yvy5000, bfb, bdg)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), db, dc) → new_pePe(new_lt6(yvy49000, yvy50000, db), new_asAs(new_esEs20(yvy49000, yvy50000, db), new_ltEs6(yvy49001, yvy50001, dc)))
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfe)) → new_ltEs9(yvy49002, yvy50002, cfe)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, cac), cad)) → new_esEs6(yvy4000, yvy3000, cac, cad)
new_gt2(yvy35, yvy30, bb) → new_esEs9(new_compare33(yvy35, yvy30, bb), GT)
new_compare0([], [], be) → EQ
new_pePe(True, yvy201) → True
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_primEqNat0(Zero, Zero) → True
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bdg) → new_ltEs11(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(ty_@2, dae), daf)) → new_esEs6(yvy4000, yvy3000, dae, daf)
new_ltEs14(yvy4900, yvy5000, be) → new_fsEs(new_compare0(yvy4900, yvy5000, be))
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, eg), eh)) → new_ltEs10(yvy49001, yvy50001, eg, eh)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_ltEs18(EQ, EQ) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, cgg) → new_esEs9(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_esEs19([], [], dbe) → True
new_compare110(yvy49000, yvy50000, False, dg, dh) → GT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, cc)) → new_esEs10(yvy4000, yvy3000, cc)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccd)) → new_esEs19(yvy4001, yvy3001, ccd)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_compare12(yvy49000, yvy50000, False, de, df) → GT
new_primCmpNat1(Zero, Zero) → EQ
new_primCompAux0(yvy49000, yvy50000, yvy202, be) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, be))
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs18(LT, LT) → True
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_esEs31(yvy400, yvy300, app(app(app(ty_@3, hf), hg), hh)) → new_esEs7(yvy400, yvy300, hf, hg, hh)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, cgg) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_esEs7(yvy49000, yvy50000, ea, eb, ec)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_lt11(yvy49000, yvy50000, de, df)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, gc)) → new_ltEs9(yvy4900, yvy5000, gc)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs19(:(yvy4000, yvy4001), [], dbe) → False
new_esEs19([], :(yvy3000, yvy3001), dbe) → False
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_ltEs18(GT, GT) → True
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(EQ, EQ) → True
new_compare24(yvy49000, yvy50000, True, ea, eb, ec) → EQ
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bdg) → new_ltEs18(yvy49000, yvy50000)
new_esEs15(True, True) → True
new_esEs30(yvy20, yvy15, app(ty_[], dch)) → new_esEs19(yvy20, yvy15, dch)
new_ltEs18(LT, GT) → True
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcg)) → new_esEs4(yvy20, yvy15, dcg)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, gb)) → new_ltEs17(yvy4900, yvy5000, gb)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, cbg)) → new_esEs10(yvy4001, yvy3001, cbg)
new_ltEs8(True, True) → True
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs7(yvy49000, yvy50000, cdf, cdg, cdh)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, dea)) → new_esEs4(yvy4000, yvy3000, dea)
new_esEs31(yvy400, yvy300, ty_Char) → new_esEs8(yvy400, yvy300)
new_ltEs18(GT, LT) → False
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, che), chf), chg), cgg) → new_esEs7(yvy4000, yvy3000, che, chf, chg)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_lt14(yvy49000, yvy50000, ea, eb, ec) → new_esEs9(new_compare14(yvy49000, yvy50000, ea, eb, ec), LT)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, ced), cee)) → new_esEs5(yvy49001, yvy50001, ced, cee)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cgf)) → new_ltEs17(yvy49002, yvy50002, cgf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcd), dce), dcf)) → new_esEs7(yvy20, yvy15, dcd, dce, dcf)
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, ge), gf)) → new_ltEs10(yvy49000, yvy50000, ge, gf)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], hd)) → new_ltEs14(yvy49000, yvy50000, hd)
new_esEs31(yvy400, yvy300, app(app(ty_Either, dab), cgg)) → new_esEs5(yvy400, yvy300, dab, cgg)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bbb)) → new_esEs19(yvy4000, yvy3000, bbb)
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cfh), cga)) → new_ltEs5(yvy49002, yvy50002, cfh, cga)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_[], dbd)) → new_esEs19(yvy4000, yvy3000, dbd)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bcc)) → new_esEs4(yvy4001, yvy3001, bcc)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, ccc)) → new_esEs4(yvy4001, yvy3001, ccc)
new_compare112(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bhg, bhh) → new_asAs(new_esEs24(yvy4000, yvy3000, bhg), new_esEs25(yvy4001, yvy3001, bhh))
new_lt19(yvy49001, yvy50001, app(app(ty_@2, cef), ceg)) → new_lt12(yvy49001, yvy50001, cef, ceg)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare12(yvy49000, yvy50000, True, de, df) → LT
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(ty_Either, dac), dad)) → new_esEs5(yvy4000, yvy3000, dac, dad)
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(app(ty_@3, bfh), bga), bgb)) → new_ltEs13(yvy49000, yvy50000, bfh, bga, bgb)
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_ltEs19(yvy4900, yvy5000, app(ty_[], be)) → new_ltEs14(yvy4900, yvy5000, be)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_Ratio, dag)) → new_esEs10(yvy4000, yvy3000, dag)
new_compare111(yvy49000, yvy50000, True, ea, eb, ec) → LT
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_primCompAux00(yvy206, LT) → LT
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(ty_Either, bfd), bfe)) → new_ltEs10(yvy49000, yvy50000, bfd, bfe)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, cgg) → new_esEs14(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, ceb)) → new_lt17(yvy49000, yvy50000, ceb)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare13(yvy175, yvy176, True, ga) → LT
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs23(yvy4002, yvy3002, app(ty_[], bdf)) → new_esEs19(yvy4002, yvy3002, bdf)
new_lt15(yvy49000, yvy50000, ed) → new_esEs9(new_compare0(yvy49000, yvy50000, ed), LT)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_lt17(yvy49000, yvy50000, ee)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, gd)) → new_ltEs9(yvy49000, yvy50000, gd)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_compare14(yvy49000, yvy50000, ea, eb, ec) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, bg), bh)) → new_esEs5(yvy4000, yvy3000, bg, bh)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_esEs5(yvy49000, yvy50000, de, df)
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs31(yvy400, yvy300, ty_Int) → new_esEs14(yvy400, yvy300)
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_esEs31(yvy400, yvy300, app(ty_Ratio, bd)) → new_esEs10(yvy400, yvy300, bd)
new_ltEs20(yvy49002, yvy50002, app(ty_[], cge)) → new_ltEs14(yvy49002, yvy50002, cge)
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dda), ddb)) → new_esEs5(yvy4000, yvy3000, dda, ddb)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, ca), cb)) → new_esEs6(yvy4000, yvy3000, ca, cb)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs31(yvy400, yvy300, app(ty_[], dbe)) → new_esEs19(yvy400, yvy300, dbe)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bbe), bbf)) → new_esEs6(yvy4001, yvy3001, bbe, bbf)
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_compare28(yvy49000, yvy50000, app(ty_[], bhe)) → new_compare0(yvy49000, yvy50000, bhe)
new_ltEs9(Just(yvy49000), Nothing, gc) → False
new_primCompAux00(yvy206, EQ) → yvy206
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, cgg) → new_esEs15(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bda)) → new_esEs10(yvy4002, yvy3002, bda)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, cgg) → new_esEs8(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_compare26(Just(yvy4900), Just(yvy5000), False, cce) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, cce), cce)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bhb), bhc), bhd)) → new_compare14(yvy49000, yvy50000, bhb, bhc, bhd)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, ccf), ccg), cch)) → new_ltEs13(yvy4900, yvy5000, ccf, ccg, cch)
new_compare26(yvy490, yvy500, True, cce) → EQ
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs18(GT, EQ) → False
new_compare17(yvy49000, yvy50000, de, df) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, de, df), de, df)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcc)) → new_esEs10(yvy20, yvy15, dcc)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bdg) → new_ltEs16(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_esEs10(yvy49000, yvy50000, ee)
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bcg), bch)) → new_esEs6(yvy4002, yvy3002, bcg, bch)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, gc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, cgg) → new_esEs17(yvy4000, yvy3000)
new_esEs9(GT, GT) → True
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bge)) → new_compare19(yvy49000, yvy50000, bge)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bdg) → new_ltEs15(yvy49000, yvy50000)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs18(EQ, LT) → False
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_compare0(:(yvy49000, yvy49001), [], be) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_ltEs18(LT, EQ) → True
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cdb), cdc)) → new_esEs5(yvy49000, yvy50000, cdb, cdc)
new_lt6(yvy49000, yvy50000, app(ty_[], ed)) → new_lt15(yvy49000, yvy50000, ed)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fg)) → new_ltEs14(yvy49001, yvy50001, fg)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs7(yvy4001, yvy3001, bbh, bca, bcb)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_lt10(yvy49000, yvy50000, dd)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, ceh), cfa), cfb)) → new_lt14(yvy49001, yvy50001, ceh, cfa, cfb)
new_lt19(yvy49001, yvy50001, app(ty_[], cfc)) → new_lt15(yvy49001, yvy50001, cfc)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, ddf), ddg), ddh)) → new_esEs7(yvy4000, yvy3000, ddf, ddg, ddh)
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), hf, hg, hh) → new_asAs(new_esEs21(yvy4000, yvy3000, hf), new_asAs(new_esEs22(yvy4001, yvy3001, hg), new_esEs23(yvy4002, yvy3002, hh)))
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs5(Left(yvy4000), Right(yvy3000), dab, cgg) → False
new_esEs5(Right(yvy4000), Left(yvy3000), dab, cgg) → False
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, cef), ceg)) → new_esEs6(yvy49001, yvy50001, cef, ceg)
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bae)) → new_esEs10(yvy4000, yvy3000, bae)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_ltEs8(False, False) → True
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_compare19(yvy49000, yvy50000, dd) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, dd), dd)
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdd), cde)) → new_lt12(yvy49000, yvy50000, cdd, cde)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, ha), hb), hc)) → new_ltEs13(yvy49000, yvy50000, ha, hb, hc)
new_gt(h) → new_esEs9(new_compare30(h), GT)
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_compare25(yvy49000, yvy50000, True, dg, dh) → EQ
new_lt19(yvy49001, yvy50001, app(app(ty_Either, ced), cee)) → new_lt11(yvy49001, yvy50001, ced, cee)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cda)) → new_lt10(yvy49000, yvy50000, cda)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, bf) → True
new_compare111(yvy49000, yvy50000, False, ea, eb, ec) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_compare210(yvy49000, yvy50000, True) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bdg) → new_ltEs7(yvy49000, yvy50000)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cec)) → new_esEs4(yvy49001, yvy50001, cec)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cff), cfg)) → new_ltEs10(yvy49002, yvy50002, cff, cfg)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bgf), bgg)) → new_compare17(yvy49000, yvy50000, bgf, bgg)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cdb), cdc)) → new_lt11(yvy49000, yvy50000, cdb, cdc)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cfd)) → new_esEs10(yvy49001, yvy50001, cfd)
new_compare13(yvy175, yvy176, False, ga) → GT
new_compare23(yvy49000, yvy50000, True, de, df) → EQ
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], beh), bdg) → new_ltEs14(yvy49000, yvy50000, beh)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, cgg) → new_esEs13(yvy4000, yvy3000)
new_lt17(yvy49000, yvy50000, ee) → new_esEs9(new_compare8(yvy49000, yvy50000, ee), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs7(yvy4000, yvy3000, dah, dba, dbb)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cgb), cgc), cgd)) → new_ltEs13(yvy49002, yvy50002, cgb, cgc, cgd)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddc), ddd)) → new_esEs6(yvy4000, yvy3000, ddc, ddd)
new_gt0(yvy300, h) → new_esEs9(new_compare31(yvy300, h), GT)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bba)) → new_esEs4(yvy4000, yvy3000, bba)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, fa), fb)) → new_ltEs5(yvy49001, yvy50001, fa, fb)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bdh), bdg) → new_ltEs9(yvy49000, yvy50000, bdh)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_lt14(yvy49000, yvy50000, ea, eb, ec)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, caf), cag), cah)) → new_esEs7(yvy4000, yvy3000, caf, cag, cah)
new_lt20(yvy49000, yvy50000, app(ty_[], cea)) → new_lt15(yvy49000, yvy50000, cea)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt12(yvy49000, yvy50000, dg, dh) → new_esEs9(new_compare18(yvy49000, yvy50000, dg, dh), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bd) → new_asAs(new_esEs11(yvy4000, yvy3000, bd), new_esEs12(yvy4001, yvy3001, bd))
new_asAs(False, yvy182) → False
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_gt1(yvy400, h) → new_esEs9(new_compare32(yvy400, h), GT)
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, baa), bab)) → new_esEs5(yvy4000, yvy3000, baa, bab)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_esEs31(yvy400, yvy300, ty_Double) → new_esEs16(yvy400, yvy300)
new_lt10(yvy49000, yvy50000, dd) → new_esEs9(new_compare19(yvy49000, yvy50000, dd), LT)
new_compare25(yvy49000, yvy50000, False, dg, dh) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, dg, dh), dg, dh)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, bhf)) → new_compare8(yvy49000, yvy50000, bhf)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), ccf, ccg, cch) → new_pePe(new_lt20(yvy49000, yvy50000, ccf), new_asAs(new_esEs26(yvy49000, yvy50000, ccf), new_pePe(new_lt19(yvy49001, yvy50001, ccg), new_asAs(new_esEs27(yvy49001, yvy50001, ccg), new_ltEs20(yvy49002, yvy50002, cch)))))
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cae)) → new_esEs10(yvy4000, yvy3000, cae)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbg), dbh)) → new_esEs5(yvy20, yvy15, dbg, dbh)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_Ratio, bgd)) → new_ltEs17(yvy49000, yvy50000, bgd)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bbg)) → new_esEs10(yvy4001, yvy3001, bbg)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs7(yvy4001, yvy3001, cbh, cca, ccb)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_Maybe, dbc)) → new_esEs4(yvy4000, yvy3000, dbc)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare11(yvy49000, yvy50000, False) → GT
new_esEs30(yvy20, yvy15, app(app(ty_@2, dca), dcb)) → new_esEs6(yvy20, yvy15, dca, dcb)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Left(yvy50000), bfb, bdg) → False
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_compare11(yvy49000, yvy50000, True) → LT
new_esEs31(yvy400, yvy300, app(ty_Maybe, bf)) → new_esEs4(yvy400, yvy300, bf)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], da)) → new_esEs19(yvy4000, yvy3000, da)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, cgh), cha), cgg) → new_esEs5(yvy4000, yvy3000, cgh, cha)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_Maybe, bfc)) → new_ltEs9(yvy49000, yvy50000, bfc)
new_compare112(yvy49000, yvy50000, False) → GT
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(ty_[], ed)) → new_esEs19(yvy49000, yvy50000, ed)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cfc)) → new_esEs19(yvy49001, yvy50001, cfc)
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_esEs31(yvy400, yvy300, ty_@0) → new_esEs18(yvy400, yvy300)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy50000, yvy50001), be) → LT
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_asAs(True, yvy182) → yvy182
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_esEs18(@0, @0) → True
new_compare211(yvy49000, yvy50000, True) → EQ
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdd), cde)) → new_esEs6(yvy49000, yvy50000, cdd, cde)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cd), ce), cf)) → new_esEs7(yvy4000, yvy3000, cd, ce, cf)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, chd), cgg) → new_esEs10(yvy4000, yvy3000, chd)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, bfa), bdg) → new_ltEs17(yvy49000, yvy50000, bfa)
new_lt11(yvy49000, yvy50000, de, df) → new_esEs9(new_compare17(yvy49000, yvy50000, de, df), LT)
new_esEs9(LT, LT) → True
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), dbe) → new_asAs(new_esEs28(yvy4000, yvy3000, dbe), new_esEs19(yvy4001, yvy3001, dbe))
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bbc), bbd)) → new_esEs5(yvy4001, yvy3001, bbc, bbd)
new_primCompAux00(yvy206, GT) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bdg) → new_ltEs8(yvy49000, yvy50000)
new_esEs31(yvy400, yvy300, app(app(ty_@2, bhg), bhh)) → new_esEs6(yvy400, yvy300, bhg, bhh)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_lt12(yvy49000, yvy50000, dg, dh)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bgh), bha)) → new_compare18(yvy49000, yvy50000, bgh, bha)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_ltEs17(yvy4900, yvy5000, gb) → new_fsEs(new_compare8(yvy4900, yvy5000, gb))
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Int)
new_esEs19(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_@0)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs9(Nothing, Nothing, x0)
new_esEs18(@0, @0)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_asAs(True, x0)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Char)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs31(x0, x1, ty_Float)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpNat0(x0, Zero)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_@0)
new_gt2(x0, x1, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs31(x0, x1, ty_Ordering)
new_compare26(Nothing, Nothing, False, x0)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs19([], :(x0, x1), x2)
new_compare6(Char(x0), Char(x1))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primCmpNat1(Zero, Zero)
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs31(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_@0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Nothing, Just(x0), x1)
new_esEs12(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, True, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_compare110(x0, x1, False, x2, x3)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_compare111(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Nothing, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs22(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare33(x0, x1, x2)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primPlusNat1(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs9(Just(x0), Nothing, x1)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_gt(x0)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs9(GT, GT)
new_ltEs8(False, False)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, x2, x3)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_compare32(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_esEs19([], [], x0)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Ordering)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_gt0(x0, x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_compare26(Nothing, Just(x0), False, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_ltEs6(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs12(x0, x1)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_esEs28(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_compare18(x0, x1, x2, x3)
new_compare31(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_lt19(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(Char(x0), Char(x1))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs17(x0, x1, x2)
new_esEs31(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_compare0([], :(x0, x1), x2)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_esEs31(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare27(Double(x0, x1), Double(x2, x3))
new_compare28(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare28(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_compare26(x0, x1, True, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare12(x0, x1, False, x2, x3)
new_gt1(x0, x1)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare13(x0, x1, False, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)

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

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

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

new_splitLT(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Nothing, h, ba)
new_splitLT2(yvy300, yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, True, h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Nothing, h, ba)
new_splitLT2(yvy300, yvy31, yvy32, yvy33, yvy34, False, h, ba) → new_splitLT10(yvy300, yvy31, yvy32, yvy33, yvy34, new_gt0(yvy300, h), h, ba)
new_splitLT1(yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitLT(yvy34, h, ba)
new_splitLT10(yvy300, yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitLT(yvy34, h, ba)
new_splitLT3(Nothing, yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitLT1(yvy31, yvy32, yvy33, yvy34, new_gt(h), h, ba)
new_splitLT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitLT2(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare26(Nothing, Just(yvy300), False, h), LT), h, ba)

The TRS R consists of the following rules:

new_gt(h) → new_esEs9(new_compare30(h), GT)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_compare26(yvy490, yvy500, True, cce) → EQ
new_gt0(yvy300, h) → new_esEs9(new_compare31(yvy300, h), GT)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_compare26(Nothing, Just(yvy5000), False, cce) → LT
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Int)
new_esEs19(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_@0)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs9(Nothing, Nothing, x0)
new_esEs18(@0, @0)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_asAs(True, x0)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Char)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs31(x0, x1, ty_Float)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpNat0(x0, Zero)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_@0)
new_gt2(x0, x1, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs31(x0, x1, ty_Ordering)
new_compare26(Nothing, Nothing, False, x0)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs19([], :(x0, x1), x2)
new_compare6(Char(x0), Char(x1))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primCmpNat1(Zero, Zero)
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs31(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_@0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Nothing, Just(x0), x1)
new_esEs12(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, True, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_compare110(x0, x1, False, x2, x3)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_compare111(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Nothing, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs22(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare33(x0, x1, x2)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primPlusNat1(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs9(Just(x0), Nothing, x1)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_gt(x0)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs9(GT, GT)
new_ltEs8(False, False)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, x2, x3)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_compare32(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_esEs19([], [], x0)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Ordering)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_gt0(x0, x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_compare26(Nothing, Just(x0), False, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_ltEs6(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs12(x0, x1)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_esEs28(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_compare18(x0, x1, x2, x3)
new_compare31(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_lt19(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(Char(x0), Char(x1))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs17(x0, x1, x2)
new_esEs31(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_compare0([], :(x0, x1), x2)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_esEs31(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare27(Double(x0, x1), Double(x2, x3))
new_compare28(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare28(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_compare26(x0, x1, True, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare12(x0, x1, False, x2, x3)
new_gt1(x0, x1)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare13(x0, x1, False, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)

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

new_ltEs20(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Int)
new_esEs19(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_@0)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs9(Nothing, Nothing, x0)
new_esEs18(@0, @0)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_asAs(True, x0)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Char)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs31(x0, x1, ty_Float)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpNat0(x0, Zero)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_@0)
new_gt2(x0, x1, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs31(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs19([], :(x0, x1), x2)
new_compare6(Char(x0), Char(x1))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primCmpNat1(Zero, Zero)
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs31(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_@0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Nothing, Just(x0), x1)
new_esEs12(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, True, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_compare110(x0, x1, False, x2, x3)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_compare111(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Nothing, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs22(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare33(x0, x1, x2)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primPlusNat1(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs9(Just(x0), Nothing, x1)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_ltEs8(False, False)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, x2, x3)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_compare32(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_esEs19([], [], x0)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Ordering)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_ltEs6(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs12(x0, x1)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_esEs28(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_compare18(x0, x1, x2, x3)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_lt19(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(Char(x0), Char(x1))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs17(x0, x1, x2)
new_esEs31(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_compare0([], :(x0, x1), x2)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_esEs31(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare27(Double(x0, x1), Double(x2, x3))
new_compare28(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare28(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare12(x0, x1, False, x2, x3)
new_gt1(x0, x1)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare13(x0, x1, False, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)



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

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

new_splitLT(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Nothing, h, ba)
new_splitLT2(yvy300, yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, True, h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Nothing, h, ba)
new_splitLT2(yvy300, yvy31, yvy32, yvy33, yvy34, False, h, ba) → new_splitLT10(yvy300, yvy31, yvy32, yvy33, yvy34, new_gt0(yvy300, h), h, ba)
new_splitLT1(yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitLT(yvy34, h, ba)
new_splitLT3(Nothing, yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitLT1(yvy31, yvy32, yvy33, yvy34, new_gt(h), h, ba)
new_splitLT10(yvy300, yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitLT(yvy34, h, ba)
new_splitLT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitLT2(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare26(Nothing, Just(yvy300), False, h), LT), h, ba)

The TRS R consists of the following rules:

new_gt(h) → new_esEs9(new_compare30(h), GT)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_compare26(yvy490, yvy500, True, cce) → EQ
new_gt0(yvy300, h) → new_esEs9(new_compare31(yvy300, h), GT)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_compare26(Nothing, Just(yvy5000), False, cce) → LT
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True

The set Q consists of the following terms:

new_compare26(Nothing, Nothing, False, x0)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_gt(x0)
new_esEs9(GT, GT)
new_esEs9(EQ, EQ)
new_gt0(x0, x1)
new_compare26(Nothing, Just(x0), False, x1)
new_compare31(x0, x1)
new_compare26(Just(x0), Nothing, False, x1)
new_compare30(x0)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare26(x0, x1, True, x2)
new_esEs9(LT, 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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ AND
                                        ↳ QDP
                                        ↳ QDP
                                          ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP

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

new_splitLT12(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, True, bb, bc) → new_splitLT0(yvy34, yvy35, bb, bc)
new_splitLT3(Nothing, yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitLT20(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), LT), h, ba)
new_splitLT20(yvy31, yvy32, yvy33, yvy34, yvy400, False, h, ba) → new_splitLT11(yvy31, yvy32, yvy33, yvy34, yvy400, new_gt1(yvy400, h), h, ba)
new_splitLT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitLT21(yvy300, yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Just(yvy300), new_esEs31(yvy400, yvy300, h), h), LT), h, ba)
new_splitLT21(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, False, bb, bc) → new_splitLT12(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, new_gt2(yvy35, yvy30, bb), bb, bc)
new_splitLT20(yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, yvy400, True, h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Just(yvy400), h, ba)
new_splitLT0(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy400, h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Just(yvy400), h, ba)
new_splitLT11(yvy31, yvy32, yvy33, yvy34, yvy400, True, h, ba) → new_splitLT0(yvy34, yvy400, h, ba)
new_splitLT21(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, True, bb, bc) → new_splitLT0(yvy33, yvy35, bb, bc)

The TRS R consists of the following rules:

new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, cg)) → new_esEs4(yvy4000, yvy3000, cg)
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, db), dc)) → new_ltEs5(yvy4900, yvy5000, db, dc)
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, caa), cab)) → new_esEs5(yvy4000, yvy3000, caa, cab)
new_esEs28(yvy4000, yvy3000, app(ty_[], deb)) → new_esEs19(yvy4000, yvy3000, deb)
new_esEs31(yvy400, yvy300, ty_Ordering) → new_esEs9(yvy400, yvy300)
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, bac), bad)) → new_esEs6(yvy4000, yvy3000, bac, bad)
new_primCmpNat2(Zero, yvy4900) → LT
new_ltEs8(False, True) → True
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, bec), bed), bdg) → new_ltEs5(yvy49000, yvy50000, bec, bed)
new_esEs22(yvy4001, yvy3001, app(ty_[], bcd)) → new_esEs19(yvy4001, yvy3001, bcd)
new_ltEs18(EQ, GT) → True
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_ltEs10(Left(yvy49000), Right(yvy50000), bfb, bdg) → True
new_compare110(yvy49000, yvy50000, True, dg, dh) → LT
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bce), bcf)) → new_esEs5(yvy4002, yvy3002, bce, bcf)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_compare24(yvy49000, yvy50000, False, ea, eb, ec) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cba)) → new_esEs4(yvy4000, yvy3000, cba)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, fh)) → new_ltEs17(yvy49001, yvy50001, fh)
new_esEs4(Just(yvy4000), Nothing, bf) → False
new_esEs4(Nothing, Just(yvy3000), bf) → False
new_ltEs9(Nothing, Just(yvy50000), gc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], daa), cgg) → new_esEs19(yvy4000, yvy3000, daa)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_primMulNat0(Zero, Zero) → Zero
new_compare26(Just(yvy4900), Nothing, False, cce) → GT
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, ceb)) → new_esEs10(yvy49000, yvy50000, ceb)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, dde)) → new_esEs10(yvy4000, yvy3000, dde)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_esEs4(yvy49000, yvy50000, dd)
new_compare33(yvy20, yvy15, dbf) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, dbf), dbf)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, cgg) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_[], cea)) → new_esEs19(yvy49000, yvy50000, cea)
new_compare16(@0, @0) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, bde)) → new_esEs4(yvy4002, yvy3002, bde)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_compare26(Nothing, Just(yvy5000), False, cce) → LT
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), be) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, be), be)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_[], bgc)) → new_ltEs14(yvy49000, yvy50000, bgc)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs7(yvy4000, yvy3000, baf, bag, bah)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bdg) → new_ltEs12(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cda)) → new_esEs4(yvy49000, yvy50000, cda)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_esEs6(yvy49000, yvy50000, dg, dh)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_compare18(yvy49000, yvy50000, dg, dh) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, dg, dh), dg, dh)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_pePe(False, yvy201) → yvy201
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs31(yvy400, yvy300, ty_Float) → new_esEs17(yvy400, yvy300)
new_compare23(yvy49000, yvy50000, False, de, df) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, de, df), de, df)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_compare26(Nothing, Nothing, False, cce) → LT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bdg) → new_ltEs4(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cfd)) → new_lt17(yvy49001, yvy50001, cfd)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bee), bef), beg), bdg) → new_ltEs13(yvy49000, yvy50000, bee, bef, beg)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bea), beb), bdg) → new_ltEs10(yvy49000, yvy50000, bea, beb)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs13(yvy49001, yvy50001, fc, fd, ff)
new_esEs31(yvy400, yvy300, ty_Bool) → new_esEs15(yvy400, yvy300)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cec)) → new_lt10(yvy49001, yvy50001, cec)
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chb), chc), cgg) → new_esEs6(yvy4000, yvy3000, chb, chc)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbb)) → new_esEs19(yvy4000, yvy3000, cbb)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, chh), cgg) → new_esEs4(yvy4000, yvy3000, chh)
new_esEs31(yvy400, yvy300, ty_Integer) → new_esEs13(yvy400, yvy300)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, gg), gh)) → new_ltEs5(yvy49000, yvy50000, gg, gh)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(ty_@2, bff), bfg)) → new_ltEs5(yvy49000, yvy50000, bff, bfg)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs7(yvy4002, yvy3002, bdb, bdc, bdd)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs7(yvy49001, yvy50001, ceh, cfa, cfb)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cdf), cdg), cdh)) → new_lt14(yvy49000, yvy50000, cdf, cdg, cdh)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbc), cbd)) → new_esEs5(yvy4001, yvy3001, cbc, cbd)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbe), cbf)) → new_esEs6(yvy4001, yvy3001, cbe, cbf)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ef)) → new_ltEs9(yvy49001, yvy50001, ef)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, he)) → new_ltEs17(yvy49000, yvy50000, he)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, bfb), bdg)) → new_ltEs10(yvy4900, yvy5000, bfb, bdg)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), db, dc) → new_pePe(new_lt6(yvy49000, yvy50000, db), new_asAs(new_esEs20(yvy49000, yvy50000, db), new_ltEs6(yvy49001, yvy50001, dc)))
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfe)) → new_ltEs9(yvy49002, yvy50002, cfe)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, cac), cad)) → new_esEs6(yvy4000, yvy3000, cac, cad)
new_gt2(yvy35, yvy30, bb) → new_esEs9(new_compare33(yvy35, yvy30, bb), GT)
new_compare0([], [], be) → EQ
new_pePe(True, yvy201) → True
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_primEqNat0(Zero, Zero) → True
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bdg) → new_ltEs11(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(ty_@2, dae), daf)) → new_esEs6(yvy4000, yvy3000, dae, daf)
new_ltEs14(yvy4900, yvy5000, be) → new_fsEs(new_compare0(yvy4900, yvy5000, be))
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, eg), eh)) → new_ltEs10(yvy49001, yvy50001, eg, eh)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_ltEs18(EQ, EQ) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, cgg) → new_esEs9(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_esEs19([], [], dbe) → True
new_compare110(yvy49000, yvy50000, False, dg, dh) → GT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, cc)) → new_esEs10(yvy4000, yvy3000, cc)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccd)) → new_esEs19(yvy4001, yvy3001, ccd)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_compare12(yvy49000, yvy50000, False, de, df) → GT
new_primCmpNat1(Zero, Zero) → EQ
new_primCompAux0(yvy49000, yvy50000, yvy202, be) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, be))
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs18(LT, LT) → True
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_esEs31(yvy400, yvy300, app(app(app(ty_@3, hf), hg), hh)) → new_esEs7(yvy400, yvy300, hf, hg, hh)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, cgg) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_esEs7(yvy49000, yvy50000, ea, eb, ec)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_lt11(yvy49000, yvy50000, de, df)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, gc)) → new_ltEs9(yvy4900, yvy5000, gc)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs19(:(yvy4000, yvy4001), [], dbe) → False
new_esEs19([], :(yvy3000, yvy3001), dbe) → False
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_ltEs18(GT, GT) → True
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(EQ, EQ) → True
new_compare24(yvy49000, yvy50000, True, ea, eb, ec) → EQ
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bdg) → new_ltEs18(yvy49000, yvy50000)
new_esEs15(True, True) → True
new_esEs30(yvy20, yvy15, app(ty_[], dch)) → new_esEs19(yvy20, yvy15, dch)
new_ltEs18(LT, GT) → True
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcg)) → new_esEs4(yvy20, yvy15, dcg)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, gb)) → new_ltEs17(yvy4900, yvy5000, gb)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, cbg)) → new_esEs10(yvy4001, yvy3001, cbg)
new_ltEs8(True, True) → True
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs7(yvy49000, yvy50000, cdf, cdg, cdh)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, dea)) → new_esEs4(yvy4000, yvy3000, dea)
new_esEs31(yvy400, yvy300, ty_Char) → new_esEs8(yvy400, yvy300)
new_ltEs18(GT, LT) → False
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, che), chf), chg), cgg) → new_esEs7(yvy4000, yvy3000, che, chf, chg)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_lt14(yvy49000, yvy50000, ea, eb, ec) → new_esEs9(new_compare14(yvy49000, yvy50000, ea, eb, ec), LT)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, ced), cee)) → new_esEs5(yvy49001, yvy50001, ced, cee)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cgf)) → new_ltEs17(yvy49002, yvy50002, cgf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcd), dce), dcf)) → new_esEs7(yvy20, yvy15, dcd, dce, dcf)
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, ge), gf)) → new_ltEs10(yvy49000, yvy50000, ge, gf)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], hd)) → new_ltEs14(yvy49000, yvy50000, hd)
new_esEs31(yvy400, yvy300, app(app(ty_Either, dab), cgg)) → new_esEs5(yvy400, yvy300, dab, cgg)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bbb)) → new_esEs19(yvy4000, yvy3000, bbb)
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cfh), cga)) → new_ltEs5(yvy49002, yvy50002, cfh, cga)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_[], dbd)) → new_esEs19(yvy4000, yvy3000, dbd)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bcc)) → new_esEs4(yvy4001, yvy3001, bcc)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, ccc)) → new_esEs4(yvy4001, yvy3001, ccc)
new_compare112(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bhg, bhh) → new_asAs(new_esEs24(yvy4000, yvy3000, bhg), new_esEs25(yvy4001, yvy3001, bhh))
new_lt19(yvy49001, yvy50001, app(app(ty_@2, cef), ceg)) → new_lt12(yvy49001, yvy50001, cef, ceg)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare12(yvy49000, yvy50000, True, de, df) → LT
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(ty_Either, dac), dad)) → new_esEs5(yvy4000, yvy3000, dac, dad)
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(app(ty_@3, bfh), bga), bgb)) → new_ltEs13(yvy49000, yvy50000, bfh, bga, bgb)
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_ltEs19(yvy4900, yvy5000, app(ty_[], be)) → new_ltEs14(yvy4900, yvy5000, be)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_Ratio, dag)) → new_esEs10(yvy4000, yvy3000, dag)
new_compare111(yvy49000, yvy50000, True, ea, eb, ec) → LT
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_primCompAux00(yvy206, LT) → LT
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(ty_Either, bfd), bfe)) → new_ltEs10(yvy49000, yvy50000, bfd, bfe)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, cgg) → new_esEs14(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, ceb)) → new_lt17(yvy49000, yvy50000, ceb)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare13(yvy175, yvy176, True, ga) → LT
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs23(yvy4002, yvy3002, app(ty_[], bdf)) → new_esEs19(yvy4002, yvy3002, bdf)
new_lt15(yvy49000, yvy50000, ed) → new_esEs9(new_compare0(yvy49000, yvy50000, ed), LT)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_lt17(yvy49000, yvy50000, ee)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, gd)) → new_ltEs9(yvy49000, yvy50000, gd)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_compare14(yvy49000, yvy50000, ea, eb, ec) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, bg), bh)) → new_esEs5(yvy4000, yvy3000, bg, bh)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_esEs5(yvy49000, yvy50000, de, df)
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs31(yvy400, yvy300, ty_Int) → new_esEs14(yvy400, yvy300)
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_esEs31(yvy400, yvy300, app(ty_Ratio, bd)) → new_esEs10(yvy400, yvy300, bd)
new_ltEs20(yvy49002, yvy50002, app(ty_[], cge)) → new_ltEs14(yvy49002, yvy50002, cge)
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dda), ddb)) → new_esEs5(yvy4000, yvy3000, dda, ddb)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, ca), cb)) → new_esEs6(yvy4000, yvy3000, ca, cb)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs31(yvy400, yvy300, app(ty_[], dbe)) → new_esEs19(yvy400, yvy300, dbe)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bbe), bbf)) → new_esEs6(yvy4001, yvy3001, bbe, bbf)
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_compare28(yvy49000, yvy50000, app(ty_[], bhe)) → new_compare0(yvy49000, yvy50000, bhe)
new_ltEs9(Just(yvy49000), Nothing, gc) → False
new_primCompAux00(yvy206, EQ) → yvy206
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, cgg) → new_esEs15(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bda)) → new_esEs10(yvy4002, yvy3002, bda)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, cgg) → new_esEs8(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_compare26(Just(yvy4900), Just(yvy5000), False, cce) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, cce), cce)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bhb), bhc), bhd)) → new_compare14(yvy49000, yvy50000, bhb, bhc, bhd)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, ccf), ccg), cch)) → new_ltEs13(yvy4900, yvy5000, ccf, ccg, cch)
new_compare26(yvy490, yvy500, True, cce) → EQ
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs18(GT, EQ) → False
new_compare17(yvy49000, yvy50000, de, df) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, de, df), de, df)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcc)) → new_esEs10(yvy20, yvy15, dcc)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bdg) → new_ltEs16(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_esEs10(yvy49000, yvy50000, ee)
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bcg), bch)) → new_esEs6(yvy4002, yvy3002, bcg, bch)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, gc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, cgg) → new_esEs17(yvy4000, yvy3000)
new_esEs9(GT, GT) → True
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bge)) → new_compare19(yvy49000, yvy50000, bge)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bdg) → new_ltEs15(yvy49000, yvy50000)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs18(EQ, LT) → False
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_compare0(:(yvy49000, yvy49001), [], be) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_ltEs18(LT, EQ) → True
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cdb), cdc)) → new_esEs5(yvy49000, yvy50000, cdb, cdc)
new_lt6(yvy49000, yvy50000, app(ty_[], ed)) → new_lt15(yvy49000, yvy50000, ed)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fg)) → new_ltEs14(yvy49001, yvy50001, fg)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs7(yvy4001, yvy3001, bbh, bca, bcb)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_lt10(yvy49000, yvy50000, dd)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, ceh), cfa), cfb)) → new_lt14(yvy49001, yvy50001, ceh, cfa, cfb)
new_lt19(yvy49001, yvy50001, app(ty_[], cfc)) → new_lt15(yvy49001, yvy50001, cfc)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, ddf), ddg), ddh)) → new_esEs7(yvy4000, yvy3000, ddf, ddg, ddh)
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), hf, hg, hh) → new_asAs(new_esEs21(yvy4000, yvy3000, hf), new_asAs(new_esEs22(yvy4001, yvy3001, hg), new_esEs23(yvy4002, yvy3002, hh)))
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs5(Left(yvy4000), Right(yvy3000), dab, cgg) → False
new_esEs5(Right(yvy4000), Left(yvy3000), dab, cgg) → False
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, cef), ceg)) → new_esEs6(yvy49001, yvy50001, cef, ceg)
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bae)) → new_esEs10(yvy4000, yvy3000, bae)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_ltEs8(False, False) → True
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_compare19(yvy49000, yvy50000, dd) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, dd), dd)
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdd), cde)) → new_lt12(yvy49000, yvy50000, cdd, cde)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, ha), hb), hc)) → new_ltEs13(yvy49000, yvy50000, ha, hb, hc)
new_gt(h) → new_esEs9(new_compare30(h), GT)
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_compare25(yvy49000, yvy50000, True, dg, dh) → EQ
new_lt19(yvy49001, yvy50001, app(app(ty_Either, ced), cee)) → new_lt11(yvy49001, yvy50001, ced, cee)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cda)) → new_lt10(yvy49000, yvy50000, cda)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, bf) → True
new_compare111(yvy49000, yvy50000, False, ea, eb, ec) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_compare210(yvy49000, yvy50000, True) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bdg) → new_ltEs7(yvy49000, yvy50000)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cec)) → new_esEs4(yvy49001, yvy50001, cec)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cff), cfg)) → new_ltEs10(yvy49002, yvy50002, cff, cfg)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bgf), bgg)) → new_compare17(yvy49000, yvy50000, bgf, bgg)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cdb), cdc)) → new_lt11(yvy49000, yvy50000, cdb, cdc)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cfd)) → new_esEs10(yvy49001, yvy50001, cfd)
new_compare13(yvy175, yvy176, False, ga) → GT
new_compare23(yvy49000, yvy50000, True, de, df) → EQ
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], beh), bdg) → new_ltEs14(yvy49000, yvy50000, beh)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, cgg) → new_esEs13(yvy4000, yvy3000)
new_lt17(yvy49000, yvy50000, ee) → new_esEs9(new_compare8(yvy49000, yvy50000, ee), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs7(yvy4000, yvy3000, dah, dba, dbb)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cgb), cgc), cgd)) → new_ltEs13(yvy49002, yvy50002, cgb, cgc, cgd)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddc), ddd)) → new_esEs6(yvy4000, yvy3000, ddc, ddd)
new_gt0(yvy300, h) → new_esEs9(new_compare31(yvy300, h), GT)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bba)) → new_esEs4(yvy4000, yvy3000, bba)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, fa), fb)) → new_ltEs5(yvy49001, yvy50001, fa, fb)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bdh), bdg) → new_ltEs9(yvy49000, yvy50000, bdh)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_lt14(yvy49000, yvy50000, ea, eb, ec)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, caf), cag), cah)) → new_esEs7(yvy4000, yvy3000, caf, cag, cah)
new_lt20(yvy49000, yvy50000, app(ty_[], cea)) → new_lt15(yvy49000, yvy50000, cea)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt12(yvy49000, yvy50000, dg, dh) → new_esEs9(new_compare18(yvy49000, yvy50000, dg, dh), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bd) → new_asAs(new_esEs11(yvy4000, yvy3000, bd), new_esEs12(yvy4001, yvy3001, bd))
new_asAs(False, yvy182) → False
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_gt1(yvy400, h) → new_esEs9(new_compare32(yvy400, h), GT)
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, baa), bab)) → new_esEs5(yvy4000, yvy3000, baa, bab)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_esEs31(yvy400, yvy300, ty_Double) → new_esEs16(yvy400, yvy300)
new_lt10(yvy49000, yvy50000, dd) → new_esEs9(new_compare19(yvy49000, yvy50000, dd), LT)
new_compare25(yvy49000, yvy50000, False, dg, dh) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, dg, dh), dg, dh)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, bhf)) → new_compare8(yvy49000, yvy50000, bhf)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), ccf, ccg, cch) → new_pePe(new_lt20(yvy49000, yvy50000, ccf), new_asAs(new_esEs26(yvy49000, yvy50000, ccf), new_pePe(new_lt19(yvy49001, yvy50001, ccg), new_asAs(new_esEs27(yvy49001, yvy50001, ccg), new_ltEs20(yvy49002, yvy50002, cch)))))
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cae)) → new_esEs10(yvy4000, yvy3000, cae)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbg), dbh)) → new_esEs5(yvy20, yvy15, dbg, dbh)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_Ratio, bgd)) → new_ltEs17(yvy49000, yvy50000, bgd)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bbg)) → new_esEs10(yvy4001, yvy3001, bbg)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs7(yvy4001, yvy3001, cbh, cca, ccb)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_Maybe, dbc)) → new_esEs4(yvy4000, yvy3000, dbc)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare11(yvy49000, yvy50000, False) → GT
new_esEs30(yvy20, yvy15, app(app(ty_@2, dca), dcb)) → new_esEs6(yvy20, yvy15, dca, dcb)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Left(yvy50000), bfb, bdg) → False
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_compare11(yvy49000, yvy50000, True) → LT
new_esEs31(yvy400, yvy300, app(ty_Maybe, bf)) → new_esEs4(yvy400, yvy300, bf)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], da)) → new_esEs19(yvy4000, yvy3000, da)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, cgh), cha), cgg) → new_esEs5(yvy4000, yvy3000, cgh, cha)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_Maybe, bfc)) → new_ltEs9(yvy49000, yvy50000, bfc)
new_compare112(yvy49000, yvy50000, False) → GT
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(ty_[], ed)) → new_esEs19(yvy49000, yvy50000, ed)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cfc)) → new_esEs19(yvy49001, yvy50001, cfc)
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_esEs31(yvy400, yvy300, ty_@0) → new_esEs18(yvy400, yvy300)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy50000, yvy50001), be) → LT
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_asAs(True, yvy182) → yvy182
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_esEs18(@0, @0) → True
new_compare211(yvy49000, yvy50000, True) → EQ
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdd), cde)) → new_esEs6(yvy49000, yvy50000, cdd, cde)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cd), ce), cf)) → new_esEs7(yvy4000, yvy3000, cd, ce, cf)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, chd), cgg) → new_esEs10(yvy4000, yvy3000, chd)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, bfa), bdg) → new_ltEs17(yvy49000, yvy50000, bfa)
new_lt11(yvy49000, yvy50000, de, df) → new_esEs9(new_compare17(yvy49000, yvy50000, de, df), LT)
new_esEs9(LT, LT) → True
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), dbe) → new_asAs(new_esEs28(yvy4000, yvy3000, dbe), new_esEs19(yvy4001, yvy3001, dbe))
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bbc), bbd)) → new_esEs5(yvy4001, yvy3001, bbc, bbd)
new_primCompAux00(yvy206, GT) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bdg) → new_ltEs8(yvy49000, yvy50000)
new_esEs31(yvy400, yvy300, app(app(ty_@2, bhg), bhh)) → new_esEs6(yvy400, yvy300, bhg, bhh)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_lt12(yvy49000, yvy50000, dg, dh)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bgh), bha)) → new_compare18(yvy49000, yvy50000, bgh, bha)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_ltEs17(yvy4900, yvy5000, gb) → new_fsEs(new_compare8(yvy4900, yvy5000, gb))
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Int)
new_esEs19(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_@0)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs9(Nothing, Nothing, x0)
new_esEs18(@0, @0)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_asAs(True, x0)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Char)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs31(x0, x1, ty_Float)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpNat0(x0, Zero)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_@0)
new_gt2(x0, x1, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs31(x0, x1, ty_Ordering)
new_compare26(Nothing, Nothing, False, x0)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs19([], :(x0, x1), x2)
new_compare6(Char(x0), Char(x1))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primCmpNat1(Zero, Zero)
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs31(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_@0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Nothing, Just(x0), x1)
new_esEs12(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, True, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_compare110(x0, x1, False, x2, x3)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_compare111(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Nothing, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs22(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare33(x0, x1, x2)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primPlusNat1(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs9(Just(x0), Nothing, x1)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_gt(x0)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs9(GT, GT)
new_ltEs8(False, False)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, x2, x3)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_compare32(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_esEs19([], [], x0)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Ordering)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_gt0(x0, x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_compare26(Nothing, Just(x0), False, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_ltEs6(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs12(x0, x1)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_esEs28(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_compare18(x0, x1, x2, x3)
new_compare31(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_lt19(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(Char(x0), Char(x1))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs17(x0, x1, x2)
new_esEs31(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_compare0([], :(x0, x1), x2)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_esEs31(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare27(Double(x0, x1), Double(x2, x3))
new_compare28(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare28(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_compare26(x0, x1, True, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare12(x0, x1, False, x2, x3)
new_gt1(x0, x1)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare13(x0, x1, False, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)

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

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

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

new_splitLT12(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, True, bb, bc) → new_splitLT0(yvy34, yvy35, bb, bc)
new_splitLT3(Nothing, yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitLT20(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), LT), h, ba)
new_splitLT20(yvy31, yvy32, yvy33, yvy34, yvy400, False, h, ba) → new_splitLT11(yvy31, yvy32, yvy33, yvy34, yvy400, new_gt1(yvy400, h), h, ba)
new_splitLT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitLT21(yvy300, yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Just(yvy300), new_esEs31(yvy400, yvy300, h), h), LT), h, ba)
new_splitLT21(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, False, bb, bc) → new_splitLT12(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, new_gt2(yvy35, yvy30, bb), bb, bc)
new_splitLT20(yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, yvy400, True, h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Just(yvy400), h, ba)
new_splitLT0(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy400, h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Just(yvy400), h, ba)
new_splitLT11(yvy31, yvy32, yvy33, yvy34, yvy400, True, h, ba) → new_splitLT0(yvy34, yvy400, h, ba)
new_splitLT21(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, True, bb, bc) → new_splitLT0(yvy33, yvy35, bb, bc)

The TRS R consists of the following rules:

new_compare26(Just(yvy4900), Nothing, False, cce) → GT
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True
new_esEs31(yvy400, yvy300, ty_Ordering) → new_esEs9(yvy400, yvy300)
new_esEs31(yvy400, yvy300, ty_Float) → new_esEs17(yvy400, yvy300)
new_esEs31(yvy400, yvy300, ty_Bool) → new_esEs15(yvy400, yvy300)
new_esEs31(yvy400, yvy300, ty_Integer) → new_esEs13(yvy400, yvy300)
new_esEs31(yvy400, yvy300, app(app(app(ty_@3, hf), hg), hh)) → new_esEs7(yvy400, yvy300, hf, hg, hh)
new_esEs31(yvy400, yvy300, ty_Char) → new_esEs8(yvy400, yvy300)
new_esEs31(yvy400, yvy300, app(app(ty_Either, dab), cgg)) → new_esEs5(yvy400, yvy300, dab, cgg)
new_esEs31(yvy400, yvy300, ty_Int) → new_esEs14(yvy400, yvy300)
new_esEs31(yvy400, yvy300, app(ty_Ratio, bd)) → new_esEs10(yvy400, yvy300, bd)
new_esEs31(yvy400, yvy300, app(ty_[], dbe)) → new_esEs19(yvy400, yvy300, dbe)
new_esEs31(yvy400, yvy300, ty_Double) → new_esEs16(yvy400, yvy300)
new_esEs31(yvy400, yvy300, app(ty_Maybe, bf)) → new_esEs4(yvy400, yvy300, bf)
new_esEs31(yvy400, yvy300, ty_@0) → new_esEs18(yvy400, yvy300)
new_esEs31(yvy400, yvy300, app(app(ty_@2, bhg), bhh)) → new_esEs6(yvy400, yvy300, bhg, bhh)
new_compare26(Just(yvy4900), Just(yvy5000), False, cce) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, cce), cce)
new_compare26(yvy490, yvy500, True, cce) → EQ
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, db), dc)) → new_ltEs5(yvy4900, yvy5000, db, dc)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, bfb), bdg)) → new_ltEs10(yvy4900, yvy5000, bfb, bdg)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, gc)) → new_ltEs9(yvy4900, yvy5000, gc)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, gb)) → new_ltEs17(yvy4900, yvy5000, gb)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(ty_[], be)) → new_ltEs14(yvy4900, yvy5000, be)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, ccf), ccg), cch)) → new_ltEs13(yvy4900, yvy5000, ccf, ccg, cch)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare13(yvy175, yvy176, True, ga) → LT
new_compare13(yvy175, yvy176, False, ga) → GT
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_compare16(@0, @0) → EQ
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_not(False) → True
new_not(True) → False
new_ltEs18(EQ, GT) → True
new_ltEs18(EQ, EQ) → True
new_ltEs18(LT, LT) → True
new_ltEs18(GT, GT) → True
new_ltEs18(LT, GT) → True
new_ltEs18(GT, LT) → False
new_ltEs18(GT, EQ) → False
new_ltEs18(EQ, LT) → False
new_ltEs18(LT, EQ) → True
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), ccf, ccg, cch) → new_pePe(new_lt20(yvy49000, yvy50000, ccf), new_asAs(new_esEs26(yvy49000, yvy50000, ccf), new_pePe(new_lt19(yvy49001, yvy50001, ccg), new_asAs(new_esEs27(yvy49001, yvy50001, ccg), new_ltEs20(yvy49002, yvy50002, cch)))))
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cdf), cdg), cdh)) → new_lt14(yvy49000, yvy50000, cdf, cdg, cdh)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, ceb)) → new_lt17(yvy49000, yvy50000, ceb)
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdd), cde)) → new_lt12(yvy49000, yvy50000, cdd, cde)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cda)) → new_lt10(yvy49000, yvy50000, cda)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cdb), cdc)) → new_lt11(yvy49000, yvy50000, cdb, cdc)
new_lt20(yvy49000, yvy50000, app(ty_[], cea)) → new_lt15(yvy49000, yvy50000, cea)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, ceb)) → new_esEs10(yvy49000, yvy50000, ceb)
new_esEs26(yvy49000, yvy50000, app(ty_[], cea)) → new_esEs19(yvy49000, yvy50000, cea)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cda)) → new_esEs4(yvy49000, yvy50000, cda)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs7(yvy49000, yvy50000, cdf, cdg, cdh)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cdb), cdc)) → new_esEs5(yvy49000, yvy50000, cdb, cdc)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdd), cde)) → new_esEs6(yvy49000, yvy50000, cdd, cde)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cfd)) → new_lt17(yvy49001, yvy50001, cfd)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cec)) → new_lt10(yvy49001, yvy50001, cec)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, app(app(ty_@2, cef), ceg)) → new_lt12(yvy49001, yvy50001, cef, ceg)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, ceh), cfa), cfb)) → new_lt14(yvy49001, yvy50001, ceh, cfa, cfb)
new_lt19(yvy49001, yvy50001, app(ty_[], cfc)) → new_lt15(yvy49001, yvy50001, cfc)
new_lt19(yvy49001, yvy50001, app(app(ty_Either, ced), cee)) → new_lt11(yvy49001, yvy50001, ced, cee)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs7(yvy49001, yvy50001, ceh, cfa, cfb)
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, ced), cee)) → new_esEs5(yvy49001, yvy50001, ced, cee)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, cef), ceg)) → new_esEs6(yvy49001, yvy50001, cef, ceg)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cec)) → new_esEs4(yvy49001, yvy50001, cec)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cfd)) → new_esEs10(yvy49001, yvy50001, cfd)
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cfc)) → new_esEs19(yvy49001, yvy50001, cfc)
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfe)) → new_ltEs9(yvy49002, yvy50002, cfe)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cgf)) → new_ltEs17(yvy49002, yvy50002, cgf)
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cfh), cga)) → new_ltEs5(yvy49002, yvy50002, cfh, cga)
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(ty_[], cge)) → new_ltEs14(yvy49002, yvy50002, cge)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cff), cfg)) → new_ltEs10(yvy49002, yvy50002, cff, cfg)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cgb), cgc), cgd)) → new_ltEs13(yvy49002, yvy50002, cgb, cgc, cgd)
new_asAs(False, yvy182) → False
new_asAs(True, yvy182) → yvy182
new_pePe(False, yvy201) → yvy201
new_pePe(True, yvy201) → True
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, bec), bed), bdg) → new_ltEs5(yvy49000, yvy50000, bec, bed)
new_ltEs10(Left(yvy49000), Right(yvy50000), bfb, bdg) → True
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_[], bgc)) → new_ltEs14(yvy49000, yvy50000, bgc)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bdg) → new_ltEs12(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bdg) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bee), bef), beg), bdg) → new_ltEs13(yvy49000, yvy50000, bee, bef, beg)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(ty_@2, bff), bfg)) → new_ltEs5(yvy49000, yvy50000, bff, bfg)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bdg) → new_ltEs11(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bdg) → new_ltEs18(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(app(ty_@3, bfh), bga), bgb)) → new_ltEs13(yvy49000, yvy50000, bfh, bga, bgb)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, gd)) → new_ltEs9(yvy49000, yvy50000, gd)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bdh), bdg) → new_ltEs9(yvy49000, yvy50000, bdh)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bea), beb), bdg) → new_ltEs10(yvy49000, yvy50000, bea, beb)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_Maybe, bfc)) → new_ltEs9(yvy49000, yvy50000, bfc)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(ty_Either, bfd), bfe)) → new_ltEs10(yvy49000, yvy50000, bfd, bfe)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, ge), gf)) → new_ltEs10(yvy49000, yvy50000, ge, gf)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bdg) → new_ltEs16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bdg) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bdg) → new_ltEs7(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], beh), bdg) → new_ltEs14(yvy49000, yvy50000, beh)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_Ratio, bgd)) → new_ltEs17(yvy49000, yvy50000, bgd)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Left(yvy50000), bfb, bdg) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, bfa), bdg) → new_ltEs17(yvy49000, yvy50000, bfa)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bdg) → new_ltEs8(yvy49000, yvy50000)
new_ltEs8(False, True) → True
new_ltEs8(True, True) → True
new_ltEs8(True, False) → False
new_ltEs8(False, False) → True
new_ltEs17(yvy4900, yvy5000, gb) → new_fsEs(new_compare8(yvy4900, yvy5000, gb))
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs14(yvy4900, yvy5000, be) → new_fsEs(new_compare0(yvy4900, yvy5000, be))
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), be) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, be), be)
new_compare0([], [], be) → EQ
new_compare0(:(yvy49000, yvy49001), [], be) → GT
new_compare0([], :(yvy50000, yvy50001), be) → LT
new_primCompAux0(yvy49000, yvy50000, yvy202, be) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, be))
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(ty_[], bhe)) → new_compare0(yvy49000, yvy50000, bhe)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bhb), bhc), bhd)) → new_compare14(yvy49000, yvy50000, bhb, bhc, bhd)
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bge)) → new_compare19(yvy49000, yvy50000, bge)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bgf), bgg)) → new_compare17(yvy49000, yvy50000, bgf, bgg)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, bhf)) → new_compare8(yvy49000, yvy50000, bhf)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bgh), bha)) → new_compare18(yvy49000, yvy50000, bgh, bha)
new_primCompAux00(yvy206, LT) → LT
new_primCompAux00(yvy206, EQ) → yvy206
new_primCompAux00(yvy206, GT) → GT
new_compare18(yvy49000, yvy50000, dg, dh) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, dg, dh), dg, dh)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bhg, bhh) → new_asAs(new_esEs24(yvy4000, yvy3000, bhg), new_esEs25(yvy4001, yvy3001, bhh))
new_compare25(yvy49000, yvy50000, True, dg, dh) → EQ
new_compare25(yvy49000, yvy50000, False, dg, dh) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, dg, dh), dg, dh)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), db, dc) → new_pePe(new_lt6(yvy49000, yvy50000, db), new_asAs(new_esEs20(yvy49000, yvy50000, db), new_ltEs6(yvy49001, yvy50001, dc)))
new_compare110(yvy49000, yvy50000, True, dg, dh) → LT
new_compare110(yvy49000, yvy50000, False, dg, dh) → GT
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_lt11(yvy49000, yvy50000, de, df)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_lt17(yvy49000, yvy50000, ee)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_[], ed)) → new_lt15(yvy49000, yvy50000, ed)
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_lt10(yvy49000, yvy50000, dd)
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_lt14(yvy49000, yvy50000, ea, eb, ec)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_lt12(yvy49000, yvy50000, dg, dh)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_esEs4(yvy49000, yvy50000, dd)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_esEs6(yvy49000, yvy50000, dg, dh)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_esEs7(yvy49000, yvy50000, ea, eb, ec)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_esEs5(yvy49000, yvy50000, de, df)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_esEs10(yvy49000, yvy50000, ee)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_[], ed)) → new_esEs19(yvy49000, yvy50000, ed)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, fh)) → new_ltEs17(yvy49001, yvy50001, fh)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs13(yvy49001, yvy50001, fc, fd, ff)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ef)) → new_ltEs9(yvy49001, yvy50001, ef)
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, eg), eh)) → new_ltEs10(yvy49001, yvy50001, eg, eh)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fg)) → new_ltEs14(yvy49001, yvy50001, fg)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, fa), fb)) → new_ltEs5(yvy49001, yvy50001, fa, fb)
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs9(Nothing, Just(yvy50000), gc) → True
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, gg), gh)) → new_ltEs5(yvy49000, yvy50000, gg, gh)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, he)) → new_ltEs17(yvy49000, yvy50000, he)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], hd)) → new_ltEs14(yvy49000, yvy50000, hd)
new_ltEs9(Just(yvy49000), Nothing, gc) → False
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, gc) → True
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, ha), hb), hc)) → new_ltEs13(yvy49000, yvy50000, ha, hb, hc)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs19([], [], dbe) → True
new_esEs19(:(yvy4000, yvy4001), [], dbe) → False
new_esEs19([], :(yvy3000, yvy3001), dbe) → False
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), dbe) → new_asAs(new_esEs28(yvy4000, yvy3000, dbe), new_esEs19(yvy4001, yvy3001, dbe))
new_esEs28(yvy4000, yvy3000, app(ty_[], deb)) → new_esEs19(yvy4000, yvy3000, deb)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, dde)) → new_esEs10(yvy4000, yvy3000, dde)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, dea)) → new_esEs4(yvy4000, yvy3000, dea)
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dda), ddb)) → new_esEs5(yvy4000, yvy3000, dda, ddb)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, ddf), ddg), ddh)) → new_esEs7(yvy4000, yvy3000, ddf, ddg, ddh)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddc), ddd)) → new_esEs6(yvy4000, yvy3000, ddc, ddd)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_esEs15(True, True) → True
new_esEs15(False, False) → True
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), hf, hg, hh) → new_asAs(new_esEs21(yvy4000, yvy3000, hf), new_asAs(new_esEs22(yvy4001, yvy3001, hg), new_esEs23(yvy4002, yvy3002, hh)))
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, bac), bad)) → new_esEs6(yvy4000, yvy3000, bac, bad)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs7(yvy4000, yvy3000, baf, bag, bah)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bbb)) → new_esEs19(yvy4000, yvy3000, bbb)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bae)) → new_esEs10(yvy4000, yvy3000, bae)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bba)) → new_esEs4(yvy4000, yvy3000, bba)
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, baa), bab)) → new_esEs5(yvy4000, yvy3000, baa, bab)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, app(ty_[], bcd)) → new_esEs19(yvy4001, yvy3001, bcd)
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bcc)) → new_esEs4(yvy4001, yvy3001, bcc)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bbe), bbf)) → new_esEs6(yvy4001, yvy3001, bbe, bbf)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs7(yvy4001, yvy3001, bbh, bca, bcb)
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bbg)) → new_esEs10(yvy4001, yvy3001, bbg)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bbc), bbd)) → new_esEs5(yvy4001, yvy3001, bbc, bbd)
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bce), bcf)) → new_esEs5(yvy4002, yvy3002, bce, bcf)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, bde)) → new_esEs4(yvy4002, yvy3002, bde)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs7(yvy4002, yvy3002, bdb, bdc, bdd)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_[], bdf)) → new_esEs19(yvy4002, yvy3002, bdf)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bda)) → new_esEs10(yvy4002, yvy3002, bda)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bcg), bch)) → new_esEs6(yvy4002, yvy3002, bcg, bch)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(LT, EQ) → False
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bd) → new_asAs(new_esEs11(yvy4000, yvy3000, bd), new_esEs12(yvy4001, yvy3001, bd))
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs18(@0, @0) → True
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Nothing, bf) → False
new_esEs4(Nothing, Just(yvy3000), bf) → False
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, cc)) → new_esEs10(yvy4000, yvy3000, cc)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_Maybe, dbc)) → new_esEs4(yvy4000, yvy3000, dbc)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, chh), cgg) → new_esEs4(yvy4000, yvy3000, chh)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, cg)) → new_esEs4(yvy4000, yvy3000, cg)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(ty_Either, dac), dad)) → new_esEs5(yvy4000, yvy3000, dac, dad)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, cgh), cha), cgg) → new_esEs5(yvy4000, yvy3000, cgh, cha)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, bg), bh)) → new_esEs5(yvy4000, yvy3000, bg, bh)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, ca), cb)) → new_esEs6(yvy4000, yvy3000, ca, cb)
new_esEs4(Nothing, Nothing, bf) → True
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], da)) → new_esEs19(yvy4000, yvy3000, da)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cd), ce), cf)) → new_esEs7(yvy4000, yvy3000, cd, ce, cf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], daa), cgg) → new_esEs19(yvy4000, yvy3000, daa)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, cgg) → new_esEs18(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chb), chc), cgg) → new_esEs6(yvy4000, yvy3000, chb, chc)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(ty_@2, dae), daf)) → new_esEs6(yvy4000, yvy3000, dae, daf)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, cgg) → new_esEs9(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, cgg) → new_esEs16(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, che), chf), chg), cgg) → new_esEs7(yvy4000, yvy3000, che, chf, chg)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_[], dbd)) → new_esEs19(yvy4000, yvy3000, dbd)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_Ratio, dag)) → new_esEs10(yvy4000, yvy3000, dag)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, cgg) → new_esEs14(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, cgg) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, cgg) → new_esEs8(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, cgg) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Right(yvy3000), dab, cgg) → False
new_esEs5(Right(yvy4000), Left(yvy3000), dab, cgg) → False
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, cgg) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs7(yvy4000, yvy3000, dah, dba, dbb)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, chd), cgg) → new_esEs10(yvy4000, yvy3000, chd)
new_lt12(yvy49000, yvy50000, dg, dh) → new_esEs9(new_compare18(yvy49000, yvy50000, dg, dh), LT)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_lt14(yvy49000, yvy50000, ea, eb, ec) → new_esEs9(new_compare14(yvy49000, yvy50000, ea, eb, ec), LT)
new_compare14(yvy49000, yvy50000, ea, eb, ec) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_compare24(yvy49000, yvy50000, False, ea, eb, ec) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_compare24(yvy49000, yvy50000, True, ea, eb, ec) → EQ
new_compare111(yvy49000, yvy50000, True, ea, eb, ec) → LT
new_compare111(yvy49000, yvy50000, False, ea, eb, ec) → GT
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_compare211(yvy49000, yvy50000, True) → EQ
new_compare112(yvy49000, yvy50000, True) → LT
new_compare112(yvy49000, yvy50000, False) → GT
new_lt10(yvy49000, yvy50000, dd) → new_esEs9(new_compare19(yvy49000, yvy50000, dd), LT)
new_compare19(yvy49000, yvy50000, dd) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, dd), dd)
new_compare26(Nothing, Just(yvy5000), False, cce) → LT
new_compare26(Nothing, Nothing, False, cce) → LT
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_lt15(yvy49000, yvy50000, ed) → new_esEs9(new_compare0(yvy49000, yvy50000, ed), LT)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_lt17(yvy49000, yvy50000, ee) → new_esEs9(new_compare8(yvy49000, yvy50000, ee), LT)
new_lt11(yvy49000, yvy50000, de, df) → new_esEs9(new_compare17(yvy49000, yvy50000, de, df), LT)
new_compare17(yvy49000, yvy50000, de, df) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, de, df), de, df)
new_compare23(yvy49000, yvy50000, False, de, df) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, de, df), de, df)
new_compare23(yvy49000, yvy50000, True, de, df) → EQ
new_compare12(yvy49000, yvy50000, False, de, df) → GT
new_compare12(yvy49000, yvy50000, True, de, df) → LT
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_compare210(yvy49000, yvy50000, True) → EQ
new_compare11(yvy49000, yvy50000, False) → GT
new_compare11(yvy49000, yvy50000, True) → LT
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, caa), cab)) → new_esEs5(yvy4000, yvy3000, caa, cab)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cba)) → new_esEs4(yvy4000, yvy3000, cba)
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbb)) → new_esEs19(yvy4000, yvy3000, cbb)
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, cac), cad)) → new_esEs6(yvy4000, yvy3000, cac, cad)
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, caf), cag), cah)) → new_esEs7(yvy4000, yvy3000, caf, cag, cah)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cae)) → new_esEs10(yvy4000, yvy3000, cae)
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbc), cbd)) → new_esEs5(yvy4001, yvy3001, cbc, cbd)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbe), cbf)) → new_esEs6(yvy4001, yvy3001, cbe, cbf)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccd)) → new_esEs19(yvy4001, yvy3001, ccd)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, cbg)) → new_esEs10(yvy4001, yvy3001, cbg)
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, ccc)) → new_esEs4(yvy4001, yvy3001, ccc)
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs7(yvy4001, yvy3001, cbh, cca, ccb)
new_gt2(yvy35, yvy30, bb) → new_esEs9(new_compare33(yvy35, yvy30, bb), GT)
new_compare33(yvy20, yvy15, dbf) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, dbf), dbf)
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(ty_[], dch)) → new_esEs19(yvy20, yvy15, dch)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcg)) → new_esEs4(yvy20, yvy15, dcg)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcd), dce), dcf)) → new_esEs7(yvy20, yvy15, dcd, dce, dcf)
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcc)) → new_esEs10(yvy20, yvy15, dcc)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbg), dbh)) → new_esEs5(yvy20, yvy15, dbg, dbh)
new_esEs30(yvy20, yvy15, app(app(ty_@2, dca), dcb)) → new_esEs6(yvy20, yvy15, dca, dcb)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_gt1(yvy400, h) → new_esEs9(new_compare32(yvy400, h), GT)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Int)
new_esEs19(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_@0)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs9(Nothing, Nothing, x0)
new_esEs18(@0, @0)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_asAs(True, x0)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Char)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs31(x0, x1, ty_Float)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpNat0(x0, Zero)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_@0)
new_gt2(x0, x1, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs31(x0, x1, ty_Ordering)
new_compare26(Nothing, Nothing, False, x0)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs19([], :(x0, x1), x2)
new_compare6(Char(x0), Char(x1))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primCmpNat1(Zero, Zero)
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs31(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_@0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Nothing, Just(x0), x1)
new_esEs12(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, True, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_compare110(x0, x1, False, x2, x3)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_compare111(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Nothing, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs22(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare33(x0, x1, x2)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primPlusNat1(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs9(Just(x0), Nothing, x1)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_gt(x0)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs9(GT, GT)
new_ltEs8(False, False)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, x2, x3)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_compare32(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_esEs19([], [], x0)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Ordering)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_gt0(x0, x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_compare26(Nothing, Just(x0), False, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_ltEs6(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs12(x0, x1)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_esEs28(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_compare18(x0, x1, x2, x3)
new_compare31(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_lt19(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(Char(x0), Char(x1))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs17(x0, x1, x2)
new_esEs31(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_compare0([], :(x0, x1), x2)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_esEs31(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare27(Double(x0, x1), Double(x2, x3))
new_compare28(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare28(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_compare26(x0, x1, True, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare12(x0, x1, False, x2, x3)
new_gt1(x0, x1)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare13(x0, x1, False, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)

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

new_gt(x0)
new_gt0(x0, x1)
new_compare31(x0, x1)
new_compare30(x0)



↳ 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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ AND
                                        ↳ QDP
                                        ↳ QDP
                                          ↳ UsableRulesProof
                                            ↳ QDP
                                              ↳ QReductionProof
                                                ↳ QDP
                                                  ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP

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

new_splitLT3(Nothing, yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitLT20(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), LT), h, ba)
new_splitLT12(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, True, bb, bc) → new_splitLT0(yvy34, yvy35, bb, bc)
new_splitLT20(yvy31, yvy32, yvy33, yvy34, yvy400, False, h, ba) → new_splitLT11(yvy31, yvy32, yvy33, yvy34, yvy400, new_gt1(yvy400, h), h, ba)
new_splitLT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitLT21(yvy300, yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Just(yvy300), new_esEs31(yvy400, yvy300, h), h), LT), h, ba)
new_splitLT21(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, False, bb, bc) → new_splitLT12(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, new_gt2(yvy35, yvy30, bb), bb, bc)
new_splitLT0(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy400, h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Just(yvy400), h, ba)
new_splitLT20(yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, yvy400, True, h, ba) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, Just(yvy400), h, ba)
new_splitLT11(yvy31, yvy32, yvy33, yvy34, yvy400, True, h, ba) → new_splitLT0(yvy34, yvy400, h, ba)
new_splitLT21(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, True, bb, bc) → new_splitLT0(yvy33, yvy35, bb, bc)

The TRS R consists of the following rules:

new_compare26(Just(yvy4900), Nothing, False, cce) → GT
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True
new_esEs31(yvy400, yvy300, ty_Ordering) → new_esEs9(yvy400, yvy300)
new_esEs31(yvy400, yvy300, ty_Float) → new_esEs17(yvy400, yvy300)
new_esEs31(yvy400, yvy300, ty_Bool) → new_esEs15(yvy400, yvy300)
new_esEs31(yvy400, yvy300, ty_Integer) → new_esEs13(yvy400, yvy300)
new_esEs31(yvy400, yvy300, app(app(app(ty_@3, hf), hg), hh)) → new_esEs7(yvy400, yvy300, hf, hg, hh)
new_esEs31(yvy400, yvy300, ty_Char) → new_esEs8(yvy400, yvy300)
new_esEs31(yvy400, yvy300, app(app(ty_Either, dab), cgg)) → new_esEs5(yvy400, yvy300, dab, cgg)
new_esEs31(yvy400, yvy300, ty_Int) → new_esEs14(yvy400, yvy300)
new_esEs31(yvy400, yvy300, app(ty_Ratio, bd)) → new_esEs10(yvy400, yvy300, bd)
new_esEs31(yvy400, yvy300, app(ty_[], dbe)) → new_esEs19(yvy400, yvy300, dbe)
new_esEs31(yvy400, yvy300, ty_Double) → new_esEs16(yvy400, yvy300)
new_esEs31(yvy400, yvy300, app(ty_Maybe, bf)) → new_esEs4(yvy400, yvy300, bf)
new_esEs31(yvy400, yvy300, ty_@0) → new_esEs18(yvy400, yvy300)
new_esEs31(yvy400, yvy300, app(app(ty_@2, bhg), bhh)) → new_esEs6(yvy400, yvy300, bhg, bhh)
new_compare26(Just(yvy4900), Just(yvy5000), False, cce) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, cce), cce)
new_compare26(yvy490, yvy500, True, cce) → EQ
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, db), dc)) → new_ltEs5(yvy4900, yvy5000, db, dc)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, bfb), bdg)) → new_ltEs10(yvy4900, yvy5000, bfb, bdg)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, gc)) → new_ltEs9(yvy4900, yvy5000, gc)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, gb)) → new_ltEs17(yvy4900, yvy5000, gb)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(ty_[], be)) → new_ltEs14(yvy4900, yvy5000, be)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, ccf), ccg), cch)) → new_ltEs13(yvy4900, yvy5000, ccf, ccg, cch)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare13(yvy175, yvy176, True, ga) → LT
new_compare13(yvy175, yvy176, False, ga) → GT
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_compare16(@0, @0) → EQ
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_not(False) → True
new_not(True) → False
new_ltEs18(EQ, GT) → True
new_ltEs18(EQ, EQ) → True
new_ltEs18(LT, LT) → True
new_ltEs18(GT, GT) → True
new_ltEs18(LT, GT) → True
new_ltEs18(GT, LT) → False
new_ltEs18(GT, EQ) → False
new_ltEs18(EQ, LT) → False
new_ltEs18(LT, EQ) → True
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), ccf, ccg, cch) → new_pePe(new_lt20(yvy49000, yvy50000, ccf), new_asAs(new_esEs26(yvy49000, yvy50000, ccf), new_pePe(new_lt19(yvy49001, yvy50001, ccg), new_asAs(new_esEs27(yvy49001, yvy50001, ccg), new_ltEs20(yvy49002, yvy50002, cch)))))
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cdf), cdg), cdh)) → new_lt14(yvy49000, yvy50000, cdf, cdg, cdh)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, ceb)) → new_lt17(yvy49000, yvy50000, ceb)
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdd), cde)) → new_lt12(yvy49000, yvy50000, cdd, cde)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cda)) → new_lt10(yvy49000, yvy50000, cda)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cdb), cdc)) → new_lt11(yvy49000, yvy50000, cdb, cdc)
new_lt20(yvy49000, yvy50000, app(ty_[], cea)) → new_lt15(yvy49000, yvy50000, cea)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, ceb)) → new_esEs10(yvy49000, yvy50000, ceb)
new_esEs26(yvy49000, yvy50000, app(ty_[], cea)) → new_esEs19(yvy49000, yvy50000, cea)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cda)) → new_esEs4(yvy49000, yvy50000, cda)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs7(yvy49000, yvy50000, cdf, cdg, cdh)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cdb), cdc)) → new_esEs5(yvy49000, yvy50000, cdb, cdc)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdd), cde)) → new_esEs6(yvy49000, yvy50000, cdd, cde)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cfd)) → new_lt17(yvy49001, yvy50001, cfd)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cec)) → new_lt10(yvy49001, yvy50001, cec)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, app(app(ty_@2, cef), ceg)) → new_lt12(yvy49001, yvy50001, cef, ceg)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, ceh), cfa), cfb)) → new_lt14(yvy49001, yvy50001, ceh, cfa, cfb)
new_lt19(yvy49001, yvy50001, app(ty_[], cfc)) → new_lt15(yvy49001, yvy50001, cfc)
new_lt19(yvy49001, yvy50001, app(app(ty_Either, ced), cee)) → new_lt11(yvy49001, yvy50001, ced, cee)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs7(yvy49001, yvy50001, ceh, cfa, cfb)
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, ced), cee)) → new_esEs5(yvy49001, yvy50001, ced, cee)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, cef), ceg)) → new_esEs6(yvy49001, yvy50001, cef, ceg)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cec)) → new_esEs4(yvy49001, yvy50001, cec)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cfd)) → new_esEs10(yvy49001, yvy50001, cfd)
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cfc)) → new_esEs19(yvy49001, yvy50001, cfc)
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfe)) → new_ltEs9(yvy49002, yvy50002, cfe)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cgf)) → new_ltEs17(yvy49002, yvy50002, cgf)
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cfh), cga)) → new_ltEs5(yvy49002, yvy50002, cfh, cga)
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(ty_[], cge)) → new_ltEs14(yvy49002, yvy50002, cge)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cff), cfg)) → new_ltEs10(yvy49002, yvy50002, cff, cfg)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cgb), cgc), cgd)) → new_ltEs13(yvy49002, yvy50002, cgb, cgc, cgd)
new_asAs(False, yvy182) → False
new_asAs(True, yvy182) → yvy182
new_pePe(False, yvy201) → yvy201
new_pePe(True, yvy201) → True
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, bec), bed), bdg) → new_ltEs5(yvy49000, yvy50000, bec, bed)
new_ltEs10(Left(yvy49000), Right(yvy50000), bfb, bdg) → True
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_[], bgc)) → new_ltEs14(yvy49000, yvy50000, bgc)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bdg) → new_ltEs12(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bdg) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bee), bef), beg), bdg) → new_ltEs13(yvy49000, yvy50000, bee, bef, beg)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(ty_@2, bff), bfg)) → new_ltEs5(yvy49000, yvy50000, bff, bfg)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bdg) → new_ltEs11(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bdg) → new_ltEs18(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(app(ty_@3, bfh), bga), bgb)) → new_ltEs13(yvy49000, yvy50000, bfh, bga, bgb)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, gd)) → new_ltEs9(yvy49000, yvy50000, gd)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bdh), bdg) → new_ltEs9(yvy49000, yvy50000, bdh)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bea), beb), bdg) → new_ltEs10(yvy49000, yvy50000, bea, beb)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_Maybe, bfc)) → new_ltEs9(yvy49000, yvy50000, bfc)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(app(ty_Either, bfd), bfe)) → new_ltEs10(yvy49000, yvy50000, bfd, bfe)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, ge), gf)) → new_ltEs10(yvy49000, yvy50000, ge, gf)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bdg) → new_ltEs16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bdg) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bdg) → new_ltEs7(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], beh), bdg) → new_ltEs14(yvy49000, yvy50000, beh)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, app(ty_Ratio, bgd)) → new_ltEs17(yvy49000, yvy50000, bgd)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Left(yvy50000), bfb, bdg) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfb, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, bfa), bdg) → new_ltEs17(yvy49000, yvy50000, bfa)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bdg) → new_ltEs8(yvy49000, yvy50000)
new_ltEs8(False, True) → True
new_ltEs8(True, True) → True
new_ltEs8(True, False) → False
new_ltEs8(False, False) → True
new_ltEs17(yvy4900, yvy5000, gb) → new_fsEs(new_compare8(yvy4900, yvy5000, gb))
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs14(yvy4900, yvy5000, be) → new_fsEs(new_compare0(yvy4900, yvy5000, be))
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), be) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, be), be)
new_compare0([], [], be) → EQ
new_compare0(:(yvy49000, yvy49001), [], be) → GT
new_compare0([], :(yvy50000, yvy50001), be) → LT
new_primCompAux0(yvy49000, yvy50000, yvy202, be) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, be))
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(ty_[], bhe)) → new_compare0(yvy49000, yvy50000, bhe)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bhb), bhc), bhd)) → new_compare14(yvy49000, yvy50000, bhb, bhc, bhd)
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bge)) → new_compare19(yvy49000, yvy50000, bge)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bgf), bgg)) → new_compare17(yvy49000, yvy50000, bgf, bgg)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, bhf)) → new_compare8(yvy49000, yvy50000, bhf)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bgh), bha)) → new_compare18(yvy49000, yvy50000, bgh, bha)
new_primCompAux00(yvy206, LT) → LT
new_primCompAux00(yvy206, EQ) → yvy206
new_primCompAux00(yvy206, GT) → GT
new_compare18(yvy49000, yvy50000, dg, dh) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, dg, dh), dg, dh)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bhg, bhh) → new_asAs(new_esEs24(yvy4000, yvy3000, bhg), new_esEs25(yvy4001, yvy3001, bhh))
new_compare25(yvy49000, yvy50000, True, dg, dh) → EQ
new_compare25(yvy49000, yvy50000, False, dg, dh) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, dg, dh), dg, dh)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), db, dc) → new_pePe(new_lt6(yvy49000, yvy50000, db), new_asAs(new_esEs20(yvy49000, yvy50000, db), new_ltEs6(yvy49001, yvy50001, dc)))
new_compare110(yvy49000, yvy50000, True, dg, dh) → LT
new_compare110(yvy49000, yvy50000, False, dg, dh) → GT
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_lt11(yvy49000, yvy50000, de, df)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_lt17(yvy49000, yvy50000, ee)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_[], ed)) → new_lt15(yvy49000, yvy50000, ed)
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_lt10(yvy49000, yvy50000, dd)
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_lt14(yvy49000, yvy50000, ea, eb, ec)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_lt12(yvy49000, yvy50000, dg, dh)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_esEs4(yvy49000, yvy50000, dd)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_esEs6(yvy49000, yvy50000, dg, dh)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_esEs7(yvy49000, yvy50000, ea, eb, ec)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_esEs5(yvy49000, yvy50000, de, df)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_esEs10(yvy49000, yvy50000, ee)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_[], ed)) → new_esEs19(yvy49000, yvy50000, ed)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, fh)) → new_ltEs17(yvy49001, yvy50001, fh)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs13(yvy49001, yvy50001, fc, fd, ff)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ef)) → new_ltEs9(yvy49001, yvy50001, ef)
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, eg), eh)) → new_ltEs10(yvy49001, yvy50001, eg, eh)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fg)) → new_ltEs14(yvy49001, yvy50001, fg)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, fa), fb)) → new_ltEs5(yvy49001, yvy50001, fa, fb)
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs9(Nothing, Just(yvy50000), gc) → True
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, gg), gh)) → new_ltEs5(yvy49000, yvy50000, gg, gh)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, he)) → new_ltEs17(yvy49000, yvy50000, he)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], hd)) → new_ltEs14(yvy49000, yvy50000, hd)
new_ltEs9(Just(yvy49000), Nothing, gc) → False
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, gc) → True
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, ha), hb), hc)) → new_ltEs13(yvy49000, yvy50000, ha, hb, hc)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs19([], [], dbe) → True
new_esEs19(:(yvy4000, yvy4001), [], dbe) → False
new_esEs19([], :(yvy3000, yvy3001), dbe) → False
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), dbe) → new_asAs(new_esEs28(yvy4000, yvy3000, dbe), new_esEs19(yvy4001, yvy3001, dbe))
new_esEs28(yvy4000, yvy3000, app(ty_[], deb)) → new_esEs19(yvy4000, yvy3000, deb)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, dde)) → new_esEs10(yvy4000, yvy3000, dde)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, dea)) → new_esEs4(yvy4000, yvy3000, dea)
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dda), ddb)) → new_esEs5(yvy4000, yvy3000, dda, ddb)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, ddf), ddg), ddh)) → new_esEs7(yvy4000, yvy3000, ddf, ddg, ddh)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddc), ddd)) → new_esEs6(yvy4000, yvy3000, ddc, ddd)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_esEs15(True, True) → True
new_esEs15(False, False) → True
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), hf, hg, hh) → new_asAs(new_esEs21(yvy4000, yvy3000, hf), new_asAs(new_esEs22(yvy4001, yvy3001, hg), new_esEs23(yvy4002, yvy3002, hh)))
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, bac), bad)) → new_esEs6(yvy4000, yvy3000, bac, bad)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs7(yvy4000, yvy3000, baf, bag, bah)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bbb)) → new_esEs19(yvy4000, yvy3000, bbb)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bae)) → new_esEs10(yvy4000, yvy3000, bae)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bba)) → new_esEs4(yvy4000, yvy3000, bba)
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, baa), bab)) → new_esEs5(yvy4000, yvy3000, baa, bab)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, app(ty_[], bcd)) → new_esEs19(yvy4001, yvy3001, bcd)
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bcc)) → new_esEs4(yvy4001, yvy3001, bcc)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bbe), bbf)) → new_esEs6(yvy4001, yvy3001, bbe, bbf)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs7(yvy4001, yvy3001, bbh, bca, bcb)
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bbg)) → new_esEs10(yvy4001, yvy3001, bbg)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bbc), bbd)) → new_esEs5(yvy4001, yvy3001, bbc, bbd)
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bce), bcf)) → new_esEs5(yvy4002, yvy3002, bce, bcf)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, bde)) → new_esEs4(yvy4002, yvy3002, bde)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs7(yvy4002, yvy3002, bdb, bdc, bdd)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_[], bdf)) → new_esEs19(yvy4002, yvy3002, bdf)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bda)) → new_esEs10(yvy4002, yvy3002, bda)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bcg), bch)) → new_esEs6(yvy4002, yvy3002, bcg, bch)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(LT, EQ) → False
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bd) → new_asAs(new_esEs11(yvy4000, yvy3000, bd), new_esEs12(yvy4001, yvy3001, bd))
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs18(@0, @0) → True
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Nothing, bf) → False
new_esEs4(Nothing, Just(yvy3000), bf) → False
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, cc)) → new_esEs10(yvy4000, yvy3000, cc)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_Maybe, dbc)) → new_esEs4(yvy4000, yvy3000, dbc)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, chh), cgg) → new_esEs4(yvy4000, yvy3000, chh)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, cg)) → new_esEs4(yvy4000, yvy3000, cg)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(ty_Either, dac), dad)) → new_esEs5(yvy4000, yvy3000, dac, dad)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, cgh), cha), cgg) → new_esEs5(yvy4000, yvy3000, cgh, cha)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, bg), bh)) → new_esEs5(yvy4000, yvy3000, bg, bh)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, ca), cb)) → new_esEs6(yvy4000, yvy3000, ca, cb)
new_esEs4(Nothing, Nothing, bf) → True
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], da)) → new_esEs19(yvy4000, yvy3000, da)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cd), ce), cf)) → new_esEs7(yvy4000, yvy3000, cd, ce, cf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], daa), cgg) → new_esEs19(yvy4000, yvy3000, daa)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, cgg) → new_esEs18(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chb), chc), cgg) → new_esEs6(yvy4000, yvy3000, chb, chc)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(ty_@2, dae), daf)) → new_esEs6(yvy4000, yvy3000, dae, daf)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, cgg) → new_esEs9(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, cgg) → new_esEs16(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, che), chf), chg), cgg) → new_esEs7(yvy4000, yvy3000, che, chf, chg)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_[], dbd)) → new_esEs19(yvy4000, yvy3000, dbd)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(ty_Ratio, dag)) → new_esEs10(yvy4000, yvy3000, dag)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, cgg) → new_esEs14(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, cgg) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, cgg) → new_esEs8(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, cgg) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Right(yvy3000), dab, cgg) → False
new_esEs5(Right(yvy4000), Left(yvy3000), dab, cgg) → False
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, cgg) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs7(yvy4000, yvy3000, dah, dba, dbb)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), dab, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, chd), cgg) → new_esEs10(yvy4000, yvy3000, chd)
new_lt12(yvy49000, yvy50000, dg, dh) → new_esEs9(new_compare18(yvy49000, yvy50000, dg, dh), LT)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_lt14(yvy49000, yvy50000, ea, eb, ec) → new_esEs9(new_compare14(yvy49000, yvy50000, ea, eb, ec), LT)
new_compare14(yvy49000, yvy50000, ea, eb, ec) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_compare24(yvy49000, yvy50000, False, ea, eb, ec) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_compare24(yvy49000, yvy50000, True, ea, eb, ec) → EQ
new_compare111(yvy49000, yvy50000, True, ea, eb, ec) → LT
new_compare111(yvy49000, yvy50000, False, ea, eb, ec) → GT
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_compare211(yvy49000, yvy50000, True) → EQ
new_compare112(yvy49000, yvy50000, True) → LT
new_compare112(yvy49000, yvy50000, False) → GT
new_lt10(yvy49000, yvy50000, dd) → new_esEs9(new_compare19(yvy49000, yvy50000, dd), LT)
new_compare19(yvy49000, yvy50000, dd) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, dd), dd)
new_compare26(Nothing, Just(yvy5000), False, cce) → LT
new_compare26(Nothing, Nothing, False, cce) → LT
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_lt15(yvy49000, yvy50000, ed) → new_esEs9(new_compare0(yvy49000, yvy50000, ed), LT)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_lt17(yvy49000, yvy50000, ee) → new_esEs9(new_compare8(yvy49000, yvy50000, ee), LT)
new_lt11(yvy49000, yvy50000, de, df) → new_esEs9(new_compare17(yvy49000, yvy50000, de, df), LT)
new_compare17(yvy49000, yvy50000, de, df) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, de, df), de, df)
new_compare23(yvy49000, yvy50000, False, de, df) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, de, df), de, df)
new_compare23(yvy49000, yvy50000, True, de, df) → EQ
new_compare12(yvy49000, yvy50000, False, de, df) → GT
new_compare12(yvy49000, yvy50000, True, de, df) → LT
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_compare210(yvy49000, yvy50000, True) → EQ
new_compare11(yvy49000, yvy50000, False) → GT
new_compare11(yvy49000, yvy50000, True) → LT
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, caa), cab)) → new_esEs5(yvy4000, yvy3000, caa, cab)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cba)) → new_esEs4(yvy4000, yvy3000, cba)
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbb)) → new_esEs19(yvy4000, yvy3000, cbb)
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, cac), cad)) → new_esEs6(yvy4000, yvy3000, cac, cad)
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, caf), cag), cah)) → new_esEs7(yvy4000, yvy3000, caf, cag, cah)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cae)) → new_esEs10(yvy4000, yvy3000, cae)
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbc), cbd)) → new_esEs5(yvy4001, yvy3001, cbc, cbd)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbe), cbf)) → new_esEs6(yvy4001, yvy3001, cbe, cbf)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccd)) → new_esEs19(yvy4001, yvy3001, ccd)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, cbg)) → new_esEs10(yvy4001, yvy3001, cbg)
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, ccc)) → new_esEs4(yvy4001, yvy3001, ccc)
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs7(yvy4001, yvy3001, cbh, cca, ccb)
new_gt2(yvy35, yvy30, bb) → new_esEs9(new_compare33(yvy35, yvy30, bb), GT)
new_compare33(yvy20, yvy15, dbf) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, dbf), dbf)
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(ty_[], dch)) → new_esEs19(yvy20, yvy15, dch)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcg)) → new_esEs4(yvy20, yvy15, dcg)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcd), dce), dcf)) → new_esEs7(yvy20, yvy15, dcd, dce, dcf)
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcc)) → new_esEs10(yvy20, yvy15, dcc)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbg), dbh)) → new_esEs5(yvy20, yvy15, dbg, dbh)
new_esEs30(yvy20, yvy15, app(app(ty_@2, dca), dcb)) → new_esEs6(yvy20, yvy15, dca, dcb)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_gt1(yvy400, h) → new_esEs9(new_compare32(yvy400, h), GT)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Int)
new_esEs19(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_@0)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs9(Nothing, Nothing, x0)
new_esEs18(@0, @0)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_asAs(True, x0)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Char)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs31(x0, x1, ty_Float)
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCmpNat0(x0, Zero)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_@0)
new_gt2(x0, x1, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs31(x0, x1, ty_Ordering)
new_compare26(Nothing, Nothing, False, x0)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs19([], :(x0, x1), x2)
new_compare6(Char(x0), Char(x1))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primCmpNat1(Zero, Zero)
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs30(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs31(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_lt20(x0, x1, ty_Double)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs27(x0, x1, ty_@0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Nothing, Just(x0), x1)
new_esEs12(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare110(x0, x1, True, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_compare110(x0, x1, False, x2, x3)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_compare111(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs25(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Nothing, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs22(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare33(x0, x1, x2)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primPlusNat1(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_ltEs9(Just(x0), Nothing, x1)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs9(GT, GT)
new_ltEs8(False, False)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt11(x0, x1, x2, x3)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_compare32(x0, x1)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_esEs19([], [], x0)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Ordering)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(Just(x0), Just(x1), ty_Double)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_compare26(Nothing, Just(x0), False, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_ltEs6(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs12(x0, x1)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_esEs28(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_compare18(x0, x1, x2, x3)
new_primMulNat0(Zero, Succ(x0))
new_ltEs18(EQ, EQ)
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_lt19(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(Char(x0), Char(x1))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs17(x0, x1, x2)
new_esEs31(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_compare0([], :(x0, x1), x2)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(GT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_esEs31(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare27(Double(x0, x1), Double(x2, x3))
new_compare28(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare28(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_compare26(x0, x1, True, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare12(x0, x1, False, x2, x3)
new_gt1(x0, x1)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare13(x0, x1, False, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)

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

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



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

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

new_splitGT21(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, False, bb, bc) → new_splitGT12(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, new_esEs9(new_compare33(yvy20, yvy15, bb), LT), bb, bc)
new_splitGT3(Nothing, yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitGT20(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), GT), h, ba)
new_splitGT2(yvy300, yvy31, yvy32, yvy33, Branch(yvy340, yvy341, yvy342, yvy343, yvy344), True, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Nothing, h, ba)
new_splitGT11(yvy31, yvy32, yvy33, yvy34, yvy400, True, h, ba) → new_splitGT0(yvy33, yvy400, h, ba)
new_splitGT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitGT21(yvy300, yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Just(yvy300), new_esEs32(yvy400, yvy300, h), h), GT), h, ba)
new_splitGT2(yvy300, yvy31, yvy32, yvy33, yvy34, False, h, ba) → new_splitGT10(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare31(yvy300, h), LT), h, ba)
new_splitGT0(Branch(yvy340, yvy341, yvy342, yvy343, yvy344), yvy400, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Just(yvy400), h, ba)
new_splitGT(Branch(yvy340, yvy341, yvy342, yvy343, yvy344), h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Nothing, h, ba)
new_splitGT1(yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitGT(yvy33, h, ba)
new_splitGT20(yvy31, yvy32, yvy33, Branch(yvy340, yvy341, yvy342, yvy343, yvy344), yvy400, True, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Just(yvy400), h, ba)
new_splitGT10(yvy300, yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitGT(yvy33, h, ba)
new_splitGT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitGT2(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare26(Nothing, Just(yvy300), False, h), GT), h, ba)
new_splitGT12(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, True, bb, bc) → new_splitGT0(yvy18, yvy20, bb, bc)
new_splitGT21(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, True, bb, bc) → new_splitGT0(yvy19, yvy20, bb, bc)
new_splitGT20(yvy31, yvy32, yvy33, yvy34, yvy400, False, h, ba) → new_splitGT11(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare32(yvy400, h), LT), h, ba)
new_splitGT3(Nothing, yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitGT1(yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare30(h), LT), h, ba)

The TRS R consists of the following rules:

new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, cg)) → new_esEs4(yvy4000, yvy3000, cg)
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, db), dc)) → new_ltEs5(yvy4900, yvy5000, db, dc)
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs32(yvy400, yvy300, ty_Float) → new_esEs17(yvy400, yvy300)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, cad), cae)) → new_esEs5(yvy4000, yvy3000, cad, cae)
new_esEs28(yvy4000, yvy3000, app(ty_[], dea)) → new_esEs19(yvy4000, yvy3000, dea)
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, bah), bba)) → new_esEs6(yvy4000, yvy3000, bah, bba)
new_primCmpNat2(Zero, yvy4900) → LT
new_ltEs8(False, True) → True
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, beh), bfa), bed) → new_ltEs5(yvy49000, yvy50000, beh, bfa)
new_esEs22(yvy4001, yvy3001, app(ty_[], bda)) → new_esEs19(yvy4001, yvy3001, bda)
new_ltEs18(EQ, GT) → True
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_ltEs10(Left(yvy49000), Right(yvy50000), bfg, bed) → True
new_compare110(yvy49000, yvy50000, True, dg, dh) → LT
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bdb), bdc)) → new_esEs5(yvy4002, yvy3002, bdb, bdc)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_compare24(yvy49000, yvy50000, False, ea, eb, ec) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cbd)) → new_esEs4(yvy4000, yvy3000, cbd)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, fh)) → new_ltEs17(yvy49001, yvy50001, fh)
new_esEs4(Just(yvy4000), Nothing, bf) → False
new_esEs4(Nothing, Just(yvy3000), bf) → False
new_ltEs9(Nothing, Just(yvy50000), hc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], dac), gc) → new_esEs19(yvy4000, yvy3000, dac)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_primMulNat0(Zero, Zero) → Zero
new_compare26(Just(yvy4900), Nothing, False, cch) → GT
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, cee)) → new_esEs10(yvy49000, yvy50000, cee)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, ddd)) → new_esEs10(yvy4000, yvy3000, ddd)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_esEs4(yvy49000, yvy50000, dd)
new_compare33(yvy20, yvy15, bb) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, bb), bb)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, gc) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_[], ced)) → new_esEs19(yvy49000, yvy50000, ced)
new_compare16(@0, @0) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, beb)) → new_esEs4(yvy4002, yvy3002, beb)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_compare26(Nothing, Just(yvy5000), False, cch) → LT
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), be) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, be), be)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_[], bgh)) → new_ltEs14(yvy49000, yvy50000, bgh)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs7(yvy4000, yvy3000, bbc, bbd, bbe)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bed) → new_ltEs12(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cdd)) → new_esEs4(yvy49000, yvy50000, cdd)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_esEs6(yvy49000, yvy50000, dg, dh)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_compare18(yvy49000, yvy50000, dg, dh) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, dg, dh), dg, dh)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_esEs32(yvy400, yvy300, app(app(ty_@2, gd), ge)) → new_esEs6(yvy400, yvy300, gd, ge)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_pePe(False, yvy201) → yvy201
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_compare23(yvy49000, yvy50000, False, de, df) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, de, df), de, df)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_compare26(Nothing, Nothing, False, cch) → LT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bed) → new_ltEs4(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cfg)) → new_lt17(yvy49001, yvy50001, cfg)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bfb), bfc), bfd), bed) → new_ltEs13(yvy49000, yvy50000, bfb, bfc, bfd)
new_esEs32(yvy400, yvy300, ty_Ordering) → new_esEs9(yvy400, yvy300)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bef), beg), bed) → new_ltEs10(yvy49000, yvy50000, bef, beg)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs13(yvy49001, yvy50001, fc, fd, ff)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cef)) → new_lt10(yvy49001, yvy50001, cef)
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chd), che), gc) → new_esEs6(yvy4000, yvy3000, chd, che)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbe)) → new_esEs19(yvy4000, yvy3000, cbe)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, dab), gc) → new_esEs4(yvy4000, yvy3000, dab)
new_esEs32(yvy400, yvy300, app(ty_Maybe, bf)) → new_esEs4(yvy400, yvy300, bf)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, hg), hh)) → new_ltEs5(yvy49000, yvy50000, hg, hh)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(ty_@2, bgc), bgd)) → new_ltEs5(yvy49000, yvy50000, bgc, bgd)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs7(yvy4002, yvy3002, bdg, bdh, bea)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs7(yvy49001, yvy50001, cfc, cfd, cfe)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cea), ceb), cec)) → new_lt14(yvy49000, yvy50000, cea, ceb, cec)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbf), cbg)) → new_esEs5(yvy4001, yvy3001, cbf, cbg)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbh), cca)) → new_esEs6(yvy4001, yvy3001, cbh, cca)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ef)) → new_ltEs9(yvy49001, yvy50001, ef)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, bae)) → new_ltEs17(yvy49000, yvy50000, bae)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, bfg), bed)) → new_ltEs10(yvy4900, yvy5000, bfg, bed)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), db, dc) → new_pePe(new_lt6(yvy49000, yvy50000, db), new_asAs(new_esEs20(yvy49000, yvy50000, db), new_ltEs6(yvy49001, yvy50001, dc)))
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfh)) → new_ltEs9(yvy49002, yvy50002, cfh)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, caf), cag)) → new_esEs6(yvy4000, yvy3000, caf, cag)
new_compare0([], [], be) → EQ
new_pePe(True, yvy201) → True
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_primEqNat0(Zero, Zero) → True
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bed) → new_ltEs11(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(ty_@2, daf), dag)) → new_esEs6(yvy4000, yvy3000, daf, dag)
new_ltEs14(yvy4900, yvy5000, be) → new_fsEs(new_compare0(yvy4900, yvy5000, be))
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, eg), eh)) → new_ltEs10(yvy49001, yvy50001, eg, eh)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_ltEs18(EQ, EQ) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, gc) → new_esEs9(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_esEs19([], [], ha) → True
new_compare110(yvy49000, yvy50000, False, dg, dh) → GT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, cc)) → new_esEs10(yvy4000, yvy3000, cc)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccg)) → new_esEs19(yvy4001, yvy3001, ccg)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_compare12(yvy49000, yvy50000, False, de, df) → GT
new_primCmpNat1(Zero, Zero) → EQ
new_primCompAux0(yvy49000, yvy50000, yvy202, be) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, be))
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs18(LT, LT) → True
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, gc) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_esEs7(yvy49000, yvy50000, ea, eb, ec)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_lt11(yvy49000, yvy50000, de, df)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, hc)) → new_ltEs9(yvy4900, yvy5000, hc)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs19(:(yvy4000, yvy4001), [], ha) → False
new_esEs19([], :(yvy3000, yvy3001), ha) → False
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_ltEs18(GT, GT) → True
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(EQ, EQ) → True
new_esEs32(yvy400, yvy300, ty_Int) → new_esEs14(yvy400, yvy300)
new_compare24(yvy49000, yvy50000, True, ea, eb, ec) → EQ
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bed) → new_ltEs18(yvy49000, yvy50000)
new_esEs15(True, True) → True
new_esEs30(yvy20, yvy15, app(ty_[], dcg)) → new_esEs19(yvy20, yvy15, dcg)
new_ltEs18(LT, GT) → True
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcf)) → new_esEs4(yvy20, yvy15, dcf)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, hb)) → new_ltEs17(yvy4900, yvy5000, hb)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, ccb)) → new_esEs10(yvy4001, yvy3001, ccb)
new_ltEs8(True, True) → True
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cea), ceb), cec)) → new_esEs7(yvy49000, yvy50000, cea, ceb, cec)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, ddh)) → new_esEs4(yvy4000, yvy3000, ddh)
new_ltEs18(GT, LT) → False
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, chg), chh), daa), gc) → new_esEs7(yvy4000, yvy3000, chg, chh, daa)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_lt14(yvy49000, yvy50000, ea, eb, ec) → new_esEs9(new_compare14(yvy49000, yvy50000, ea, eb, ec), LT)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, ceg), ceh)) → new_esEs5(yvy49001, yvy50001, ceg, ceh)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cha)) → new_ltEs17(yvy49002, yvy50002, cha)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs7(yvy20, yvy15, dcc, dcd, dce)
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, he), hf)) → new_ltEs10(yvy49000, yvy50000, he, hf)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], bad)) → new_ltEs14(yvy49000, yvy50000, bad)
new_esEs32(yvy400, yvy300, app(ty_Ratio, bd)) → new_esEs10(yvy400, yvy300, bd)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bbg)) → new_esEs19(yvy4000, yvy3000, bbg)
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cgc), cgd)) → new_ltEs5(yvy49002, yvy50002, cgc, cgd)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_[], dbe)) → new_esEs19(yvy4000, yvy3000, dbe)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bch)) → new_esEs4(yvy4001, yvy3001, bch)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, ccf)) → new_esEs4(yvy4001, yvy3001, ccf)
new_compare112(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), gd, ge) → new_asAs(new_esEs24(yvy4000, yvy3000, gd), new_esEs25(yvy4001, yvy3001, ge))
new_lt19(yvy49001, yvy50001, app(app(ty_@2, cfa), cfb)) → new_lt12(yvy49001, yvy50001, cfa, cfb)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare12(yvy49000, yvy50000, True, de, df) → LT
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(ty_Either, dad), dae)) → new_esEs5(yvy4000, yvy3000, dad, dae)
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(app(ty_@3, bge), bgf), bgg)) → new_ltEs13(yvy49000, yvy50000, bge, bgf, bgg)
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_ltEs19(yvy4900, yvy5000, app(ty_[], be)) → new_ltEs14(yvy4900, yvy5000, be)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_Ratio, dah)) → new_esEs10(yvy4000, yvy3000, dah)
new_compare111(yvy49000, yvy50000, True, ea, eb, ec) → LT
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_primCompAux00(yvy206, LT) → LT
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(ty_Either, bga), bgb)) → new_ltEs10(yvy49000, yvy50000, bga, bgb)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, gc) → new_esEs14(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, cee)) → new_lt17(yvy49000, yvy50000, cee)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare13(yvy175, yvy176, True, ga) → LT
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs23(yvy4002, yvy3002, app(ty_[], bec)) → new_esEs19(yvy4002, yvy3002, bec)
new_esEs32(yvy400, yvy300, ty_@0) → new_esEs18(yvy400, yvy300)
new_lt15(yvy49000, yvy50000, ed) → new_esEs9(new_compare0(yvy49000, yvy50000, ed), LT)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_lt17(yvy49000, yvy50000, ee)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, hd)) → new_ltEs9(yvy49000, yvy50000, hd)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_compare14(yvy49000, yvy50000, ea, eb, ec) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, bg), bh)) → new_esEs5(yvy4000, yvy3000, bg, bh)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_esEs5(yvy49000, yvy50000, de, df)
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_ltEs20(yvy49002, yvy50002, app(ty_[], cgh)) → new_ltEs14(yvy49002, yvy50002, cgh)
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dch), dda)) → new_esEs5(yvy4000, yvy3000, dch, dda)
new_esEs32(yvy400, yvy300, app(app(ty_Either, gb), gc)) → new_esEs5(yvy400, yvy300, gb, gc)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, ca), cb)) → new_esEs6(yvy4000, yvy3000, ca, cb)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs32(yvy400, yvy300, ty_Integer) → new_esEs13(yvy400, yvy300)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bcb), bcc)) → new_esEs6(yvy4001, yvy3001, bcb, bcc)
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_compare28(yvy49000, yvy50000, app(ty_[], cab)) → new_compare0(yvy49000, yvy50000, cab)
new_ltEs9(Just(yvy49000), Nothing, hc) → False
new_primCompAux00(yvy206, EQ) → yvy206
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, gc) → new_esEs15(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bdf)) → new_esEs10(yvy4002, yvy3002, bdf)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, gc) → new_esEs8(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_compare26(Just(yvy4900), Just(yvy5000), False, cch) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, cch), cch)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bhg), bhh), caa)) → new_compare14(yvy49000, yvy50000, bhg, bhh, caa)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, cda), cdb), cdc)) → new_ltEs13(yvy4900, yvy5000, cda, cdb, cdc)
new_compare26(yvy490, yvy500, True, cch) → EQ
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs18(GT, EQ) → False
new_compare17(yvy49000, yvy50000, de, df) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, de, df), de, df)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcb)) → new_esEs10(yvy20, yvy15, dcb)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bed) → new_ltEs16(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_esEs10(yvy49000, yvy50000, ee)
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bdd), bde)) → new_esEs6(yvy4002, yvy3002, bdd, bde)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, hc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, gc) → new_esEs17(yvy4000, yvy3000)
new_esEs9(GT, GT) → True
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bhb)) → new_compare19(yvy49000, yvy50000, bhb)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bed) → new_ltEs15(yvy49000, yvy50000)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs18(EQ, LT) → False
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_compare0(:(yvy49000, yvy49001), [], be) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_ltEs18(LT, EQ) → True
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cde), cdf)) → new_esEs5(yvy49000, yvy50000, cde, cdf)
new_lt6(yvy49000, yvy50000, app(ty_[], ed)) → new_lt15(yvy49000, yvy50000, ed)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fg)) → new_ltEs14(yvy49001, yvy50001, fg)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs7(yvy4001, yvy3001, bce, bcf, bcg)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_lt10(yvy49000, yvy50000, dd)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, cfc), cfd), cfe)) → new_lt14(yvy49001, yvy50001, cfc, cfd, cfe)
new_lt19(yvy49001, yvy50001, app(ty_[], cff)) → new_lt15(yvy49001, yvy50001, cff)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs7(yvy4000, yvy3000, dde, ddf, ddg)
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gf, gg, gh) → new_asAs(new_esEs21(yvy4000, yvy3000, gf), new_asAs(new_esEs22(yvy4001, yvy3001, gg), new_esEs23(yvy4002, yvy3002, gh)))
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs5(Left(yvy4000), Right(yvy3000), gb, gc) → False
new_esEs5(Right(yvy4000), Left(yvy3000), gb, gc) → False
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, cfa), cfb)) → new_esEs6(yvy49001, yvy50001, cfa, cfb)
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bbb)) → new_esEs10(yvy4000, yvy3000, bbb)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_ltEs8(False, False) → True
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_compare19(yvy49000, yvy50000, dd) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, dd), dd)
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdg), cdh)) → new_lt12(yvy49000, yvy50000, cdg, cdh)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, baa), bab), bac)) → new_ltEs13(yvy49000, yvy50000, baa, bab, bac)
new_compare25(yvy49000, yvy50000, True, dg, dh) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_lt19(yvy49001, yvy50001, app(app(ty_Either, ceg), ceh)) → new_lt11(yvy49001, yvy50001, ceg, ceh)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cdd)) → new_lt10(yvy49000, yvy50000, cdd)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, bf) → True
new_compare111(yvy49000, yvy50000, False, ea, eb, ec) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_compare210(yvy49000, yvy50000, True) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bed) → new_ltEs7(yvy49000, yvy50000)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cef)) → new_esEs4(yvy49001, yvy50001, cef)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cga), cgb)) → new_ltEs10(yvy49002, yvy50002, cga, cgb)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bhc), bhd)) → new_compare17(yvy49000, yvy50000, bhc, bhd)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cde), cdf)) → new_lt11(yvy49000, yvy50000, cde, cdf)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cfg)) → new_esEs10(yvy49001, yvy50001, cfg)
new_compare13(yvy175, yvy176, False, ga) → GT
new_compare23(yvy49000, yvy50000, True, de, df) → EQ
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], bfe), bed) → new_ltEs14(yvy49000, yvy50000, bfe)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, gc) → new_esEs13(yvy4000, yvy3000)
new_lt17(yvy49000, yvy50000, ee) → new_esEs9(new_compare8(yvy49000, yvy50000, ee), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(app(ty_@3, dba), dbb), dbc)) → new_esEs7(yvy4000, yvy3000, dba, dbb, dbc)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cge), cgf), cgg)) → new_ltEs13(yvy49002, yvy50002, cge, cgf, cgg)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddb), ddc)) → new_esEs6(yvy4000, yvy3000, ddb, ddc)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bbf)) → new_esEs4(yvy4000, yvy3000, bbf)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, fa), fb)) → new_ltEs5(yvy49001, yvy50001, fa, fb)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bee), bed) → new_ltEs9(yvy49000, yvy50000, bee)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_lt14(yvy49000, yvy50000, ea, eb, ec)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs7(yvy4000, yvy3000, cba, cbb, cbc)
new_lt20(yvy49000, yvy50000, app(ty_[], ced)) → new_lt15(yvy49000, yvy50000, ced)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt12(yvy49000, yvy50000, dg, dh) → new_esEs9(new_compare18(yvy49000, yvy50000, dg, dh), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bd) → new_asAs(new_esEs11(yvy4000, yvy3000, bd), new_esEs12(yvy4001, yvy3001, bd))
new_asAs(False, yvy182) → False
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, baf), bag)) → new_esEs5(yvy4000, yvy3000, baf, bag)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs32(yvy400, yvy300, app(app(app(ty_@3, gf), gg), gh)) → new_esEs7(yvy400, yvy300, gf, gg, gh)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_esEs32(yvy400, yvy300, ty_Bool) → new_esEs15(yvy400, yvy300)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_lt10(yvy49000, yvy50000, dd) → new_esEs9(new_compare19(yvy49000, yvy50000, dd), LT)
new_compare25(yvy49000, yvy50000, False, dg, dh) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, dg, dh), dg, dh)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, cac)) → new_compare8(yvy49000, yvy50000, cac)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), cda, cdb, cdc) → new_pePe(new_lt20(yvy49000, yvy50000, cda), new_asAs(new_esEs26(yvy49000, yvy50000, cda), new_pePe(new_lt19(yvy49001, yvy50001, cdb), new_asAs(new_esEs27(yvy49001, yvy50001, cdb), new_ltEs20(yvy49002, yvy50002, cdc)))))
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cah)) → new_esEs10(yvy4000, yvy3000, cah)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbf), dbg)) → new_esEs5(yvy20, yvy15, dbf, dbg)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_esEs32(yvy400, yvy300, app(ty_[], ha)) → new_esEs19(yvy400, yvy300, ha)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_Ratio, bha)) → new_ltEs17(yvy49000, yvy50000, bha)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bcd)) → new_esEs10(yvy4001, yvy3001, bcd)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs7(yvy4001, yvy3001, ccc, ccd, cce)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_Maybe, dbd)) → new_esEs4(yvy4000, yvy3000, dbd)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare11(yvy49000, yvy50000, False) → GT
new_esEs30(yvy20, yvy15, app(app(ty_@2, dbh), dca)) → new_esEs6(yvy20, yvy15, dbh, dca)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Left(yvy50000), bfg, bed) → False
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_compare11(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], da)) → new_esEs19(yvy4000, yvy3000, da)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, chb), chc), gc) → new_esEs5(yvy4000, yvy3000, chb, chc)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_Maybe, bfh)) → new_ltEs9(yvy49000, yvy50000, bfh)
new_compare112(yvy49000, yvy50000, False) → GT
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(ty_[], ed)) → new_esEs19(yvy49000, yvy50000, ed)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cff)) → new_esEs19(yvy49001, yvy50001, cff)
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy50000, yvy50001), be) → LT
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_asAs(True, yvy182) → yvy182
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_esEs32(yvy400, yvy300, ty_Double) → new_esEs16(yvy400, yvy300)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_esEs18(@0, @0) → True
new_compare211(yvy49000, yvy50000, True) → EQ
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdg), cdh)) → new_esEs6(yvy49000, yvy50000, cdg, cdh)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs32(yvy400, yvy300, ty_Char) → new_esEs8(yvy400, yvy300)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cd), ce), cf)) → new_esEs7(yvy4000, yvy3000, cd, ce, cf)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, chf), gc) → new_esEs10(yvy4000, yvy3000, chf)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, bff), bed) → new_ltEs17(yvy49000, yvy50000, bff)
new_lt11(yvy49000, yvy50000, de, df) → new_esEs9(new_compare17(yvy49000, yvy50000, de, df), LT)
new_esEs9(LT, LT) → True
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), ha) → new_asAs(new_esEs28(yvy4000, yvy3000, ha), new_esEs19(yvy4001, yvy3001, ha))
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bbh), bca)) → new_esEs5(yvy4001, yvy3001, bbh, bca)
new_primCompAux00(yvy206, GT) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bed) → new_ltEs8(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_lt12(yvy49000, yvy50000, dg, dh)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bhe), bhf)) → new_compare18(yvy49000, yvy50000, bhe, bhf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_ltEs17(yvy4900, yvy5000, hb) → new_fsEs(new_compare8(yvy4900, yvy5000, hb))
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_esEs32(x0, x1, ty_Bool)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_compare210(x0, x1, False)
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare9(x0, x1)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(x0, Zero)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_lt19(x0, x1, ty_Int)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs15(x0, x1)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_compare28(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, ty_Char)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs32(x0, x1, ty_@0)
new_esEs19([], :(x0, x1), x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs32(x0, x1, ty_Int)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare12(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Char)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Nothing, Just(x0), x1)
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Nothing, Just(x0), False, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt6(x0, x1, ty_Integer)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt10(x0, x1, x2)
new_compare26(x0, x1, True, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Succ(x0))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs9(GT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(False, False)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_lt11(x0, x1, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_compare32(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(x0, x1, x2)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs19(:(x0, x1), [], x2)
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs6(x0, x1, ty_Int)
new_esEs19([], [], x0)
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs12(x0, x1)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, True)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs32(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare31(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs18(EQ, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Char(x0), Char(x1))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_ltEs18(GT, GT)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_ltEs9(Nothing, Nothing, x0)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare28(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_compare12(x0, x1, False, x2, x3)
new_compare26(Nothing, Nothing, False, x0)
new_compare13(x0, x1, False, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)

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

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

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

new_splitGT2(yvy300, yvy31, yvy32, yvy33, Branch(yvy340, yvy341, yvy342, yvy343, yvy344), True, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Nothing, h, ba)
new_splitGT10(yvy300, yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitGT(yvy33, h, ba)
new_splitGT2(yvy300, yvy31, yvy32, yvy33, yvy34, False, h, ba) → new_splitGT10(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare31(yvy300, h), LT), h, ba)
new_splitGT(Branch(yvy340, yvy341, yvy342, yvy343, yvy344), h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Nothing, h, ba)
new_splitGT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitGT2(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare26(Nothing, Just(yvy300), False, h), GT), h, ba)
new_splitGT1(yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitGT(yvy33, h, ba)
new_splitGT3(Nothing, yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitGT1(yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare30(h), LT), h, ba)

The TRS R consists of the following rules:

new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, cg)) → new_esEs4(yvy4000, yvy3000, cg)
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, db), dc)) → new_ltEs5(yvy4900, yvy5000, db, dc)
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs32(yvy400, yvy300, ty_Float) → new_esEs17(yvy400, yvy300)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, cad), cae)) → new_esEs5(yvy4000, yvy3000, cad, cae)
new_esEs28(yvy4000, yvy3000, app(ty_[], dea)) → new_esEs19(yvy4000, yvy3000, dea)
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, bah), bba)) → new_esEs6(yvy4000, yvy3000, bah, bba)
new_primCmpNat2(Zero, yvy4900) → LT
new_ltEs8(False, True) → True
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, beh), bfa), bed) → new_ltEs5(yvy49000, yvy50000, beh, bfa)
new_esEs22(yvy4001, yvy3001, app(ty_[], bda)) → new_esEs19(yvy4001, yvy3001, bda)
new_ltEs18(EQ, GT) → True
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_ltEs10(Left(yvy49000), Right(yvy50000), bfg, bed) → True
new_compare110(yvy49000, yvy50000, True, dg, dh) → LT
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bdb), bdc)) → new_esEs5(yvy4002, yvy3002, bdb, bdc)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_compare24(yvy49000, yvy50000, False, ea, eb, ec) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cbd)) → new_esEs4(yvy4000, yvy3000, cbd)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, fh)) → new_ltEs17(yvy49001, yvy50001, fh)
new_esEs4(Just(yvy4000), Nothing, bf) → False
new_esEs4(Nothing, Just(yvy3000), bf) → False
new_ltEs9(Nothing, Just(yvy50000), hc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], dac), gc) → new_esEs19(yvy4000, yvy3000, dac)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_primMulNat0(Zero, Zero) → Zero
new_compare26(Just(yvy4900), Nothing, False, cch) → GT
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, cee)) → new_esEs10(yvy49000, yvy50000, cee)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, ddd)) → new_esEs10(yvy4000, yvy3000, ddd)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_esEs4(yvy49000, yvy50000, dd)
new_compare33(yvy20, yvy15, bb) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, bb), bb)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, gc) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_[], ced)) → new_esEs19(yvy49000, yvy50000, ced)
new_compare16(@0, @0) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, beb)) → new_esEs4(yvy4002, yvy3002, beb)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_compare26(Nothing, Just(yvy5000), False, cch) → LT
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), be) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, be), be)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_[], bgh)) → new_ltEs14(yvy49000, yvy50000, bgh)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs7(yvy4000, yvy3000, bbc, bbd, bbe)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bed) → new_ltEs12(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cdd)) → new_esEs4(yvy49000, yvy50000, cdd)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_esEs6(yvy49000, yvy50000, dg, dh)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_compare18(yvy49000, yvy50000, dg, dh) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, dg, dh), dg, dh)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_esEs32(yvy400, yvy300, app(app(ty_@2, gd), ge)) → new_esEs6(yvy400, yvy300, gd, ge)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_pePe(False, yvy201) → yvy201
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_compare23(yvy49000, yvy50000, False, de, df) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, de, df), de, df)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_compare26(Nothing, Nothing, False, cch) → LT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bed) → new_ltEs4(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cfg)) → new_lt17(yvy49001, yvy50001, cfg)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bfb), bfc), bfd), bed) → new_ltEs13(yvy49000, yvy50000, bfb, bfc, bfd)
new_esEs32(yvy400, yvy300, ty_Ordering) → new_esEs9(yvy400, yvy300)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bef), beg), bed) → new_ltEs10(yvy49000, yvy50000, bef, beg)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs13(yvy49001, yvy50001, fc, fd, ff)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cef)) → new_lt10(yvy49001, yvy50001, cef)
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chd), che), gc) → new_esEs6(yvy4000, yvy3000, chd, che)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbe)) → new_esEs19(yvy4000, yvy3000, cbe)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, dab), gc) → new_esEs4(yvy4000, yvy3000, dab)
new_esEs32(yvy400, yvy300, app(ty_Maybe, bf)) → new_esEs4(yvy400, yvy300, bf)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, hg), hh)) → new_ltEs5(yvy49000, yvy50000, hg, hh)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(ty_@2, bgc), bgd)) → new_ltEs5(yvy49000, yvy50000, bgc, bgd)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs7(yvy4002, yvy3002, bdg, bdh, bea)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs7(yvy49001, yvy50001, cfc, cfd, cfe)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cea), ceb), cec)) → new_lt14(yvy49000, yvy50000, cea, ceb, cec)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbf), cbg)) → new_esEs5(yvy4001, yvy3001, cbf, cbg)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbh), cca)) → new_esEs6(yvy4001, yvy3001, cbh, cca)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ef)) → new_ltEs9(yvy49001, yvy50001, ef)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, bae)) → new_ltEs17(yvy49000, yvy50000, bae)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, bfg), bed)) → new_ltEs10(yvy4900, yvy5000, bfg, bed)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), db, dc) → new_pePe(new_lt6(yvy49000, yvy50000, db), new_asAs(new_esEs20(yvy49000, yvy50000, db), new_ltEs6(yvy49001, yvy50001, dc)))
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfh)) → new_ltEs9(yvy49002, yvy50002, cfh)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, caf), cag)) → new_esEs6(yvy4000, yvy3000, caf, cag)
new_compare0([], [], be) → EQ
new_pePe(True, yvy201) → True
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_primEqNat0(Zero, Zero) → True
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bed) → new_ltEs11(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(ty_@2, daf), dag)) → new_esEs6(yvy4000, yvy3000, daf, dag)
new_ltEs14(yvy4900, yvy5000, be) → new_fsEs(new_compare0(yvy4900, yvy5000, be))
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, eg), eh)) → new_ltEs10(yvy49001, yvy50001, eg, eh)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_ltEs18(EQ, EQ) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, gc) → new_esEs9(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_esEs19([], [], ha) → True
new_compare110(yvy49000, yvy50000, False, dg, dh) → GT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, cc)) → new_esEs10(yvy4000, yvy3000, cc)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccg)) → new_esEs19(yvy4001, yvy3001, ccg)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_compare12(yvy49000, yvy50000, False, de, df) → GT
new_primCmpNat1(Zero, Zero) → EQ
new_primCompAux0(yvy49000, yvy50000, yvy202, be) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, be))
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs18(LT, LT) → True
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, gc) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_esEs7(yvy49000, yvy50000, ea, eb, ec)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_lt11(yvy49000, yvy50000, de, df)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, hc)) → new_ltEs9(yvy4900, yvy5000, hc)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs19(:(yvy4000, yvy4001), [], ha) → False
new_esEs19([], :(yvy3000, yvy3001), ha) → False
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_ltEs18(GT, GT) → True
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(EQ, EQ) → True
new_esEs32(yvy400, yvy300, ty_Int) → new_esEs14(yvy400, yvy300)
new_compare24(yvy49000, yvy50000, True, ea, eb, ec) → EQ
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bed) → new_ltEs18(yvy49000, yvy50000)
new_esEs15(True, True) → True
new_esEs30(yvy20, yvy15, app(ty_[], dcg)) → new_esEs19(yvy20, yvy15, dcg)
new_ltEs18(LT, GT) → True
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcf)) → new_esEs4(yvy20, yvy15, dcf)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, hb)) → new_ltEs17(yvy4900, yvy5000, hb)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, ccb)) → new_esEs10(yvy4001, yvy3001, ccb)
new_ltEs8(True, True) → True
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cea), ceb), cec)) → new_esEs7(yvy49000, yvy50000, cea, ceb, cec)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, ddh)) → new_esEs4(yvy4000, yvy3000, ddh)
new_ltEs18(GT, LT) → False
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, chg), chh), daa), gc) → new_esEs7(yvy4000, yvy3000, chg, chh, daa)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_lt14(yvy49000, yvy50000, ea, eb, ec) → new_esEs9(new_compare14(yvy49000, yvy50000, ea, eb, ec), LT)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, ceg), ceh)) → new_esEs5(yvy49001, yvy50001, ceg, ceh)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cha)) → new_ltEs17(yvy49002, yvy50002, cha)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs7(yvy20, yvy15, dcc, dcd, dce)
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, he), hf)) → new_ltEs10(yvy49000, yvy50000, he, hf)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], bad)) → new_ltEs14(yvy49000, yvy50000, bad)
new_esEs32(yvy400, yvy300, app(ty_Ratio, bd)) → new_esEs10(yvy400, yvy300, bd)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bbg)) → new_esEs19(yvy4000, yvy3000, bbg)
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cgc), cgd)) → new_ltEs5(yvy49002, yvy50002, cgc, cgd)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_[], dbe)) → new_esEs19(yvy4000, yvy3000, dbe)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bch)) → new_esEs4(yvy4001, yvy3001, bch)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, ccf)) → new_esEs4(yvy4001, yvy3001, ccf)
new_compare112(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), gd, ge) → new_asAs(new_esEs24(yvy4000, yvy3000, gd), new_esEs25(yvy4001, yvy3001, ge))
new_lt19(yvy49001, yvy50001, app(app(ty_@2, cfa), cfb)) → new_lt12(yvy49001, yvy50001, cfa, cfb)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare12(yvy49000, yvy50000, True, de, df) → LT
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(ty_Either, dad), dae)) → new_esEs5(yvy4000, yvy3000, dad, dae)
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(app(ty_@3, bge), bgf), bgg)) → new_ltEs13(yvy49000, yvy50000, bge, bgf, bgg)
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_ltEs19(yvy4900, yvy5000, app(ty_[], be)) → new_ltEs14(yvy4900, yvy5000, be)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_Ratio, dah)) → new_esEs10(yvy4000, yvy3000, dah)
new_compare111(yvy49000, yvy50000, True, ea, eb, ec) → LT
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_primCompAux00(yvy206, LT) → LT
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(ty_Either, bga), bgb)) → new_ltEs10(yvy49000, yvy50000, bga, bgb)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, gc) → new_esEs14(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, cee)) → new_lt17(yvy49000, yvy50000, cee)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare13(yvy175, yvy176, True, ga) → LT
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs23(yvy4002, yvy3002, app(ty_[], bec)) → new_esEs19(yvy4002, yvy3002, bec)
new_esEs32(yvy400, yvy300, ty_@0) → new_esEs18(yvy400, yvy300)
new_lt15(yvy49000, yvy50000, ed) → new_esEs9(new_compare0(yvy49000, yvy50000, ed), LT)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_lt17(yvy49000, yvy50000, ee)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, hd)) → new_ltEs9(yvy49000, yvy50000, hd)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_compare14(yvy49000, yvy50000, ea, eb, ec) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, bg), bh)) → new_esEs5(yvy4000, yvy3000, bg, bh)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_esEs5(yvy49000, yvy50000, de, df)
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_ltEs20(yvy49002, yvy50002, app(ty_[], cgh)) → new_ltEs14(yvy49002, yvy50002, cgh)
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dch), dda)) → new_esEs5(yvy4000, yvy3000, dch, dda)
new_esEs32(yvy400, yvy300, app(app(ty_Either, gb), gc)) → new_esEs5(yvy400, yvy300, gb, gc)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, ca), cb)) → new_esEs6(yvy4000, yvy3000, ca, cb)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs32(yvy400, yvy300, ty_Integer) → new_esEs13(yvy400, yvy300)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bcb), bcc)) → new_esEs6(yvy4001, yvy3001, bcb, bcc)
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_compare28(yvy49000, yvy50000, app(ty_[], cab)) → new_compare0(yvy49000, yvy50000, cab)
new_ltEs9(Just(yvy49000), Nothing, hc) → False
new_primCompAux00(yvy206, EQ) → yvy206
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, gc) → new_esEs15(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bdf)) → new_esEs10(yvy4002, yvy3002, bdf)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, gc) → new_esEs8(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_compare26(Just(yvy4900), Just(yvy5000), False, cch) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, cch), cch)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bhg), bhh), caa)) → new_compare14(yvy49000, yvy50000, bhg, bhh, caa)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, cda), cdb), cdc)) → new_ltEs13(yvy4900, yvy5000, cda, cdb, cdc)
new_compare26(yvy490, yvy500, True, cch) → EQ
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs18(GT, EQ) → False
new_compare17(yvy49000, yvy50000, de, df) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, de, df), de, df)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcb)) → new_esEs10(yvy20, yvy15, dcb)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bed) → new_ltEs16(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_esEs10(yvy49000, yvy50000, ee)
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bdd), bde)) → new_esEs6(yvy4002, yvy3002, bdd, bde)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, hc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, gc) → new_esEs17(yvy4000, yvy3000)
new_esEs9(GT, GT) → True
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bhb)) → new_compare19(yvy49000, yvy50000, bhb)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bed) → new_ltEs15(yvy49000, yvy50000)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs18(EQ, LT) → False
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_compare0(:(yvy49000, yvy49001), [], be) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_ltEs18(LT, EQ) → True
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cde), cdf)) → new_esEs5(yvy49000, yvy50000, cde, cdf)
new_lt6(yvy49000, yvy50000, app(ty_[], ed)) → new_lt15(yvy49000, yvy50000, ed)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fg)) → new_ltEs14(yvy49001, yvy50001, fg)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs7(yvy4001, yvy3001, bce, bcf, bcg)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_lt10(yvy49000, yvy50000, dd)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, cfc), cfd), cfe)) → new_lt14(yvy49001, yvy50001, cfc, cfd, cfe)
new_lt19(yvy49001, yvy50001, app(ty_[], cff)) → new_lt15(yvy49001, yvy50001, cff)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs7(yvy4000, yvy3000, dde, ddf, ddg)
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gf, gg, gh) → new_asAs(new_esEs21(yvy4000, yvy3000, gf), new_asAs(new_esEs22(yvy4001, yvy3001, gg), new_esEs23(yvy4002, yvy3002, gh)))
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs5(Left(yvy4000), Right(yvy3000), gb, gc) → False
new_esEs5(Right(yvy4000), Left(yvy3000), gb, gc) → False
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, cfa), cfb)) → new_esEs6(yvy49001, yvy50001, cfa, cfb)
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bbb)) → new_esEs10(yvy4000, yvy3000, bbb)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_ltEs8(False, False) → True
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_compare19(yvy49000, yvy50000, dd) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, dd), dd)
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdg), cdh)) → new_lt12(yvy49000, yvy50000, cdg, cdh)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, baa), bab), bac)) → new_ltEs13(yvy49000, yvy50000, baa, bab, bac)
new_compare25(yvy49000, yvy50000, True, dg, dh) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_lt19(yvy49001, yvy50001, app(app(ty_Either, ceg), ceh)) → new_lt11(yvy49001, yvy50001, ceg, ceh)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cdd)) → new_lt10(yvy49000, yvy50000, cdd)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, bf) → True
new_compare111(yvy49000, yvy50000, False, ea, eb, ec) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_compare210(yvy49000, yvy50000, True) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bed) → new_ltEs7(yvy49000, yvy50000)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cef)) → new_esEs4(yvy49001, yvy50001, cef)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cga), cgb)) → new_ltEs10(yvy49002, yvy50002, cga, cgb)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bhc), bhd)) → new_compare17(yvy49000, yvy50000, bhc, bhd)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cde), cdf)) → new_lt11(yvy49000, yvy50000, cde, cdf)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cfg)) → new_esEs10(yvy49001, yvy50001, cfg)
new_compare13(yvy175, yvy176, False, ga) → GT
new_compare23(yvy49000, yvy50000, True, de, df) → EQ
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], bfe), bed) → new_ltEs14(yvy49000, yvy50000, bfe)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, gc) → new_esEs13(yvy4000, yvy3000)
new_lt17(yvy49000, yvy50000, ee) → new_esEs9(new_compare8(yvy49000, yvy50000, ee), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(app(ty_@3, dba), dbb), dbc)) → new_esEs7(yvy4000, yvy3000, dba, dbb, dbc)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cge), cgf), cgg)) → new_ltEs13(yvy49002, yvy50002, cge, cgf, cgg)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddb), ddc)) → new_esEs6(yvy4000, yvy3000, ddb, ddc)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bbf)) → new_esEs4(yvy4000, yvy3000, bbf)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, fa), fb)) → new_ltEs5(yvy49001, yvy50001, fa, fb)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bee), bed) → new_ltEs9(yvy49000, yvy50000, bee)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_lt14(yvy49000, yvy50000, ea, eb, ec)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs7(yvy4000, yvy3000, cba, cbb, cbc)
new_lt20(yvy49000, yvy50000, app(ty_[], ced)) → new_lt15(yvy49000, yvy50000, ced)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt12(yvy49000, yvy50000, dg, dh) → new_esEs9(new_compare18(yvy49000, yvy50000, dg, dh), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bd) → new_asAs(new_esEs11(yvy4000, yvy3000, bd), new_esEs12(yvy4001, yvy3001, bd))
new_asAs(False, yvy182) → False
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, baf), bag)) → new_esEs5(yvy4000, yvy3000, baf, bag)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs32(yvy400, yvy300, app(app(app(ty_@3, gf), gg), gh)) → new_esEs7(yvy400, yvy300, gf, gg, gh)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_esEs32(yvy400, yvy300, ty_Bool) → new_esEs15(yvy400, yvy300)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_lt10(yvy49000, yvy50000, dd) → new_esEs9(new_compare19(yvy49000, yvy50000, dd), LT)
new_compare25(yvy49000, yvy50000, False, dg, dh) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, dg, dh), dg, dh)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, cac)) → new_compare8(yvy49000, yvy50000, cac)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), cda, cdb, cdc) → new_pePe(new_lt20(yvy49000, yvy50000, cda), new_asAs(new_esEs26(yvy49000, yvy50000, cda), new_pePe(new_lt19(yvy49001, yvy50001, cdb), new_asAs(new_esEs27(yvy49001, yvy50001, cdb), new_ltEs20(yvy49002, yvy50002, cdc)))))
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cah)) → new_esEs10(yvy4000, yvy3000, cah)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbf), dbg)) → new_esEs5(yvy20, yvy15, dbf, dbg)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_esEs32(yvy400, yvy300, app(ty_[], ha)) → new_esEs19(yvy400, yvy300, ha)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_Ratio, bha)) → new_ltEs17(yvy49000, yvy50000, bha)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bcd)) → new_esEs10(yvy4001, yvy3001, bcd)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs7(yvy4001, yvy3001, ccc, ccd, cce)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_Maybe, dbd)) → new_esEs4(yvy4000, yvy3000, dbd)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare11(yvy49000, yvy50000, False) → GT
new_esEs30(yvy20, yvy15, app(app(ty_@2, dbh), dca)) → new_esEs6(yvy20, yvy15, dbh, dca)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Left(yvy50000), bfg, bed) → False
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_compare11(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], da)) → new_esEs19(yvy4000, yvy3000, da)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, chb), chc), gc) → new_esEs5(yvy4000, yvy3000, chb, chc)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_Maybe, bfh)) → new_ltEs9(yvy49000, yvy50000, bfh)
new_compare112(yvy49000, yvy50000, False) → GT
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(ty_[], ed)) → new_esEs19(yvy49000, yvy50000, ed)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cff)) → new_esEs19(yvy49001, yvy50001, cff)
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy50000, yvy50001), be) → LT
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_asAs(True, yvy182) → yvy182
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_esEs32(yvy400, yvy300, ty_Double) → new_esEs16(yvy400, yvy300)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_esEs18(@0, @0) → True
new_compare211(yvy49000, yvy50000, True) → EQ
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdg), cdh)) → new_esEs6(yvy49000, yvy50000, cdg, cdh)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs32(yvy400, yvy300, ty_Char) → new_esEs8(yvy400, yvy300)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cd), ce), cf)) → new_esEs7(yvy4000, yvy3000, cd, ce, cf)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, chf), gc) → new_esEs10(yvy4000, yvy3000, chf)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, bff), bed) → new_ltEs17(yvy49000, yvy50000, bff)
new_lt11(yvy49000, yvy50000, de, df) → new_esEs9(new_compare17(yvy49000, yvy50000, de, df), LT)
new_esEs9(LT, LT) → True
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), ha) → new_asAs(new_esEs28(yvy4000, yvy3000, ha), new_esEs19(yvy4001, yvy3001, ha))
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bbh), bca)) → new_esEs5(yvy4001, yvy3001, bbh, bca)
new_primCompAux00(yvy206, GT) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bed) → new_ltEs8(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_lt12(yvy49000, yvy50000, dg, dh)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bhe), bhf)) → new_compare18(yvy49000, yvy50000, bhe, bhf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_ltEs17(yvy4900, yvy5000, hb) → new_fsEs(new_compare8(yvy4900, yvy5000, hb))
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_esEs32(x0, x1, ty_Bool)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_compare210(x0, x1, False)
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare9(x0, x1)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(x0, Zero)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_lt19(x0, x1, ty_Int)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs15(x0, x1)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_compare28(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, ty_Char)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs32(x0, x1, ty_@0)
new_esEs19([], :(x0, x1), x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs32(x0, x1, ty_Int)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare12(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Char)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Nothing, Just(x0), x1)
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Nothing, Just(x0), False, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt6(x0, x1, ty_Integer)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt10(x0, x1, x2)
new_compare26(x0, x1, True, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Succ(x0))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs9(GT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(False, False)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_lt11(x0, x1, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_compare32(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(x0, x1, x2)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs19(:(x0, x1), [], x2)
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs6(x0, x1, ty_Int)
new_esEs19([], [], x0)
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs12(x0, x1)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, True)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs32(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare31(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs18(EQ, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Char(x0), Char(x1))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_ltEs18(GT, GT)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_ltEs9(Nothing, Nothing, x0)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare28(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_compare12(x0, x1, False, x2, x3)
new_compare26(Nothing, Nothing, False, x0)
new_compare13(x0, x1, False, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)

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

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

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

new_splitGT2(yvy300, yvy31, yvy32, yvy33, Branch(yvy340, yvy341, yvy342, yvy343, yvy344), True, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Nothing, h, ba)
new_splitGT10(yvy300, yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitGT(yvy33, h, ba)
new_splitGT2(yvy300, yvy31, yvy32, yvy33, yvy34, False, h, ba) → new_splitGT10(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare31(yvy300, h), LT), h, ba)
new_splitGT(Branch(yvy340, yvy341, yvy342, yvy343, yvy344), h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Nothing, h, ba)
new_splitGT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitGT2(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare26(Nothing, Just(yvy300), False, h), GT), h, ba)
new_splitGT1(yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitGT(yvy33, h, ba)
new_splitGT3(Nothing, yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitGT1(yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare30(h), LT), h, ba)

The TRS R consists of the following rules:

new_compare26(Nothing, Just(yvy5000), False, cch) → LT
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True
new_compare26(yvy490, yvy500, True, cch) → EQ
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_esEs32(x0, x1, ty_Bool)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_compare210(x0, x1, False)
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare9(x0, x1)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(x0, Zero)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_lt19(x0, x1, ty_Int)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs15(x0, x1)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_compare28(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, ty_Char)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs32(x0, x1, ty_@0)
new_esEs19([], :(x0, x1), x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs32(x0, x1, ty_Int)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare12(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Char)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Nothing, Just(x0), x1)
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Nothing, Just(x0), False, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt6(x0, x1, ty_Integer)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt10(x0, x1, x2)
new_compare26(x0, x1, True, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Succ(x0))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs9(GT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(False, False)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_lt11(x0, x1, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_compare32(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(x0, x1, x2)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs19(:(x0, x1), [], x2)
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs6(x0, x1, ty_Int)
new_esEs19([], [], x0)
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs12(x0, x1)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, True)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs32(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare31(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs18(EQ, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Char(x0), Char(x1))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_ltEs18(GT, GT)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_ltEs9(Nothing, Nothing, x0)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare28(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_compare12(x0, x1, False, x2, x3)
new_compare26(Nothing, Nothing, False, x0)
new_compare13(x0, x1, False, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)

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

new_ltEs20(x0, x1, ty_Int)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_esEs32(x0, x1, ty_Bool)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_compare210(x0, x1, False)
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare9(x0, x1)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(x0, Zero)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_lt19(x0, x1, ty_Int)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs15(x0, x1)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_compare28(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, ty_Char)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs32(x0, x1, ty_@0)
new_esEs19([], :(x0, x1), x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs32(x0, x1, ty_Int)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_compare12(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Char)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Nothing, Just(x0), x1)
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt6(x0, x1, ty_Integer)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt10(x0, x1, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Succ(x0))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(False, False)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_lt11(x0, x1, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_compare32(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(x0, x1, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs19(:(x0, x1), [], x2)
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs6(x0, x1, ty_Int)
new_esEs19([], [], x0)
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs12(x0, x1)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, True)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs32(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulNat0(Zero, Succ(x0))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs18(EQ, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Char(x0), Char(x1))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_ltEs18(GT, GT)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_ltEs9(Nothing, Nothing, x0)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare28(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_compare12(x0, x1, False, x2, x3)
new_compare13(x0, x1, False, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)



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

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

new_splitGT2(yvy300, yvy31, yvy32, yvy33, Branch(yvy340, yvy341, yvy342, yvy343, yvy344), True, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Nothing, h, ba)
new_splitGT2(yvy300, yvy31, yvy32, yvy33, yvy34, False, h, ba) → new_splitGT10(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare31(yvy300, h), LT), h, ba)
new_splitGT10(yvy300, yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitGT(yvy33, h, ba)
new_splitGT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitGT2(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare26(Nothing, Just(yvy300), False, h), GT), h, ba)
new_splitGT(Branch(yvy340, yvy341, yvy342, yvy343, yvy344), h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Nothing, h, ba)
new_splitGT1(yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitGT(yvy33, h, ba)
new_splitGT3(Nothing, yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitGT1(yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare30(h), LT), h, ba)

The TRS R consists of the following rules:

new_compare26(Nothing, Just(yvy5000), False, cch) → LT
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True
new_compare26(yvy490, yvy500, True, cch) → EQ
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)

The set Q consists of the following terms:

new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare26(Nothing, Just(x0), False, x1)
new_compare26(x0, x1, True, x2)
new_esEs9(GT, GT)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs9(EQ, EQ)
new_compare31(x0, x1)
new_compare30(x0)
new_compare26(Nothing, Nothing, False, x0)
new_esEs9(LT, 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
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ AND
                                        ↳ QDP
                                        ↳ QDP
                                          ↳ UsableRulesProof
                                  ↳ QDP

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

new_splitGT21(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, False, bb, bc) → new_splitGT12(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, new_esEs9(new_compare33(yvy20, yvy15, bb), LT), bb, bc)
new_splitGT3(Nothing, yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitGT20(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), GT), h, ba)
new_splitGT11(yvy31, yvy32, yvy33, yvy34, yvy400, True, h, ba) → new_splitGT0(yvy33, yvy400, h, ba)
new_splitGT20(yvy31, yvy32, yvy33, Branch(yvy340, yvy341, yvy342, yvy343, yvy344), yvy400, True, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Just(yvy400), h, ba)
new_splitGT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitGT21(yvy300, yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Just(yvy300), new_esEs32(yvy400, yvy300, h), h), GT), h, ba)
new_splitGT0(Branch(yvy340, yvy341, yvy342, yvy343, yvy344), yvy400, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Just(yvy400), h, ba)
new_splitGT12(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, True, bb, bc) → new_splitGT0(yvy18, yvy20, bb, bc)
new_splitGT21(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, True, bb, bc) → new_splitGT0(yvy19, yvy20, bb, bc)
new_splitGT20(yvy31, yvy32, yvy33, yvy34, yvy400, False, h, ba) → new_splitGT11(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare32(yvy400, h), LT), h, ba)

The TRS R consists of the following rules:

new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, cg)) → new_esEs4(yvy4000, yvy3000, cg)
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, db), dc)) → new_ltEs5(yvy4900, yvy5000, db, dc)
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs32(yvy400, yvy300, ty_Float) → new_esEs17(yvy400, yvy300)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, cad), cae)) → new_esEs5(yvy4000, yvy3000, cad, cae)
new_esEs28(yvy4000, yvy3000, app(ty_[], dea)) → new_esEs19(yvy4000, yvy3000, dea)
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, bah), bba)) → new_esEs6(yvy4000, yvy3000, bah, bba)
new_primCmpNat2(Zero, yvy4900) → LT
new_ltEs8(False, True) → True
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, beh), bfa), bed) → new_ltEs5(yvy49000, yvy50000, beh, bfa)
new_esEs22(yvy4001, yvy3001, app(ty_[], bda)) → new_esEs19(yvy4001, yvy3001, bda)
new_ltEs18(EQ, GT) → True
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_ltEs10(Left(yvy49000), Right(yvy50000), bfg, bed) → True
new_compare110(yvy49000, yvy50000, True, dg, dh) → LT
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bdb), bdc)) → new_esEs5(yvy4002, yvy3002, bdb, bdc)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_compare24(yvy49000, yvy50000, False, ea, eb, ec) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cbd)) → new_esEs4(yvy4000, yvy3000, cbd)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, fh)) → new_ltEs17(yvy49001, yvy50001, fh)
new_esEs4(Just(yvy4000), Nothing, bf) → False
new_esEs4(Nothing, Just(yvy3000), bf) → False
new_ltEs9(Nothing, Just(yvy50000), hc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], dac), gc) → new_esEs19(yvy4000, yvy3000, dac)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_primMulNat0(Zero, Zero) → Zero
new_compare26(Just(yvy4900), Nothing, False, cch) → GT
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, cee)) → new_esEs10(yvy49000, yvy50000, cee)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, ddd)) → new_esEs10(yvy4000, yvy3000, ddd)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_esEs4(yvy49000, yvy50000, dd)
new_compare33(yvy20, yvy15, bb) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, bb), bb)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, gc) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_[], ced)) → new_esEs19(yvy49000, yvy50000, ced)
new_compare16(@0, @0) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, beb)) → new_esEs4(yvy4002, yvy3002, beb)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_compare26(Nothing, Just(yvy5000), False, cch) → LT
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), be) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, be), be)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_[], bgh)) → new_ltEs14(yvy49000, yvy50000, bgh)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs7(yvy4000, yvy3000, bbc, bbd, bbe)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bed) → new_ltEs12(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cdd)) → new_esEs4(yvy49000, yvy50000, cdd)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_esEs6(yvy49000, yvy50000, dg, dh)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_compare18(yvy49000, yvy50000, dg, dh) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, dg, dh), dg, dh)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_esEs32(yvy400, yvy300, app(app(ty_@2, gd), ge)) → new_esEs6(yvy400, yvy300, gd, ge)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_pePe(False, yvy201) → yvy201
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_compare23(yvy49000, yvy50000, False, de, df) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, de, df), de, df)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_compare26(Nothing, Nothing, False, cch) → LT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bed) → new_ltEs4(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cfg)) → new_lt17(yvy49001, yvy50001, cfg)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bfb), bfc), bfd), bed) → new_ltEs13(yvy49000, yvy50000, bfb, bfc, bfd)
new_esEs32(yvy400, yvy300, ty_Ordering) → new_esEs9(yvy400, yvy300)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bef), beg), bed) → new_ltEs10(yvy49000, yvy50000, bef, beg)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs13(yvy49001, yvy50001, fc, fd, ff)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cef)) → new_lt10(yvy49001, yvy50001, cef)
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chd), che), gc) → new_esEs6(yvy4000, yvy3000, chd, che)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbe)) → new_esEs19(yvy4000, yvy3000, cbe)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, dab), gc) → new_esEs4(yvy4000, yvy3000, dab)
new_esEs32(yvy400, yvy300, app(ty_Maybe, bf)) → new_esEs4(yvy400, yvy300, bf)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, hg), hh)) → new_ltEs5(yvy49000, yvy50000, hg, hh)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(ty_@2, bgc), bgd)) → new_ltEs5(yvy49000, yvy50000, bgc, bgd)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs7(yvy4002, yvy3002, bdg, bdh, bea)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs7(yvy49001, yvy50001, cfc, cfd, cfe)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cea), ceb), cec)) → new_lt14(yvy49000, yvy50000, cea, ceb, cec)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbf), cbg)) → new_esEs5(yvy4001, yvy3001, cbf, cbg)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbh), cca)) → new_esEs6(yvy4001, yvy3001, cbh, cca)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ef)) → new_ltEs9(yvy49001, yvy50001, ef)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, bae)) → new_ltEs17(yvy49000, yvy50000, bae)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, bfg), bed)) → new_ltEs10(yvy4900, yvy5000, bfg, bed)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), db, dc) → new_pePe(new_lt6(yvy49000, yvy50000, db), new_asAs(new_esEs20(yvy49000, yvy50000, db), new_ltEs6(yvy49001, yvy50001, dc)))
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfh)) → new_ltEs9(yvy49002, yvy50002, cfh)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, caf), cag)) → new_esEs6(yvy4000, yvy3000, caf, cag)
new_compare0([], [], be) → EQ
new_pePe(True, yvy201) → True
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_primEqNat0(Zero, Zero) → True
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bed) → new_ltEs11(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(ty_@2, daf), dag)) → new_esEs6(yvy4000, yvy3000, daf, dag)
new_ltEs14(yvy4900, yvy5000, be) → new_fsEs(new_compare0(yvy4900, yvy5000, be))
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, eg), eh)) → new_ltEs10(yvy49001, yvy50001, eg, eh)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_ltEs18(EQ, EQ) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, gc) → new_esEs9(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_esEs19([], [], ha) → True
new_compare110(yvy49000, yvy50000, False, dg, dh) → GT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, cc)) → new_esEs10(yvy4000, yvy3000, cc)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccg)) → new_esEs19(yvy4001, yvy3001, ccg)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_compare12(yvy49000, yvy50000, False, de, df) → GT
new_primCmpNat1(Zero, Zero) → EQ
new_primCompAux0(yvy49000, yvy50000, yvy202, be) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, be))
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs18(LT, LT) → True
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, gc) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_esEs7(yvy49000, yvy50000, ea, eb, ec)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_lt11(yvy49000, yvy50000, de, df)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, hc)) → new_ltEs9(yvy4900, yvy5000, hc)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs19(:(yvy4000, yvy4001), [], ha) → False
new_esEs19([], :(yvy3000, yvy3001), ha) → False
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_ltEs18(GT, GT) → True
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(EQ, EQ) → True
new_esEs32(yvy400, yvy300, ty_Int) → new_esEs14(yvy400, yvy300)
new_compare24(yvy49000, yvy50000, True, ea, eb, ec) → EQ
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bed) → new_ltEs18(yvy49000, yvy50000)
new_esEs15(True, True) → True
new_esEs30(yvy20, yvy15, app(ty_[], dcg)) → new_esEs19(yvy20, yvy15, dcg)
new_ltEs18(LT, GT) → True
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcf)) → new_esEs4(yvy20, yvy15, dcf)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, hb)) → new_ltEs17(yvy4900, yvy5000, hb)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, ccb)) → new_esEs10(yvy4001, yvy3001, ccb)
new_ltEs8(True, True) → True
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cea), ceb), cec)) → new_esEs7(yvy49000, yvy50000, cea, ceb, cec)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, ddh)) → new_esEs4(yvy4000, yvy3000, ddh)
new_ltEs18(GT, LT) → False
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, chg), chh), daa), gc) → new_esEs7(yvy4000, yvy3000, chg, chh, daa)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_lt14(yvy49000, yvy50000, ea, eb, ec) → new_esEs9(new_compare14(yvy49000, yvy50000, ea, eb, ec), LT)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, ceg), ceh)) → new_esEs5(yvy49001, yvy50001, ceg, ceh)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cha)) → new_ltEs17(yvy49002, yvy50002, cha)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs7(yvy20, yvy15, dcc, dcd, dce)
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, he), hf)) → new_ltEs10(yvy49000, yvy50000, he, hf)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], bad)) → new_ltEs14(yvy49000, yvy50000, bad)
new_esEs32(yvy400, yvy300, app(ty_Ratio, bd)) → new_esEs10(yvy400, yvy300, bd)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bbg)) → new_esEs19(yvy4000, yvy3000, bbg)
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cgc), cgd)) → new_ltEs5(yvy49002, yvy50002, cgc, cgd)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_[], dbe)) → new_esEs19(yvy4000, yvy3000, dbe)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bch)) → new_esEs4(yvy4001, yvy3001, bch)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, ccf)) → new_esEs4(yvy4001, yvy3001, ccf)
new_compare112(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), gd, ge) → new_asAs(new_esEs24(yvy4000, yvy3000, gd), new_esEs25(yvy4001, yvy3001, ge))
new_lt19(yvy49001, yvy50001, app(app(ty_@2, cfa), cfb)) → new_lt12(yvy49001, yvy50001, cfa, cfb)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare12(yvy49000, yvy50000, True, de, df) → LT
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(ty_Either, dad), dae)) → new_esEs5(yvy4000, yvy3000, dad, dae)
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(app(ty_@3, bge), bgf), bgg)) → new_ltEs13(yvy49000, yvy50000, bge, bgf, bgg)
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_ltEs19(yvy4900, yvy5000, app(ty_[], be)) → new_ltEs14(yvy4900, yvy5000, be)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_Ratio, dah)) → new_esEs10(yvy4000, yvy3000, dah)
new_compare111(yvy49000, yvy50000, True, ea, eb, ec) → LT
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_primCompAux00(yvy206, LT) → LT
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(ty_Either, bga), bgb)) → new_ltEs10(yvy49000, yvy50000, bga, bgb)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, gc) → new_esEs14(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, cee)) → new_lt17(yvy49000, yvy50000, cee)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare13(yvy175, yvy176, True, ga) → LT
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs23(yvy4002, yvy3002, app(ty_[], bec)) → new_esEs19(yvy4002, yvy3002, bec)
new_esEs32(yvy400, yvy300, ty_@0) → new_esEs18(yvy400, yvy300)
new_lt15(yvy49000, yvy50000, ed) → new_esEs9(new_compare0(yvy49000, yvy50000, ed), LT)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_lt17(yvy49000, yvy50000, ee)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, hd)) → new_ltEs9(yvy49000, yvy50000, hd)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_compare14(yvy49000, yvy50000, ea, eb, ec) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, bg), bh)) → new_esEs5(yvy4000, yvy3000, bg, bh)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_esEs5(yvy49000, yvy50000, de, df)
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_ltEs20(yvy49002, yvy50002, app(ty_[], cgh)) → new_ltEs14(yvy49002, yvy50002, cgh)
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dch), dda)) → new_esEs5(yvy4000, yvy3000, dch, dda)
new_esEs32(yvy400, yvy300, app(app(ty_Either, gb), gc)) → new_esEs5(yvy400, yvy300, gb, gc)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, ca), cb)) → new_esEs6(yvy4000, yvy3000, ca, cb)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs32(yvy400, yvy300, ty_Integer) → new_esEs13(yvy400, yvy300)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bcb), bcc)) → new_esEs6(yvy4001, yvy3001, bcb, bcc)
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_compare28(yvy49000, yvy50000, app(ty_[], cab)) → new_compare0(yvy49000, yvy50000, cab)
new_ltEs9(Just(yvy49000), Nothing, hc) → False
new_primCompAux00(yvy206, EQ) → yvy206
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, gc) → new_esEs15(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bdf)) → new_esEs10(yvy4002, yvy3002, bdf)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, gc) → new_esEs8(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_compare26(Just(yvy4900), Just(yvy5000), False, cch) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, cch), cch)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bhg), bhh), caa)) → new_compare14(yvy49000, yvy50000, bhg, bhh, caa)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, cda), cdb), cdc)) → new_ltEs13(yvy4900, yvy5000, cda, cdb, cdc)
new_compare26(yvy490, yvy500, True, cch) → EQ
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs18(GT, EQ) → False
new_compare17(yvy49000, yvy50000, de, df) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, de, df), de, df)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcb)) → new_esEs10(yvy20, yvy15, dcb)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bed) → new_ltEs16(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_esEs10(yvy49000, yvy50000, ee)
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bdd), bde)) → new_esEs6(yvy4002, yvy3002, bdd, bde)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, hc) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, gc) → new_esEs17(yvy4000, yvy3000)
new_esEs9(GT, GT) → True
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bhb)) → new_compare19(yvy49000, yvy50000, bhb)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bed) → new_ltEs15(yvy49000, yvy50000)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs18(EQ, LT) → False
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_compare0(:(yvy49000, yvy49001), [], be) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_ltEs18(LT, EQ) → True
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cde), cdf)) → new_esEs5(yvy49000, yvy50000, cde, cdf)
new_lt6(yvy49000, yvy50000, app(ty_[], ed)) → new_lt15(yvy49000, yvy50000, ed)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fg)) → new_ltEs14(yvy49001, yvy50001, fg)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs7(yvy4001, yvy3001, bce, bcf, bcg)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_lt10(yvy49000, yvy50000, dd)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, cfc), cfd), cfe)) → new_lt14(yvy49001, yvy50001, cfc, cfd, cfe)
new_lt19(yvy49001, yvy50001, app(ty_[], cff)) → new_lt15(yvy49001, yvy50001, cff)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs7(yvy4000, yvy3000, dde, ddf, ddg)
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gf, gg, gh) → new_asAs(new_esEs21(yvy4000, yvy3000, gf), new_asAs(new_esEs22(yvy4001, yvy3001, gg), new_esEs23(yvy4002, yvy3002, gh)))
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs5(Left(yvy4000), Right(yvy3000), gb, gc) → False
new_esEs5(Right(yvy4000), Left(yvy3000), gb, gc) → False
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, cfa), cfb)) → new_esEs6(yvy49001, yvy50001, cfa, cfb)
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bbb)) → new_esEs10(yvy4000, yvy3000, bbb)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_ltEs8(False, False) → True
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_compare19(yvy49000, yvy50000, dd) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, dd), dd)
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdg), cdh)) → new_lt12(yvy49000, yvy50000, cdg, cdh)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, baa), bab), bac)) → new_ltEs13(yvy49000, yvy50000, baa, bab, bac)
new_compare25(yvy49000, yvy50000, True, dg, dh) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_lt19(yvy49001, yvy50001, app(app(ty_Either, ceg), ceh)) → new_lt11(yvy49001, yvy50001, ceg, ceh)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cdd)) → new_lt10(yvy49000, yvy50000, cdd)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, bf) → True
new_compare111(yvy49000, yvy50000, False, ea, eb, ec) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_compare210(yvy49000, yvy50000, True) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bed) → new_ltEs7(yvy49000, yvy50000)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cef)) → new_esEs4(yvy49001, yvy50001, cef)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cga), cgb)) → new_ltEs10(yvy49002, yvy50002, cga, cgb)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bhc), bhd)) → new_compare17(yvy49000, yvy50000, bhc, bhd)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cde), cdf)) → new_lt11(yvy49000, yvy50000, cde, cdf)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cfg)) → new_esEs10(yvy49001, yvy50001, cfg)
new_compare13(yvy175, yvy176, False, ga) → GT
new_compare23(yvy49000, yvy50000, True, de, df) → EQ
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], bfe), bed) → new_ltEs14(yvy49000, yvy50000, bfe)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, gc) → new_esEs13(yvy4000, yvy3000)
new_lt17(yvy49000, yvy50000, ee) → new_esEs9(new_compare8(yvy49000, yvy50000, ee), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(app(ty_@3, dba), dbb), dbc)) → new_esEs7(yvy4000, yvy3000, dba, dbb, dbc)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cge), cgf), cgg)) → new_ltEs13(yvy49002, yvy50002, cge, cgf, cgg)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddb), ddc)) → new_esEs6(yvy4000, yvy3000, ddb, ddc)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bbf)) → new_esEs4(yvy4000, yvy3000, bbf)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, fa), fb)) → new_ltEs5(yvy49001, yvy50001, fa, fb)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bee), bed) → new_ltEs9(yvy49000, yvy50000, bee)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_lt14(yvy49000, yvy50000, ea, eb, ec)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs7(yvy4000, yvy3000, cba, cbb, cbc)
new_lt20(yvy49000, yvy50000, app(ty_[], ced)) → new_lt15(yvy49000, yvy50000, ced)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt12(yvy49000, yvy50000, dg, dh) → new_esEs9(new_compare18(yvy49000, yvy50000, dg, dh), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bd) → new_asAs(new_esEs11(yvy4000, yvy3000, bd), new_esEs12(yvy4001, yvy3001, bd))
new_asAs(False, yvy182) → False
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, baf), bag)) → new_esEs5(yvy4000, yvy3000, baf, bag)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs32(yvy400, yvy300, app(app(app(ty_@3, gf), gg), gh)) → new_esEs7(yvy400, yvy300, gf, gg, gh)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_esEs32(yvy400, yvy300, ty_Bool) → new_esEs15(yvy400, yvy300)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_lt10(yvy49000, yvy50000, dd) → new_esEs9(new_compare19(yvy49000, yvy50000, dd), LT)
new_compare25(yvy49000, yvy50000, False, dg, dh) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, dg, dh), dg, dh)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, cac)) → new_compare8(yvy49000, yvy50000, cac)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), cda, cdb, cdc) → new_pePe(new_lt20(yvy49000, yvy50000, cda), new_asAs(new_esEs26(yvy49000, yvy50000, cda), new_pePe(new_lt19(yvy49001, yvy50001, cdb), new_asAs(new_esEs27(yvy49001, yvy50001, cdb), new_ltEs20(yvy49002, yvy50002, cdc)))))
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cah)) → new_esEs10(yvy4000, yvy3000, cah)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbf), dbg)) → new_esEs5(yvy20, yvy15, dbf, dbg)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_esEs32(yvy400, yvy300, app(ty_[], ha)) → new_esEs19(yvy400, yvy300, ha)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_Ratio, bha)) → new_ltEs17(yvy49000, yvy50000, bha)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bcd)) → new_esEs10(yvy4001, yvy3001, bcd)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs7(yvy4001, yvy3001, ccc, ccd, cce)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_Maybe, dbd)) → new_esEs4(yvy4000, yvy3000, dbd)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare11(yvy49000, yvy50000, False) → GT
new_esEs30(yvy20, yvy15, app(app(ty_@2, dbh), dca)) → new_esEs6(yvy20, yvy15, dbh, dca)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Left(yvy50000), bfg, bed) → False
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_compare11(yvy49000, yvy50000, True) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], da)) → new_esEs19(yvy4000, yvy3000, da)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, chb), chc), gc) → new_esEs5(yvy4000, yvy3000, chb, chc)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_Maybe, bfh)) → new_ltEs9(yvy49000, yvy50000, bfh)
new_compare112(yvy49000, yvy50000, False) → GT
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(ty_[], ed)) → new_esEs19(yvy49000, yvy50000, ed)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cff)) → new_esEs19(yvy49001, yvy50001, cff)
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy50000, yvy50001), be) → LT
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_asAs(True, yvy182) → yvy182
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_esEs32(yvy400, yvy300, ty_Double) → new_esEs16(yvy400, yvy300)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_esEs18(@0, @0) → True
new_compare211(yvy49000, yvy50000, True) → EQ
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdg), cdh)) → new_esEs6(yvy49000, yvy50000, cdg, cdh)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs32(yvy400, yvy300, ty_Char) → new_esEs8(yvy400, yvy300)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cd), ce), cf)) → new_esEs7(yvy4000, yvy3000, cd, ce, cf)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, chf), gc) → new_esEs10(yvy4000, yvy3000, chf)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, bff), bed) → new_ltEs17(yvy49000, yvy50000, bff)
new_lt11(yvy49000, yvy50000, de, df) → new_esEs9(new_compare17(yvy49000, yvy50000, de, df), LT)
new_esEs9(LT, LT) → True
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), ha) → new_asAs(new_esEs28(yvy4000, yvy3000, ha), new_esEs19(yvy4001, yvy3001, ha))
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bbh), bca)) → new_esEs5(yvy4001, yvy3001, bbh, bca)
new_primCompAux00(yvy206, GT) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bed) → new_ltEs8(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_lt12(yvy49000, yvy50000, dg, dh)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bhe), bhf)) → new_compare18(yvy49000, yvy50000, bhe, bhf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_ltEs17(yvy4900, yvy5000, hb) → new_fsEs(new_compare8(yvy4900, yvy5000, hb))
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_esEs32(x0, x1, ty_Bool)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_compare210(x0, x1, False)
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare9(x0, x1)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(x0, Zero)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_lt19(x0, x1, ty_Int)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs15(x0, x1)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_compare28(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, ty_Char)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs32(x0, x1, ty_@0)
new_esEs19([], :(x0, x1), x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs32(x0, x1, ty_Int)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare12(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Char)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Nothing, Just(x0), x1)
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Nothing, Just(x0), False, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt6(x0, x1, ty_Integer)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt10(x0, x1, x2)
new_compare26(x0, x1, True, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Succ(x0))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs9(GT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(False, False)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_lt11(x0, x1, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_compare32(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(x0, x1, x2)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs19(:(x0, x1), [], x2)
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs6(x0, x1, ty_Int)
new_esEs19([], [], x0)
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs12(x0, x1)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, True)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs32(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare31(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs18(EQ, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Char(x0), Char(x1))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_ltEs18(GT, GT)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_ltEs9(Nothing, Nothing, x0)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare28(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_compare12(x0, x1, False, x2, x3)
new_compare26(Nothing, Nothing, False, x0)
new_compare13(x0, x1, False, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)

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

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

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

new_splitGT21(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, False, bb, bc) → new_splitGT12(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, new_esEs9(new_compare33(yvy20, yvy15, bb), LT), bb, bc)
new_splitGT3(Nothing, yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitGT20(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), GT), h, ba)
new_splitGT11(yvy31, yvy32, yvy33, yvy34, yvy400, True, h, ba) → new_splitGT0(yvy33, yvy400, h, ba)
new_splitGT20(yvy31, yvy32, yvy33, Branch(yvy340, yvy341, yvy342, yvy343, yvy344), yvy400, True, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Just(yvy400), h, ba)
new_splitGT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitGT21(yvy300, yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Just(yvy300), new_esEs32(yvy400, yvy300, h), h), GT), h, ba)
new_splitGT0(Branch(yvy340, yvy341, yvy342, yvy343, yvy344), yvy400, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Just(yvy400), h, ba)
new_splitGT12(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, True, bb, bc) → new_splitGT0(yvy18, yvy20, bb, bc)
new_splitGT21(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, True, bb, bc) → new_splitGT0(yvy19, yvy20, bb, bc)
new_splitGT20(yvy31, yvy32, yvy33, yvy34, yvy400, False, h, ba) → new_splitGT11(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare32(yvy400, h), LT), h, ba)

The TRS R consists of the following rules:

new_compare33(yvy20, yvy15, bb) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, bb), bb)
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(ty_[], dcg)) → new_esEs19(yvy20, yvy15, dcg)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcf)) → new_esEs4(yvy20, yvy15, dcf)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs7(yvy20, yvy15, dcc, dcd, dce)
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcb)) → new_esEs10(yvy20, yvy15, dcb)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbf), dbg)) → new_esEs5(yvy20, yvy15, dbf, dbg)
new_esEs30(yvy20, yvy15, app(app(ty_@2, dbh), dca)) → new_esEs6(yvy20, yvy15, dbh, dca)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_compare26(Just(yvy4900), Just(yvy5000), False, cch) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, cch), cch)
new_compare26(yvy490, yvy500, True, cch) → EQ
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, db), dc)) → new_ltEs5(yvy4900, yvy5000, db, dc)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, bfg), bed)) → new_ltEs10(yvy4900, yvy5000, bfg, bed)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, hc)) → new_ltEs9(yvy4900, yvy5000, hc)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, hb)) → new_ltEs17(yvy4900, yvy5000, hb)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(ty_[], be)) → new_ltEs14(yvy4900, yvy5000, be)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, cda), cdb), cdc)) → new_ltEs13(yvy4900, yvy5000, cda, cdb, cdc)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare13(yvy175, yvy176, True, ga) → LT
new_compare13(yvy175, yvy176, False, ga) → GT
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_compare16(@0, @0) → EQ
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_not(False) → True
new_not(True) → False
new_ltEs18(EQ, GT) → True
new_ltEs18(EQ, EQ) → True
new_ltEs18(LT, LT) → True
new_ltEs18(GT, GT) → True
new_ltEs18(LT, GT) → True
new_ltEs18(GT, LT) → False
new_ltEs18(GT, EQ) → False
new_ltEs18(EQ, LT) → False
new_ltEs18(LT, EQ) → True
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), cda, cdb, cdc) → new_pePe(new_lt20(yvy49000, yvy50000, cda), new_asAs(new_esEs26(yvy49000, yvy50000, cda), new_pePe(new_lt19(yvy49001, yvy50001, cdb), new_asAs(new_esEs27(yvy49001, yvy50001, cdb), new_ltEs20(yvy49002, yvy50002, cdc)))))
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cea), ceb), cec)) → new_lt14(yvy49000, yvy50000, cea, ceb, cec)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, cee)) → new_lt17(yvy49000, yvy50000, cee)
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdg), cdh)) → new_lt12(yvy49000, yvy50000, cdg, cdh)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cdd)) → new_lt10(yvy49000, yvy50000, cdd)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cde), cdf)) → new_lt11(yvy49000, yvy50000, cde, cdf)
new_lt20(yvy49000, yvy50000, app(ty_[], ced)) → new_lt15(yvy49000, yvy50000, ced)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, cee)) → new_esEs10(yvy49000, yvy50000, cee)
new_esEs26(yvy49000, yvy50000, app(ty_[], ced)) → new_esEs19(yvy49000, yvy50000, ced)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cdd)) → new_esEs4(yvy49000, yvy50000, cdd)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cea), ceb), cec)) → new_esEs7(yvy49000, yvy50000, cea, ceb, cec)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cde), cdf)) → new_esEs5(yvy49000, yvy50000, cde, cdf)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdg), cdh)) → new_esEs6(yvy49000, yvy50000, cdg, cdh)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cfg)) → new_lt17(yvy49001, yvy50001, cfg)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cef)) → new_lt10(yvy49001, yvy50001, cef)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, app(app(ty_@2, cfa), cfb)) → new_lt12(yvy49001, yvy50001, cfa, cfb)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, cfc), cfd), cfe)) → new_lt14(yvy49001, yvy50001, cfc, cfd, cfe)
new_lt19(yvy49001, yvy50001, app(ty_[], cff)) → new_lt15(yvy49001, yvy50001, cff)
new_lt19(yvy49001, yvy50001, app(app(ty_Either, ceg), ceh)) → new_lt11(yvy49001, yvy50001, ceg, ceh)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs7(yvy49001, yvy50001, cfc, cfd, cfe)
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, ceg), ceh)) → new_esEs5(yvy49001, yvy50001, ceg, ceh)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, cfa), cfb)) → new_esEs6(yvy49001, yvy50001, cfa, cfb)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cef)) → new_esEs4(yvy49001, yvy50001, cef)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cfg)) → new_esEs10(yvy49001, yvy50001, cfg)
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cff)) → new_esEs19(yvy49001, yvy50001, cff)
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfh)) → new_ltEs9(yvy49002, yvy50002, cfh)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cha)) → new_ltEs17(yvy49002, yvy50002, cha)
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cgc), cgd)) → new_ltEs5(yvy49002, yvy50002, cgc, cgd)
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(ty_[], cgh)) → new_ltEs14(yvy49002, yvy50002, cgh)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cga), cgb)) → new_ltEs10(yvy49002, yvy50002, cga, cgb)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cge), cgf), cgg)) → new_ltEs13(yvy49002, yvy50002, cge, cgf, cgg)
new_asAs(False, yvy182) → False
new_asAs(True, yvy182) → yvy182
new_pePe(False, yvy201) → yvy201
new_pePe(True, yvy201) → True
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, beh), bfa), bed) → new_ltEs5(yvy49000, yvy50000, beh, bfa)
new_ltEs10(Left(yvy49000), Right(yvy50000), bfg, bed) → True
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_[], bgh)) → new_ltEs14(yvy49000, yvy50000, bgh)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bed) → new_ltEs12(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bed) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bfb), bfc), bfd), bed) → new_ltEs13(yvy49000, yvy50000, bfb, bfc, bfd)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(ty_@2, bgc), bgd)) → new_ltEs5(yvy49000, yvy50000, bgc, bgd)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bed) → new_ltEs11(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bed) → new_ltEs18(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(app(ty_@3, bge), bgf), bgg)) → new_ltEs13(yvy49000, yvy50000, bge, bgf, bgg)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, hd)) → new_ltEs9(yvy49000, yvy50000, hd)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bee), bed) → new_ltEs9(yvy49000, yvy50000, bee)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bef), beg), bed) → new_ltEs10(yvy49000, yvy50000, bef, beg)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_Maybe, bfh)) → new_ltEs9(yvy49000, yvy50000, bfh)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(ty_Either, bga), bgb)) → new_ltEs10(yvy49000, yvy50000, bga, bgb)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, he), hf)) → new_ltEs10(yvy49000, yvy50000, he, hf)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bed) → new_ltEs16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bed) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bed) → new_ltEs7(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], bfe), bed) → new_ltEs14(yvy49000, yvy50000, bfe)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_Ratio, bha)) → new_ltEs17(yvy49000, yvy50000, bha)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Left(yvy50000), bfg, bed) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, bff), bed) → new_ltEs17(yvy49000, yvy50000, bff)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bed) → new_ltEs8(yvy49000, yvy50000)
new_ltEs8(False, True) → True
new_ltEs8(True, True) → True
new_ltEs8(True, False) → False
new_ltEs8(False, False) → True
new_ltEs17(yvy4900, yvy5000, hb) → new_fsEs(new_compare8(yvy4900, yvy5000, hb))
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs14(yvy4900, yvy5000, be) → new_fsEs(new_compare0(yvy4900, yvy5000, be))
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), be) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, be), be)
new_compare0([], [], be) → EQ
new_compare0(:(yvy49000, yvy49001), [], be) → GT
new_compare0([], :(yvy50000, yvy50001), be) → LT
new_primCompAux0(yvy49000, yvy50000, yvy202, be) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, be))
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(ty_[], cab)) → new_compare0(yvy49000, yvy50000, cab)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bhg), bhh), caa)) → new_compare14(yvy49000, yvy50000, bhg, bhh, caa)
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bhb)) → new_compare19(yvy49000, yvy50000, bhb)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bhc), bhd)) → new_compare17(yvy49000, yvy50000, bhc, bhd)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, cac)) → new_compare8(yvy49000, yvy50000, cac)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bhe), bhf)) → new_compare18(yvy49000, yvy50000, bhe, bhf)
new_primCompAux00(yvy206, LT) → LT
new_primCompAux00(yvy206, EQ) → yvy206
new_primCompAux00(yvy206, GT) → GT
new_compare18(yvy49000, yvy50000, dg, dh) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, dg, dh), dg, dh)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), gd, ge) → new_asAs(new_esEs24(yvy4000, yvy3000, gd), new_esEs25(yvy4001, yvy3001, ge))
new_compare25(yvy49000, yvy50000, True, dg, dh) → EQ
new_compare25(yvy49000, yvy50000, False, dg, dh) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, dg, dh), dg, dh)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), db, dc) → new_pePe(new_lt6(yvy49000, yvy50000, db), new_asAs(new_esEs20(yvy49000, yvy50000, db), new_ltEs6(yvy49001, yvy50001, dc)))
new_compare110(yvy49000, yvy50000, True, dg, dh) → LT
new_compare110(yvy49000, yvy50000, False, dg, dh) → GT
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_lt11(yvy49000, yvy50000, de, df)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_lt17(yvy49000, yvy50000, ee)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_[], ed)) → new_lt15(yvy49000, yvy50000, ed)
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_lt10(yvy49000, yvy50000, dd)
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_lt14(yvy49000, yvy50000, ea, eb, ec)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_lt12(yvy49000, yvy50000, dg, dh)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_esEs4(yvy49000, yvy50000, dd)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_esEs6(yvy49000, yvy50000, dg, dh)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_esEs7(yvy49000, yvy50000, ea, eb, ec)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_esEs5(yvy49000, yvy50000, de, df)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_esEs10(yvy49000, yvy50000, ee)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_[], ed)) → new_esEs19(yvy49000, yvy50000, ed)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, fh)) → new_ltEs17(yvy49001, yvy50001, fh)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs13(yvy49001, yvy50001, fc, fd, ff)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ef)) → new_ltEs9(yvy49001, yvy50001, ef)
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, eg), eh)) → new_ltEs10(yvy49001, yvy50001, eg, eh)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fg)) → new_ltEs14(yvy49001, yvy50001, fg)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, fa), fb)) → new_ltEs5(yvy49001, yvy50001, fa, fb)
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs9(Nothing, Just(yvy50000), hc) → True
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, hg), hh)) → new_ltEs5(yvy49000, yvy50000, hg, hh)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, bae)) → new_ltEs17(yvy49000, yvy50000, bae)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], bad)) → new_ltEs14(yvy49000, yvy50000, bad)
new_ltEs9(Just(yvy49000), Nothing, hc) → False
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, hc) → True
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, baa), bab), bac)) → new_ltEs13(yvy49000, yvy50000, baa, bab, bac)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs19([], [], ha) → True
new_esEs19(:(yvy4000, yvy4001), [], ha) → False
new_esEs19([], :(yvy3000, yvy3001), ha) → False
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), ha) → new_asAs(new_esEs28(yvy4000, yvy3000, ha), new_esEs19(yvy4001, yvy3001, ha))
new_esEs28(yvy4000, yvy3000, app(ty_[], dea)) → new_esEs19(yvy4000, yvy3000, dea)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, ddd)) → new_esEs10(yvy4000, yvy3000, ddd)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, ddh)) → new_esEs4(yvy4000, yvy3000, ddh)
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dch), dda)) → new_esEs5(yvy4000, yvy3000, dch, dda)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs7(yvy4000, yvy3000, dde, ddf, ddg)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddb), ddc)) → new_esEs6(yvy4000, yvy3000, ddb, ddc)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_esEs15(True, True) → True
new_esEs15(False, False) → True
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gf, gg, gh) → new_asAs(new_esEs21(yvy4000, yvy3000, gf), new_asAs(new_esEs22(yvy4001, yvy3001, gg), new_esEs23(yvy4002, yvy3002, gh)))
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, bah), bba)) → new_esEs6(yvy4000, yvy3000, bah, bba)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs7(yvy4000, yvy3000, bbc, bbd, bbe)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bbg)) → new_esEs19(yvy4000, yvy3000, bbg)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bbb)) → new_esEs10(yvy4000, yvy3000, bbb)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bbf)) → new_esEs4(yvy4000, yvy3000, bbf)
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, baf), bag)) → new_esEs5(yvy4000, yvy3000, baf, bag)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, app(ty_[], bda)) → new_esEs19(yvy4001, yvy3001, bda)
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bch)) → new_esEs4(yvy4001, yvy3001, bch)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bcb), bcc)) → new_esEs6(yvy4001, yvy3001, bcb, bcc)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs7(yvy4001, yvy3001, bce, bcf, bcg)
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bcd)) → new_esEs10(yvy4001, yvy3001, bcd)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bbh), bca)) → new_esEs5(yvy4001, yvy3001, bbh, bca)
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bdb), bdc)) → new_esEs5(yvy4002, yvy3002, bdb, bdc)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, beb)) → new_esEs4(yvy4002, yvy3002, beb)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs7(yvy4002, yvy3002, bdg, bdh, bea)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_[], bec)) → new_esEs19(yvy4002, yvy3002, bec)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bdf)) → new_esEs10(yvy4002, yvy3002, bdf)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bdd), bde)) → new_esEs6(yvy4002, yvy3002, bdd, bde)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(LT, EQ) → False
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bd) → new_asAs(new_esEs11(yvy4000, yvy3000, bd), new_esEs12(yvy4001, yvy3001, bd))
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs18(@0, @0) → True
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Nothing, bf) → False
new_esEs4(Nothing, Just(yvy3000), bf) → False
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, cc)) → new_esEs10(yvy4000, yvy3000, cc)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_Maybe, dbd)) → new_esEs4(yvy4000, yvy3000, dbd)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, dab), gc) → new_esEs4(yvy4000, yvy3000, dab)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, cg)) → new_esEs4(yvy4000, yvy3000, cg)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(ty_Either, dad), dae)) → new_esEs5(yvy4000, yvy3000, dad, dae)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, chb), chc), gc) → new_esEs5(yvy4000, yvy3000, chb, chc)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, bg), bh)) → new_esEs5(yvy4000, yvy3000, bg, bh)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, ca), cb)) → new_esEs6(yvy4000, yvy3000, ca, cb)
new_esEs4(Nothing, Nothing, bf) → True
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], da)) → new_esEs19(yvy4000, yvy3000, da)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cd), ce), cf)) → new_esEs7(yvy4000, yvy3000, cd, ce, cf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], dac), gc) → new_esEs19(yvy4000, yvy3000, dac)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, gc) → new_esEs18(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chd), che), gc) → new_esEs6(yvy4000, yvy3000, chd, che)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(ty_@2, daf), dag)) → new_esEs6(yvy4000, yvy3000, daf, dag)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, gc) → new_esEs9(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, gc) → new_esEs16(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, chg), chh), daa), gc) → new_esEs7(yvy4000, yvy3000, chg, chh, daa)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_[], dbe)) → new_esEs19(yvy4000, yvy3000, dbe)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_Ratio, dah)) → new_esEs10(yvy4000, yvy3000, dah)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, gc) → new_esEs14(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, gc) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, gc) → new_esEs8(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, gc) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Right(yvy3000), gb, gc) → False
new_esEs5(Right(yvy4000), Left(yvy3000), gb, gc) → False
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, gc) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(app(ty_@3, dba), dbb), dbc)) → new_esEs7(yvy4000, yvy3000, dba, dbb, dbc)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, chf), gc) → new_esEs10(yvy4000, yvy3000, chf)
new_lt12(yvy49000, yvy50000, dg, dh) → new_esEs9(new_compare18(yvy49000, yvy50000, dg, dh), LT)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_lt14(yvy49000, yvy50000, ea, eb, ec) → new_esEs9(new_compare14(yvy49000, yvy50000, ea, eb, ec), LT)
new_compare14(yvy49000, yvy50000, ea, eb, ec) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_compare24(yvy49000, yvy50000, False, ea, eb, ec) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_compare24(yvy49000, yvy50000, True, ea, eb, ec) → EQ
new_compare111(yvy49000, yvy50000, True, ea, eb, ec) → LT
new_compare111(yvy49000, yvy50000, False, ea, eb, ec) → GT
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_compare211(yvy49000, yvy50000, True) → EQ
new_compare112(yvy49000, yvy50000, True) → LT
new_compare112(yvy49000, yvy50000, False) → GT
new_lt10(yvy49000, yvy50000, dd) → new_esEs9(new_compare19(yvy49000, yvy50000, dd), LT)
new_compare19(yvy49000, yvy50000, dd) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, dd), dd)
new_compare26(Just(yvy4900), Nothing, False, cch) → GT
new_compare26(Nothing, Just(yvy5000), False, cch) → LT
new_compare26(Nothing, Nothing, False, cch) → LT
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_lt15(yvy49000, yvy50000, ed) → new_esEs9(new_compare0(yvy49000, yvy50000, ed), LT)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_lt17(yvy49000, yvy50000, ee) → new_esEs9(new_compare8(yvy49000, yvy50000, ee), LT)
new_lt11(yvy49000, yvy50000, de, df) → new_esEs9(new_compare17(yvy49000, yvy50000, de, df), LT)
new_compare17(yvy49000, yvy50000, de, df) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, de, df), de, df)
new_compare23(yvy49000, yvy50000, False, de, df) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, de, df), de, df)
new_compare23(yvy49000, yvy50000, True, de, df) → EQ
new_compare12(yvy49000, yvy50000, False, de, df) → GT
new_compare12(yvy49000, yvy50000, True, de, df) → LT
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_compare210(yvy49000, yvy50000, True) → EQ
new_compare11(yvy49000, yvy50000, False) → GT
new_compare11(yvy49000, yvy50000, True) → LT
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, cad), cae)) → new_esEs5(yvy4000, yvy3000, cad, cae)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cbd)) → new_esEs4(yvy4000, yvy3000, cbd)
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbe)) → new_esEs19(yvy4000, yvy3000, cbe)
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, caf), cag)) → new_esEs6(yvy4000, yvy3000, caf, cag)
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs7(yvy4000, yvy3000, cba, cbb, cbc)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cah)) → new_esEs10(yvy4000, yvy3000, cah)
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbf), cbg)) → new_esEs5(yvy4001, yvy3001, cbf, cbg)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbh), cca)) → new_esEs6(yvy4001, yvy3001, cbh, cca)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccg)) → new_esEs19(yvy4001, yvy3001, ccg)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, ccb)) → new_esEs10(yvy4001, yvy3001, ccb)
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, ccf)) → new_esEs4(yvy4001, yvy3001, ccf)
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs7(yvy4001, yvy3001, ccc, ccd, cce)
new_esEs32(yvy400, yvy300, ty_Float) → new_esEs17(yvy400, yvy300)
new_esEs32(yvy400, yvy300, app(app(ty_@2, gd), ge)) → new_esEs6(yvy400, yvy300, gd, ge)
new_esEs32(yvy400, yvy300, ty_Ordering) → new_esEs9(yvy400, yvy300)
new_esEs32(yvy400, yvy300, app(ty_Maybe, bf)) → new_esEs4(yvy400, yvy300, bf)
new_esEs32(yvy400, yvy300, ty_Int) → new_esEs14(yvy400, yvy300)
new_esEs32(yvy400, yvy300, app(ty_Ratio, bd)) → new_esEs10(yvy400, yvy300, bd)
new_esEs32(yvy400, yvy300, ty_@0) → new_esEs18(yvy400, yvy300)
new_esEs32(yvy400, yvy300, app(app(ty_Either, gb), gc)) → new_esEs5(yvy400, yvy300, gb, gc)
new_esEs32(yvy400, yvy300, ty_Integer) → new_esEs13(yvy400, yvy300)
new_esEs32(yvy400, yvy300, app(app(app(ty_@3, gf), gg), gh)) → new_esEs7(yvy400, yvy300, gf, gg, gh)
new_esEs32(yvy400, yvy300, ty_Bool) → new_esEs15(yvy400, yvy300)
new_esEs32(yvy400, yvy300, app(ty_[], ha)) → new_esEs19(yvy400, yvy300, ha)
new_esEs32(yvy400, yvy300, ty_Double) → new_esEs16(yvy400, yvy300)
new_esEs32(yvy400, yvy300, ty_Char) → new_esEs8(yvy400, yvy300)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_esEs32(x0, x1, ty_Bool)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_compare210(x0, x1, False)
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare9(x0, x1)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(x0, Zero)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_lt19(x0, x1, ty_Int)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs15(x0, x1)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_compare28(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, ty_Char)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs32(x0, x1, ty_@0)
new_esEs19([], :(x0, x1), x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs32(x0, x1, ty_Int)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare12(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Char)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Nothing, Just(x0), x1)
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Nothing, Just(x0), False, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt6(x0, x1, ty_Integer)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt10(x0, x1, x2)
new_compare26(x0, x1, True, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Succ(x0))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs9(GT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(False, False)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_lt11(x0, x1, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_compare32(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(x0, x1, x2)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs19(:(x0, x1), [], x2)
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs6(x0, x1, ty_Int)
new_esEs19([], [], x0)
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs12(x0, x1)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, True)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs32(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare31(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs18(EQ, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Char(x0), Char(x1))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_ltEs18(GT, GT)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_ltEs9(Nothing, Nothing, x0)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare28(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_compare12(x0, x1, False, x2, x3)
new_compare26(Nothing, Nothing, False, x0)
new_compare13(x0, x1, False, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)

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

new_compare31(x0, x1)
new_compare30(x0)



↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ AND
                                        ↳ QDP
                                        ↳ QDP
                                          ↳ UsableRulesProof
                                            ↳ QDP
                                              ↳ QReductionProof
                                                ↳ QDP
                                                  ↳ QDPSizeChangeProof
                                  ↳ QDP

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

new_splitGT3(Nothing, yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitGT20(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), GT), h, ba)
new_splitGT21(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, False, bb, bc) → new_splitGT12(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, new_esEs9(new_compare33(yvy20, yvy15, bb), LT), bb, bc)
new_splitGT20(yvy31, yvy32, yvy33, Branch(yvy340, yvy341, yvy342, yvy343, yvy344), yvy400, True, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Just(yvy400), h, ba)
new_splitGT11(yvy31, yvy32, yvy33, yvy34, yvy400, True, h, ba) → new_splitGT0(yvy33, yvy400, h, ba)
new_splitGT3(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitGT21(yvy300, yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Just(yvy300), new_esEs32(yvy400, yvy300, h), h), GT), h, ba)
new_splitGT0(Branch(yvy340, yvy341, yvy342, yvy343, yvy344), yvy400, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, Just(yvy400), h, ba)
new_splitGT12(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, True, bb, bc) → new_splitGT0(yvy18, yvy20, bb, bc)
new_splitGT21(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, True, bb, bc) → new_splitGT0(yvy19, yvy20, bb, bc)
new_splitGT20(yvy31, yvy32, yvy33, yvy34, yvy400, False, h, ba) → new_splitGT11(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare32(yvy400, h), LT), h, ba)

The TRS R consists of the following rules:

new_compare33(yvy20, yvy15, bb) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, bb), bb)
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(ty_[], dcg)) → new_esEs19(yvy20, yvy15, dcg)
new_esEs30(yvy20, yvy15, app(ty_Maybe, dcf)) → new_esEs4(yvy20, yvy15, dcf)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dcc), dcd), dce)) → new_esEs7(yvy20, yvy15, dcc, dcd, dce)
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(ty_Ratio, dcb)) → new_esEs10(yvy20, yvy15, dcb)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, dbf), dbg)) → new_esEs5(yvy20, yvy15, dbf, dbg)
new_esEs30(yvy20, yvy15, app(app(ty_@2, dbh), dca)) → new_esEs6(yvy20, yvy15, dbh, dca)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_compare26(Just(yvy4900), Just(yvy5000), False, cch) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, cch), cch)
new_compare26(yvy490, yvy500, True, cch) → EQ
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, db), dc)) → new_ltEs5(yvy4900, yvy5000, db, dc)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, bfg), bed)) → new_ltEs10(yvy4900, yvy5000, bfg, bed)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, hc)) → new_ltEs9(yvy4900, yvy5000, hc)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, hb)) → new_ltEs17(yvy4900, yvy5000, hb)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(ty_[], be)) → new_ltEs14(yvy4900, yvy5000, be)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, cda), cdb), cdc)) → new_ltEs13(yvy4900, yvy5000, cda, cdb, cdc)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare13(yvy175, yvy176, True, ga) → LT
new_compare13(yvy175, yvy176, False, ga) → GT
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_compare16(@0, @0) → EQ
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_not(False) → True
new_not(True) → False
new_ltEs18(EQ, GT) → True
new_ltEs18(EQ, EQ) → True
new_ltEs18(LT, LT) → True
new_ltEs18(GT, GT) → True
new_ltEs18(LT, GT) → True
new_ltEs18(GT, LT) → False
new_ltEs18(GT, EQ) → False
new_ltEs18(EQ, LT) → False
new_ltEs18(LT, EQ) → True
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_primCmpNat2(Zero, yvy4900) → LT
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_primCmpNat0(yvy4900, Zero) → GT
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), cda, cdb, cdc) → new_pePe(new_lt20(yvy49000, yvy50000, cda), new_asAs(new_esEs26(yvy49000, yvy50000, cda), new_pePe(new_lt19(yvy49001, yvy50001, cdb), new_asAs(new_esEs27(yvy49001, yvy50001, cdb), new_ltEs20(yvy49002, yvy50002, cdc)))))
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, cea), ceb), cec)) → new_lt14(yvy49000, yvy50000, cea, ceb, cec)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, cee)) → new_lt17(yvy49000, yvy50000, cee)
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt20(yvy49000, yvy50000, app(app(ty_@2, cdg), cdh)) → new_lt12(yvy49000, yvy50000, cdg, cdh)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, cdd)) → new_lt10(yvy49000, yvy50000, cdd)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, cde), cdf)) → new_lt11(yvy49000, yvy50000, cde, cdf)
new_lt20(yvy49000, yvy50000, app(ty_[], ced)) → new_lt15(yvy49000, yvy50000, ced)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, cee)) → new_esEs10(yvy49000, yvy50000, cee)
new_esEs26(yvy49000, yvy50000, app(ty_[], ced)) → new_esEs19(yvy49000, yvy50000, ced)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, cdd)) → new_esEs4(yvy49000, yvy50000, cdd)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, cea), ceb), cec)) → new_esEs7(yvy49000, yvy50000, cea, ceb, cec)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, cde), cdf)) → new_esEs5(yvy49000, yvy50000, cde, cdf)
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, cdg), cdh)) → new_esEs6(yvy49000, yvy50000, cdg, cdh)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, cfg)) → new_lt17(yvy49001, yvy50001, cfg)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, cef)) → new_lt10(yvy49001, yvy50001, cef)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, app(app(ty_@2, cfa), cfb)) → new_lt12(yvy49001, yvy50001, cfa, cfb)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, cfc), cfd), cfe)) → new_lt14(yvy49001, yvy50001, cfc, cfd, cfe)
new_lt19(yvy49001, yvy50001, app(ty_[], cff)) → new_lt15(yvy49001, yvy50001, cff)
new_lt19(yvy49001, yvy50001, app(app(ty_Either, ceg), ceh)) → new_lt11(yvy49001, yvy50001, ceg, ceh)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs7(yvy49001, yvy50001, cfc, cfd, cfe)
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, ceg), ceh)) → new_esEs5(yvy49001, yvy50001, ceg, ceh)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, cfa), cfb)) → new_esEs6(yvy49001, yvy50001, cfa, cfb)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, cef)) → new_esEs4(yvy49001, yvy50001, cef)
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, cfg)) → new_esEs10(yvy49001, yvy50001, cfg)
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, app(ty_[], cff)) → new_esEs19(yvy49001, yvy50001, cff)
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, cfh)) → new_ltEs9(yvy49002, yvy50002, cfh)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, cha)) → new_ltEs17(yvy49002, yvy50002, cha)
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, cgc), cgd)) → new_ltEs5(yvy49002, yvy50002, cgc, cgd)
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(ty_[], cgh)) → new_ltEs14(yvy49002, yvy50002, cgh)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, cga), cgb)) → new_ltEs10(yvy49002, yvy50002, cga, cgb)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, cge), cgf), cgg)) → new_ltEs13(yvy49002, yvy50002, cge, cgf, cgg)
new_asAs(False, yvy182) → False
new_asAs(True, yvy182) → yvy182
new_pePe(False, yvy201) → yvy201
new_pePe(True, yvy201) → True
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, beh), bfa), bed) → new_ltEs5(yvy49000, yvy50000, beh, bfa)
new_ltEs10(Left(yvy49000), Right(yvy50000), bfg, bed) → True
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_[], bgh)) → new_ltEs14(yvy49000, yvy50000, bgh)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, bed) → new_ltEs12(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, bed) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, bfb), bfc), bfd), bed) → new_ltEs13(yvy49000, yvy50000, bfb, bfc, bfd)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(ty_@2, bgc), bgd)) → new_ltEs5(yvy49000, yvy50000, bgc, bgd)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, bed) → new_ltEs11(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, bed) → new_ltEs18(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(app(ty_@3, bge), bgf), bgg)) → new_ltEs13(yvy49000, yvy50000, bge, bgf, bgg)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, hd)) → new_ltEs9(yvy49000, yvy50000, hd)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, bee), bed) → new_ltEs9(yvy49000, yvy50000, bee)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, bef), beg), bed) → new_ltEs10(yvy49000, yvy50000, bef, beg)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_Maybe, bfh)) → new_ltEs9(yvy49000, yvy50000, bfh)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(app(ty_Either, bga), bgb)) → new_ltEs10(yvy49000, yvy50000, bga, bgb)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, he), hf)) → new_ltEs10(yvy49000, yvy50000, he, hf)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, bed) → new_ltEs16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, bed) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, bed) → new_ltEs7(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], bfe), bed) → new_ltEs14(yvy49000, yvy50000, bfe)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, app(ty_Ratio, bha)) → new_ltEs17(yvy49000, yvy50000, bha)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Left(yvy50000), bfg, bed) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), bfg, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, bff), bed) → new_ltEs17(yvy49000, yvy50000, bff)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, bed) → new_ltEs8(yvy49000, yvy50000)
new_ltEs8(False, True) → True
new_ltEs8(True, True) → True
new_ltEs8(True, False) → False
new_ltEs8(False, False) → True
new_ltEs17(yvy4900, yvy5000, hb) → new_fsEs(new_compare8(yvy4900, yvy5000, hb))
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs14(yvy4900, yvy5000, be) → new_fsEs(new_compare0(yvy4900, yvy5000, be))
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), be) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, be), be)
new_compare0([], [], be) → EQ
new_compare0(:(yvy49000, yvy49001), [], be) → GT
new_compare0([], :(yvy50000, yvy50001), be) → LT
new_primCompAux0(yvy49000, yvy50000, yvy202, be) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, be))
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(ty_[], cab)) → new_compare0(yvy49000, yvy50000, cab)
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bhg), bhh), caa)) → new_compare14(yvy49000, yvy50000, bhg, bhh, caa)
new_compare28(yvy49000, yvy50000, app(ty_Maybe, bhb)) → new_compare19(yvy49000, yvy50000, bhb)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, bhc), bhd)) → new_compare17(yvy49000, yvy50000, bhc, bhd)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, cac)) → new_compare8(yvy49000, yvy50000, cac)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, bhe), bhf)) → new_compare18(yvy49000, yvy50000, bhe, bhf)
new_primCompAux00(yvy206, LT) → LT
new_primCompAux00(yvy206, EQ) → yvy206
new_primCompAux00(yvy206, GT) → GT
new_compare18(yvy49000, yvy50000, dg, dh) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, dg, dh), dg, dh)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), gd, ge) → new_asAs(new_esEs24(yvy4000, yvy3000, gd), new_esEs25(yvy4001, yvy3001, ge))
new_compare25(yvy49000, yvy50000, True, dg, dh) → EQ
new_compare25(yvy49000, yvy50000, False, dg, dh) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, dg, dh), dg, dh)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), db, dc) → new_pePe(new_lt6(yvy49000, yvy50000, db), new_asAs(new_esEs20(yvy49000, yvy50000, db), new_ltEs6(yvy49001, yvy50001, dc)))
new_compare110(yvy49000, yvy50000, True, dg, dh) → LT
new_compare110(yvy49000, yvy50000, False, dg, dh) → GT
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_lt11(yvy49000, yvy50000, de, df)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_lt17(yvy49000, yvy50000, ee)
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_[], ed)) → new_lt15(yvy49000, yvy50000, ed)
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_lt10(yvy49000, yvy50000, dd)
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_lt14(yvy49000, yvy50000, ea, eb, ec)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_lt12(yvy49000, yvy50000, dg, dh)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, dd)) → new_esEs4(yvy49000, yvy50000, dd)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, dg), dh)) → new_esEs6(yvy49000, yvy50000, dg, dh)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, ea), eb), ec)) → new_esEs7(yvy49000, yvy50000, ea, eb, ec)
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, de), df)) → new_esEs5(yvy49000, yvy50000, de, df)
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, ee)) → new_esEs10(yvy49000, yvy50000, ee)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, app(ty_[], ed)) → new_esEs19(yvy49000, yvy50000, ed)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, fh)) → new_ltEs17(yvy49001, yvy50001, fh)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, fc), fd), ff)) → new_ltEs13(yvy49001, yvy50001, fc, fd, ff)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, ef)) → new_ltEs9(yvy49001, yvy50001, ef)
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, eg), eh)) → new_ltEs10(yvy49001, yvy50001, eg, eh)
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, app(ty_[], fg)) → new_ltEs14(yvy49001, yvy50001, fg)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, fa), fb)) → new_ltEs5(yvy49001, yvy50001, fa, fb)
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs9(Nothing, Just(yvy50000), hc) → True
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, hg), hh)) → new_ltEs5(yvy49000, yvy50000, hg, hh)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, bae)) → new_ltEs17(yvy49000, yvy50000, bae)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], bad)) → new_ltEs14(yvy49000, yvy50000, bad)
new_ltEs9(Just(yvy49000), Nothing, hc) → False
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs9(Nothing, Nothing, hc) → True
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, baa), bab), bac)) → new_ltEs13(yvy49000, yvy50000, baa, bab, bac)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs19([], [], ha) → True
new_esEs19(:(yvy4000, yvy4001), [], ha) → False
new_esEs19([], :(yvy3000, yvy3001), ha) → False
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), ha) → new_asAs(new_esEs28(yvy4000, yvy3000, ha), new_esEs19(yvy4001, yvy3001, ha))
new_esEs28(yvy4000, yvy3000, app(ty_[], dea)) → new_esEs19(yvy4000, yvy3000, dea)
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, ddd)) → new_esEs10(yvy4000, yvy3000, ddd)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, ddh)) → new_esEs4(yvy4000, yvy3000, ddh)
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, dch), dda)) → new_esEs5(yvy4000, yvy3000, dch, dda)
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs7(yvy4000, yvy3000, dde, ddf, ddg)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, ddb), ddc)) → new_esEs6(yvy4000, yvy3000, ddb, ddc)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_esEs15(True, True) → True
new_esEs15(False, False) → True
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gf, gg, gh) → new_asAs(new_esEs21(yvy4000, yvy3000, gf), new_asAs(new_esEs22(yvy4001, yvy3001, gg), new_esEs23(yvy4002, yvy3002, gh)))
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, bah), bba)) → new_esEs6(yvy4000, yvy3000, bah, bba)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs7(yvy4000, yvy3000, bbc, bbd, bbe)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_[], bbg)) → new_esEs19(yvy4000, yvy3000, bbg)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, bbb)) → new_esEs10(yvy4000, yvy3000, bbb)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, bbf)) → new_esEs4(yvy4000, yvy3000, bbf)
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, baf), bag)) → new_esEs5(yvy4000, yvy3000, baf, bag)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs22(yvy4001, yvy3001, app(ty_[], bda)) → new_esEs19(yvy4001, yvy3001, bda)
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, bch)) → new_esEs4(yvy4001, yvy3001, bch)
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, bcb), bcc)) → new_esEs6(yvy4001, yvy3001, bcb, bcc)
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs7(yvy4001, yvy3001, bce, bcf, bcg)
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, bcd)) → new_esEs10(yvy4001, yvy3001, bcd)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, bbh), bca)) → new_esEs5(yvy4001, yvy3001, bbh, bca)
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, bdb), bdc)) → new_esEs5(yvy4002, yvy3002, bdb, bdc)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, beb)) → new_esEs4(yvy4002, yvy3002, beb)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs7(yvy4002, yvy3002, bdg, bdh, bea)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_[], bec)) → new_esEs19(yvy4002, yvy3002, bec)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, bdf)) → new_esEs10(yvy4002, yvy3002, bdf)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, bdd), bde)) → new_esEs6(yvy4002, yvy3002, bdd, bde)
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(LT, EQ) → False
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bd) → new_asAs(new_esEs11(yvy4000, yvy3000, bd), new_esEs12(yvy4001, yvy3001, bd))
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs18(@0, @0) → True
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Nothing, bf) → False
new_esEs4(Nothing, Just(yvy3000), bf) → False
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, cc)) → new_esEs10(yvy4000, yvy3000, cc)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_Maybe, dbd)) → new_esEs4(yvy4000, yvy3000, dbd)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, dab), gc) → new_esEs4(yvy4000, yvy3000, dab)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, cg)) → new_esEs4(yvy4000, yvy3000, cg)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(ty_Either, dad), dae)) → new_esEs5(yvy4000, yvy3000, dad, dae)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, chb), chc), gc) → new_esEs5(yvy4000, yvy3000, chb, chc)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, bg), bh)) → new_esEs5(yvy4000, yvy3000, bg, bh)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, ca), cb)) → new_esEs6(yvy4000, yvy3000, ca, cb)
new_esEs4(Nothing, Nothing, bf) → True
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], da)) → new_esEs19(yvy4000, yvy3000, da)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, cd), ce), cf)) → new_esEs7(yvy4000, yvy3000, cd, ce, cf)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], dac), gc) → new_esEs19(yvy4000, yvy3000, dac)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, gc) → new_esEs18(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, chd), che), gc) → new_esEs6(yvy4000, yvy3000, chd, che)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(ty_@2, daf), dag)) → new_esEs6(yvy4000, yvy3000, daf, dag)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, gc) → new_esEs9(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, gc) → new_esEs16(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, chg), chh), daa), gc) → new_esEs7(yvy4000, yvy3000, chg, chh, daa)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_[], dbe)) → new_esEs19(yvy4000, yvy3000, dbe)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(ty_Ratio, dah)) → new_esEs10(yvy4000, yvy3000, dah)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, gc) → new_esEs14(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, gc) → new_esEs15(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, gc) → new_esEs8(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, gc) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Right(yvy3000), gb, gc) → False
new_esEs5(Right(yvy4000), Left(yvy3000), gb, gc) → False
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, gc) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, app(app(app(ty_@3, dba), dbb), dbc)) → new_esEs7(yvy4000, yvy3000, dba, dbb, dbc)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), gb, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, chf), gc) → new_esEs10(yvy4000, yvy3000, chf)
new_lt12(yvy49000, yvy50000, dg, dh) → new_esEs9(new_compare18(yvy49000, yvy50000, dg, dh), LT)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_lt14(yvy49000, yvy50000, ea, eb, ec) → new_esEs9(new_compare14(yvy49000, yvy50000, ea, eb, ec), LT)
new_compare14(yvy49000, yvy50000, ea, eb, ec) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_compare24(yvy49000, yvy50000, False, ea, eb, ec) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, ea, eb, ec), ea, eb, ec)
new_compare24(yvy49000, yvy50000, True, ea, eb, ec) → EQ
new_compare111(yvy49000, yvy50000, True, ea, eb, ec) → LT
new_compare111(yvy49000, yvy50000, False, ea, eb, ec) → GT
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_compare211(yvy49000, yvy50000, True) → EQ
new_compare112(yvy49000, yvy50000, True) → LT
new_compare112(yvy49000, yvy50000, False) → GT
new_lt10(yvy49000, yvy50000, dd) → new_esEs9(new_compare19(yvy49000, yvy50000, dd), LT)
new_compare19(yvy49000, yvy50000, dd) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, dd), dd)
new_compare26(Just(yvy4900), Nothing, False, cch) → GT
new_compare26(Nothing, Just(yvy5000), False, cch) → LT
new_compare26(Nothing, Nothing, False, cch) → LT
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_lt15(yvy49000, yvy50000, ed) → new_esEs9(new_compare0(yvy49000, yvy50000, ed), LT)
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_lt17(yvy49000, yvy50000, ee) → new_esEs9(new_compare8(yvy49000, yvy50000, ee), LT)
new_lt11(yvy49000, yvy50000, de, df) → new_esEs9(new_compare17(yvy49000, yvy50000, de, df), LT)
new_compare17(yvy49000, yvy50000, de, df) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, de, df), de, df)
new_compare23(yvy49000, yvy50000, False, de, df) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, de, df), de, df)
new_compare23(yvy49000, yvy50000, True, de, df) → EQ
new_compare12(yvy49000, yvy50000, False, de, df) → GT
new_compare12(yvy49000, yvy50000, True, de, df) → LT
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_compare210(yvy49000, yvy50000, True) → EQ
new_compare11(yvy49000, yvy50000, False) → GT
new_compare11(yvy49000, yvy50000, True) → LT
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, cad), cae)) → new_esEs5(yvy4000, yvy3000, cad, cae)
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, cbd)) → new_esEs4(yvy4000, yvy3000, cbd)
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(ty_[], cbe)) → new_esEs19(yvy4000, yvy3000, cbe)
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, caf), cag)) → new_esEs6(yvy4000, yvy3000, caf, cag)
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, cba), cbb), cbc)) → new_esEs7(yvy4000, yvy3000, cba, cbb, cbc)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, cah)) → new_esEs10(yvy4000, yvy3000, cah)
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, cbf), cbg)) → new_esEs5(yvy4001, yvy3001, cbf, cbg)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, cbh), cca)) → new_esEs6(yvy4001, yvy3001, cbh, cca)
new_esEs25(yvy4001, yvy3001, app(ty_[], ccg)) → new_esEs19(yvy4001, yvy3001, ccg)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, ccb)) → new_esEs10(yvy4001, yvy3001, ccb)
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, ccf)) → new_esEs4(yvy4001, yvy3001, ccf)
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs7(yvy4001, yvy3001, ccc, ccd, cce)
new_esEs32(yvy400, yvy300, ty_Float) → new_esEs17(yvy400, yvy300)
new_esEs32(yvy400, yvy300, app(app(ty_@2, gd), ge)) → new_esEs6(yvy400, yvy300, gd, ge)
new_esEs32(yvy400, yvy300, ty_Ordering) → new_esEs9(yvy400, yvy300)
new_esEs32(yvy400, yvy300, app(ty_Maybe, bf)) → new_esEs4(yvy400, yvy300, bf)
new_esEs32(yvy400, yvy300, ty_Int) → new_esEs14(yvy400, yvy300)
new_esEs32(yvy400, yvy300, app(ty_Ratio, bd)) → new_esEs10(yvy400, yvy300, bd)
new_esEs32(yvy400, yvy300, ty_@0) → new_esEs18(yvy400, yvy300)
new_esEs32(yvy400, yvy300, app(app(ty_Either, gb), gc)) → new_esEs5(yvy400, yvy300, gb, gc)
new_esEs32(yvy400, yvy300, ty_Integer) → new_esEs13(yvy400, yvy300)
new_esEs32(yvy400, yvy300, app(app(app(ty_@3, gf), gg), gh)) → new_esEs7(yvy400, yvy300, gf, gg, gh)
new_esEs32(yvy400, yvy300, ty_Bool) → new_esEs15(yvy400, yvy300)
new_esEs32(yvy400, yvy300, app(ty_[], ha)) → new_esEs19(yvy400, yvy300, ha)
new_esEs32(yvy400, yvy300, ty_Double) → new_esEs16(yvy400, yvy300)
new_esEs32(yvy400, yvy300, ty_Char) → new_esEs8(yvy400, yvy300)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_@0)
new_esEs18(@0, @0)
new_esEs32(x0, x1, ty_Bool)
new_esEs4(Nothing, Just(x0), x1)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_compare210(x0, x1, False)
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_compare9(x0, x1)
new_ltEs9(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1)
new_ltEs6(x0, x1, ty_@0)
new_esEs15(True, True)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(x0, Zero)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_lt19(x0, x1, ty_Int)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_lt14(x0, x1, x2, x3, x4)
new_primCmpNat2(Succ(x0), x1)
new_esEs23(x0, x1, ty_Bool)
new_compare14(x0, x1, x2, x3, x4)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_compare6(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs15(x0, x1)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_compare28(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_primCmpNat1(Zero, Zero)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs4(Nothing, Nothing, x0)
new_ltEs6(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, ty_Char)
new_compare28(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs32(x0, x1, ty_@0)
new_esEs19([], :(x0, x1), x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(GT, LT)
new_ltEs18(LT, GT)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2)
new_esEs25(x0, x1, app(ty_[], x2))
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs30(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primMulNat0(Zero, Zero)
new_ltEs4(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_ltEs18(EQ, LT)
new_ltEs18(LT, EQ)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs32(x0, x1, ty_Int)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_lt20(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_compare28(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_@0)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare12(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Char)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1, x2)
new_ltEs19(x0, x1, ty_Bool)
new_compare16(@0, @0)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs9(Nothing, Just(x0), x1)
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_lt12(x0, x1, x2, x3)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Char)
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare111(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Nothing, Just(x0), False, x1)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt6(x0, x1, ty_Integer)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, ty_Char)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt10(x0, x1, x2)
new_compare26(x0, x1, True, x2)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Succ(x0))
new_esEs16(Double(x0, x1), Double(x2, x3))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, True, x2, x3, x4)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs27(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Double)
new_compare111(x0, x1, True, x2, x3, x4)
new_esEs9(GT, GT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(False, False)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_lt11(x0, x1, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_compare32(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, LT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs8(False, True)
new_ltEs8(True, False)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_ltEs17(x0, x1, x2)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_compare25(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs28(x0, x1, ty_Bool)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs19(:(x0, x1), [], x2)
new_compare17(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs6(x0, x1, ty_Int)
new_esEs19([], [], x0)
new_compare24(x0, x1, False, x2, x3, x4)
new_lt4(x0, x1)
new_ltEs12(x0, x1)
new_esEs28(x0, x1, ty_Double)
new_ltEs6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Bool)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_ltEs18(EQ, GT)
new_ltEs18(GT, EQ)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Int)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_esEs24(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Double)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, True)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs32(x0, x1, ty_Integer)
new_primCompAux0(x0, x1, x2, x3)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_compare112(x0, x1, False)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare18(x0, x1, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulNat0(Zero, Succ(x0))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs18(EQ, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_lt20(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Char(x0), Char(x1))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_ltEs18(GT, GT)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_sr0(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_fsEs(x0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1, x2)
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, ty_Integer)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Integer)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_ltEs9(Nothing, Nothing, x0)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs6(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat1(Succ(x0), Zero)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare28(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_compare12(x0, x1, False, x2, x3)
new_compare26(Nothing, Nothing, False, x0)
new_compare13(x0, x1, False, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Just(x0), Just(x1), ty_Float)
new_esEs9(LT, LT)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_compare23(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, ty_Integer)
new_compare13(x0, x1, True, x2)

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

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



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

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

new_plusFM(Branch(yvy30, yvy31, yvy32, yvy33, yvy34), Branch(yvy40, yvy41, yvy42, yvy43, yvy44), h, ba) → new_plusFM(new_splitGT30(yvy30, yvy31, yvy32, yvy33, yvy34, yvy40, h, ba), yvy44, h, ba)
new_plusFM(Branch(yvy30, yvy31, yvy32, yvy33, yvy34), Branch(yvy40, yvy41, yvy42, yvy43, yvy44), h, ba) → new_plusFM(new_splitLT30(yvy30, yvy31, yvy32, yvy33, yvy34, yvy40, h, ba), yvy43, h, ba)

The TRS R consists of the following rules:

new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Maybe, cba)) → new_esEs4(yvy4000, yvy3000, cba)
new_ltEs19(yvy4900, yvy5000, app(app(ty_@2, cbc), cbd)) → new_ltEs5(yvy4900, yvy5000, cbc, cbd)
new_ltEs15(yvy4900, yvy5000) → new_fsEs(new_compare6(yvy4900, yvy5000))
new_esEs23(yvy4002, yvy3002, ty_Integer) → new_esEs13(yvy4002, yvy3002)
new_esEs32(yvy400, yvy300, ty_Float) → new_esEs17(yvy400, yvy300)
new_esEs28(yvy4000, yvy3000, app(ty_[], bhe)) → new_esEs19(yvy4000, yvy3000, bhe)
new_esEs24(yvy4000, yvy3000, app(app(ty_Either, bbc), bbd)) → new_esEs5(yvy4000, yvy3000, bbc, bbd)
new_esEs31(yvy400, yvy300, ty_Ordering) → new_esEs9(yvy400, yvy300)
new_esEs21(yvy4000, yvy3000, app(app(ty_@2, dg), dh)) → new_esEs6(yvy4000, yvy3000, dg, dh)
new_primCmpNat2(Zero, yvy4900) → LT
new_ltEs8(False, True) → True
new_lt19(yvy49001, yvy50001, ty_Double) → new_lt7(yvy49001, yvy50001)
new_esEs22(yvy4001, yvy3001, app(ty_[], ga)) → new_esEs19(yvy4001, yvy3001, ga)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_@2, ceh), cfa), ced) → new_ltEs5(yvy49000, yvy50000, ceh, cfa)
new_ltEs18(EQ, GT) → True
new_esEs25(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_esEs20(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_esEs25(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_mkBalBranch6Size_l(yvy54, yvy50, yvy51, yvy67, h, ba) → new_sizeFM(yvy67, h, ba)
new_lt19(yvy49001, yvy50001, ty_Char) → new_lt4(yvy49001, yvy50001)
new_ltEs19(yvy4900, yvy5000, ty_Char) → new_ltEs15(yvy4900, yvy5000)
new_esEs29(yvy400, yvy500, ty_Integer) → new_esEs13(yvy400, yvy500)
new_ltEs10(Left(yvy49000), Right(yvy50000), cfg, ced) → True
new_compare110(yvy49000, yvy50000, True, bhg, bhh) → LT
new_esEs29(yvy400, yvy500, app(ty_[], ce)) → new_esEs19(yvy400, yvy500, ce)
new_esEs23(yvy4002, yvy3002, app(app(ty_Either, gb), gc)) → new_esEs5(yvy4002, yvy3002, gb, gc)
new_primCmpNat1(Zero, Succ(yvy50000)) → LT
new_esEs20(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_compare27(Double(yvy49000, yvy49001), Double(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_esEs30(yvy20, yvy15, ty_Integer) → new_esEs13(yvy20, yvy15)
new_compare24(yvy49000, yvy50000, False, bah, bba, bbb) → new_compare111(yvy49000, yvy50000, new_ltEs13(yvy49000, yvy50000, bah, bba, bbb), bah, bba, bbb)
new_splitGT22(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, True, bb, bc) → new_splitGT4(yvy19, yvy20, bb, bc)
new_esEs4(Just(yvy4000), Nothing, cd) → False
new_esEs4(Nothing, Just(yvy3000), cd) → False
new_esEs24(yvy4000, yvy3000, app(ty_Maybe, bcc)) → new_esEs4(yvy4000, yvy3000, bcc)
new_ltEs6(yvy49001, yvy50001, app(ty_Ratio, cch)) → new_ltEs17(yvy49001, yvy50001, cch)
new_ltEs9(Nothing, Just(yvy50000), cda) → True
new_splitLT15(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, False, hd, bhf) → yvy33
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs28(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_[], beh), be) → new_esEs19(yvy4000, yvy3000, beh)
new_ltEs19(yvy4900, yvy5000, ty_Float) → new_ltEs4(yvy4900, yvy5000)
new_esEs22(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_ltEs12(yvy4900, yvy5000) → new_fsEs(new_compare10(yvy4900, yvy5000))
new_addToFM_C26(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_mkBalBranch(Just(yvy500), yvy51, new_addToFM_C0(yvy53, Just(yvy400), yvy41, h, ba), yvy54, h, ba)
new_esEs23(yvy4002, yvy3002, ty_Float) → new_esEs17(yvy4002, yvy3002)
new_ltEs20(yvy49002, yvy50002, ty_Double) → new_ltEs7(yvy49002, yvy50002)
new_esEs21(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs21(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_compare26(Just(yvy4900), Nothing, False, chb) → GT
new_esEs26(yvy49000, yvy50000, app(ty_Ratio, dag)) → new_esEs10(yvy49000, yvy50000, dag)
new_splitLT5(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), h, ba) → new_splitLT30(yvy330, yvy331, yvy332, yvy333, yvy334, Nothing, h, ba)
new_esEs28(yvy4000, yvy3000, app(ty_Ratio, bgh)) → new_esEs10(yvy4000, yvy3000, bgh)
new_esEs20(yvy49000, yvy50000, app(ty_Maybe, bgc)) → new_esEs4(yvy49000, yvy50000, bgc)
new_compare33(yvy20, yvy15, bb) → new_compare26(Just(yvy20), Just(yvy15), new_esEs30(yvy20, yvy15, bb), bb)
new_mkBalBranch6MkBalBranch3(yvy54, yvy50, yvy51, Branch(yvy670, yvy671, yvy672, yvy673, yvy674), True, h, ba) → new_mkBalBranch6MkBalBranch11(yvy54, yvy50, yvy51, yvy670, yvy671, yvy672, yvy673, yvy674, new_lt5(new_sizeFM(yvy674, h, ba), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM(yvy673, h, ba))), h, ba)
new_splitLT30(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitLT24(yvy300, yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Just(yvy300), new_esEs31(yvy400, yvy300, h), h), LT), h, ba)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Integer) → new_compare10(new_sr0(yvy49000, yvy50001), new_sr0(yvy50000, yvy49001))
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_lt5(yvy186, yvy185) → new_esEs9(new_compare9(yvy186, yvy185), LT)
new_esEs21(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_@0, be) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy49000, yvy50000, app(ty_[], daf)) → new_esEs19(yvy49000, yvy50000, daf)
new_compare16(@0, @0) → EQ
new_splitLT4(EmptyFM, yvy400, h, ba) → new_emptyFM(h, ba)
new_esEs25(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs23(yvy4002, yvy3002, app(ty_Maybe, hb)) → new_esEs4(yvy4002, yvy3002, hb)
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, ty_Int) → new_ltEs11(yvy49002, yvy50002)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_compare26(Nothing, Just(yvy5000), False, chb) → LT
new_splitLT24(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, False, hd, bhf) → new_splitLT15(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, new_gt2(yvy35, yvy30, hd), hd, bhf)
new_splitLT30(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitLT22(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare26(Nothing, Just(yvy300), False, h), LT), h, ba)
new_compare0(:(yvy49000, yvy49001), :(yvy50000, yvy50001), he) → new_primCompAux0(yvy49000, yvy50000, new_compare0(yvy49001, yvy50001, he), he)
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, app(ty_[], cgh)) → new_ltEs14(yvy49000, yvy50000, cgh)
new_esEs21(yvy4000, yvy3000, app(app(app(ty_@3, eb), ec), ed)) → new_esEs7(yvy4000, yvy3000, eb, ec, ed)
new_primCmpNat1(Succ(yvy49000), Succ(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, ty_Integer) → new_esEs13(yvy49001, yvy50001)
new_esEs29(yvy400, yvy500, app(app(app(ty_@3, ca), cb), cc)) → new_esEs7(yvy400, yvy500, ca, cb, cc)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Integer, ced) → new_ltEs12(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Char) → new_compare6(yvy49000, yvy50000)
new_primCmpInt3(yvy6200, yvy139) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy139)
new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt1(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_esEs20(yvy49000, yvy50000, app(app(ty_@2, bhg), bhh)) → new_esEs6(yvy49000, yvy50000, bhg, bhh)
new_esEs26(yvy49000, yvy50000, app(ty_Maybe, chf)) → new_esEs4(yvy49000, yvy50000, chf)
new_esEs23(yvy4002, yvy3002, ty_Char) → new_esEs8(yvy4002, yvy3002)
new_addToFM_C25(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_mkBalBranch(Nothing, yvy51, new_addToFM_C0(yvy53, Just(yvy400), yvy41, h, ba), yvy54, h, ba)
new_compare18(yvy49000, yvy50000, bhg, bhh) → new_compare25(yvy49000, yvy50000, new_esEs6(yvy49000, yvy50000, bhg, bhh), bhg, bhh)
new_ltEs6(yvy49001, yvy50001, ty_@0) → new_ltEs16(yvy49001, yvy50001)
new_lt20(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_esEs32(yvy400, yvy300, app(app(ty_@2, bf), bg)) → new_esEs6(yvy400, yvy300, bf, bg)
new_lt20(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_pePe(False, yvy201) → yvy201
new_esEs29(yvy400, yvy500, ty_Double) → new_esEs16(yvy400, yvy500)
new_mkBalBranch6MkBalBranch4(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), yvy50, yvy51, yvy67, True, h, ba) → new_mkBalBranch6MkBalBranch01(yvy540, yvy541, yvy542, yvy543, yvy544, yvy50, yvy51, yvy67, new_lt5(new_sizeFM(yvy543, h, ba), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM(yvy544, h, ba))), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), app(ty_Maybe, h), ba)
new_esEs15(False, True) → False
new_esEs15(True, False) → False
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, ty_Float) → new_ltEs4(yvy49000, yvy50000)
new_splitLT15(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, True, hd, bhf) → new_mkVBalBranch0(Just(yvy30), yvy31, yvy33, new_splitLT4(yvy34, yvy35, hd, bhf), hd, bhf)
new_lt6(yvy49000, yvy50000, ty_Double) → new_lt7(yvy49000, yvy50000)
new_esEs20(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_splitGT13(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, False, bb, bc) → yvy19
new_esEs31(yvy400, yvy300, ty_Float) → new_esEs17(yvy400, yvy300)
new_compare23(yvy49000, yvy50000, False, db, dc) → new_compare12(yvy49000, yvy50000, new_ltEs10(yvy49000, yvy50000, db, dc), db, dc)
new_esEs27(yvy49001, yvy50001, ty_Float) → new_esEs17(yvy49001, yvy50001)
new_esEs27(yvy49001, yvy50001, ty_Ordering) → new_esEs9(yvy49001, yvy50001)
new_splitLT23(yvy31, yvy32, yvy33, yvy34, yvy400, False, h, ba) → new_splitLT14(yvy31, yvy32, yvy33, yvy34, yvy400, new_gt1(yvy400, h), h, ba)
new_splitGT15(yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_mkVBalBranch0(Nothing, yvy31, new_splitGT5(yvy33, h, ba), yvy34, h, ba)
new_compare26(Nothing, Nothing, False, chb) → LT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Float, ced) → new_ltEs4(yvy49000, yvy50000)
new_lt19(yvy49001, yvy50001, app(ty_Ratio, dca)) → new_lt17(yvy49001, yvy50001, dca)
new_esEs30(yvy20, yvy15, ty_Bool) → new_esEs15(yvy20, yvy15)
new_esEs32(yvy400, yvy300, ty_Ordering) → new_esEs9(yvy400, yvy300)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(app(ty_@3, cfb), cfc), cfd), ced) → new_ltEs13(yvy49000, yvy50000, cfb, cfc, cfd)
new_compare9(yvy49, yvy50) → new_primCmpInt(yvy49, yvy50)
new_esEs31(yvy400, yvy300, ty_Bool) → new_esEs15(yvy400, yvy300)
new_ltEs6(yvy49001, yvy50001, app(app(app(ty_@3, ccd), cce), ccf)) → new_ltEs13(yvy49001, yvy50001, ccd, cce, ccf)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(app(ty_Either, cef), ceg), ced) → new_ltEs10(yvy49000, yvy50000, cef, ceg)
new_lt18(yvy49000, yvy50000) → new_esEs9(new_compare29(yvy49000, yvy50000), LT)
new_lt19(yvy49001, yvy50001, app(ty_Maybe, dah)) → new_lt10(yvy49001, yvy50001, dah)
new_ltEs20(yvy49002, yvy50002, ty_Integer) → new_ltEs12(yvy49002, yvy50002)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_primCmpInt0(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt3(yvy6200, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_@2, bea), beb), be) → new_esEs6(yvy4000, yvy3000, bea, beb)
new_esEs24(yvy4000, yvy3000, app(ty_[], bcd)) → new_esEs19(yvy4000, yvy3000, bcd)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Maybe, beg), be) → new_esEs4(yvy4000, yvy3000, beg)
new_esEs31(yvy400, yvy300, ty_Integer) → new_esEs13(yvy400, yvy300)
new_esEs32(yvy400, yvy300, app(ty_Maybe, cd)) → new_esEs4(yvy400, yvy300, cd)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_@2, cde), cdf)) → new_ltEs5(yvy49000, yvy50000, cde, cdf)
new_lt19(yvy49001, yvy50001, ty_Int) → new_lt5(yvy49001, yvy50001)
new_esEs23(yvy4002, yvy3002, app(app(app(ty_@3, gg), gh), ha)) → new_esEs7(yvy4002, yvy3002, gg, gh, ha)
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, app(app(ty_@2, cgc), cgd)) → new_ltEs5(yvy49000, yvy50000, cgc, cgd)
new_splitLT4(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy400, h, ba) → new_splitLT30(yvy330, yvy331, yvy332, yvy333, yvy334, Just(yvy400), h, ba)
new_esEs27(yvy49001, yvy50001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs7(yvy49001, yvy50001, dbe, dbf, dbg)
new_addToFM(yvy5, yvy40, yvy41, h, ba) → new_addToFM_C0(yvy5, yvy40, yvy41, h, ba)
new_ltEs20(yvy49002, yvy50002, ty_Bool) → new_ltEs8(yvy49002, yvy50002)
new_lt20(yvy49000, yvy50000, app(app(app(ty_@3, dac), dad), dae)) → new_lt14(yvy49000, yvy50000, dac, dad, dae)
new_esEs25(yvy4001, yvy3001, app(app(ty_Either, bce), bcf)) → new_esEs5(yvy4001, yvy3001, bce, bcf)
new_esEs25(yvy4001, yvy3001, app(app(ty_@2, bcg), bch)) → new_esEs6(yvy4001, yvy3001, bcg, bch)
new_compare28(yvy49000, yvy50000, ty_Bool) → new_compare15(yvy49000, yvy50000)
new_ltEs6(yvy49001, yvy50001, app(ty_Maybe, cbg)) → new_ltEs9(yvy49001, yvy50001, cbg)
new_splitLT5(EmptyFM, h, ba) → new_emptyFM(h, ba)
new_lt19(yvy49001, yvy50001, ty_Bool) → new_lt9(yvy49001, yvy50001)
new_esEs22(yvy4001, yvy3001, ty_Char) → new_esEs8(yvy4001, yvy3001)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Ratio, cec)) → new_ltEs17(yvy49000, yvy50000, cec)
new_esEs28(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_ltEs19(yvy4900, yvy5000, app(app(ty_Either, cfg), ced)) → new_ltEs10(yvy4900, yvy5000, cfg, ced)
new_ltEs5(@2(yvy49000, yvy49001), @2(yvy50000, yvy50001), cbc, cbd) → new_pePe(new_lt6(yvy49000, yvy50000, cbc), new_asAs(new_esEs20(yvy49000, yvy50000, cbc), new_ltEs6(yvy49001, yvy50001, cbd)))
new_splitLT14(yvy31, yvy32, yvy33, yvy34, yvy400, True, h, ba) → new_mkVBalBranch0(Nothing, yvy31, yvy33, new_splitLT4(yvy34, yvy400, h, ba), h, ba)
new_ltEs20(yvy49002, yvy50002, app(ty_Maybe, dcb)) → new_ltEs9(yvy49002, yvy50002, dcb)
new_esEs23(yvy4002, yvy3002, ty_Int) → new_esEs14(yvy4002, yvy3002)
new_esEs28(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs16(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_compare0([], [], he) → EQ
new_gt2(yvy35, yvy30, hd) → new_esEs9(new_compare33(yvy35, yvy30, hd), GT)
new_mkVBalBranch0(yvy40, yvy41, EmptyFM, yvy5, h, ba) → new_addToFM(yvy5, yvy40, yvy41, h, ba)
new_esEs24(yvy4000, yvy3000, app(app(ty_@2, bbe), bbf)) → new_esEs6(yvy4000, yvy3000, bbe, bbf)
new_pePe(True, yvy201) → True
new_primEqNat0(Zero, Zero) → True
new_esEs27(yvy49001, yvy50001, ty_@0) → new_esEs18(yvy49001, yvy50001)
new_compare28(yvy49000, yvy50000, ty_Double) → new_compare27(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Int, ced) → new_ltEs11(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bd, app(app(ty_@2, bfc), bfd)) → new_esEs6(yvy4000, yvy3000, bfc, bfd)
new_lt6(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_ltEs14(yvy4900, yvy5000, he) → new_fsEs(new_compare0(yvy4900, yvy5000, he))
new_mkBalBranch6MkBalBranch11(yvy54, yvy50, yvy51, yvy670, yvy671, yvy672, yvy673, Branch(yvy6740, yvy6741, yvy6742, yvy6743, yvy6744), False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), yvy6740, yvy6741, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), yvy670, yvy671, yvy673, yvy6743, app(ty_Maybe, h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), yvy50, yvy51, yvy6744, yvy54, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_ltEs6(yvy49001, yvy50001, app(app(ty_Either, cbh), cca)) → new_ltEs10(yvy49001, yvy50001, cbh, cca)
new_compare29(yvy49000, yvy50000) → new_compare211(yvy49000, yvy50000, new_esEs9(yvy49000, yvy50000))
new_addToFM_C23(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_mkBalBranch(Just(yvy500), yvy51, new_addToFM_C0(yvy53, Nothing, yvy41, h, ba), yvy54, h, ba)
new_esEs29(yvy400, yvy500, ty_Int) → new_esEs14(yvy400, yvy500)
new_ltEs18(EQ, EQ) → True
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Ordering, be) → new_esEs9(yvy4000, yvy3000)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_primCmpInt0(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_lt6(yvy49000, yvy50000, ty_Int) → new_lt5(yvy49000, yvy50000)
new_esEs26(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs19([], [], ce) → True
new_compare110(yvy49000, yvy50000, False, bhg, bhh) → GT
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_Ratio, cae)) → new_esEs10(yvy4000, yvy3000, cae)
new_esEs25(yvy4001, yvy3001, app(ty_[], bdf)) → new_esEs19(yvy4001, yvy3001, bdf)
new_addToFM_C23(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, False, h, ba) → new_addToFM_C14(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, new_gt0(yvy500, h), h, ba)
new_sr(yvy4001, yvy3001) → new_primMulInt(yvy4001, yvy3001)
new_primCmpInt1(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_mkBranchUnbox(yvy226, yvy224, yvy227, yvy231, cf, cg) → yvy231
new_addToFM_C14(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, False, h, ba) → Branch(Nothing, new_addToFM0(yvy51, yvy41, ba), yvy52, yvy53, yvy54)
new_compare12(yvy49000, yvy50000, False, db, dc) → GT
new_primCmpNat1(Zero, Zero) → EQ
new_primCompAux0(yvy49000, yvy50000, yvy202, he) → new_primCompAux00(yvy202, new_compare28(yvy49000, yvy50000, he))
new_esEs24(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_compare6(Char(yvy49000), Char(yvy50000)) → new_primCmpNat1(yvy49000, yvy50000)
new_ltEs18(LT, LT) → True
new_primCmpInt(Neg(Zero), Neg(Succ(yvy5000))) → new_primCmpNat0(yvy5000, Zero)
new_mkBalBranch6MkBalBranch5(yvy54, yvy50, yvy51, yvy67, False, h, ba) → new_mkBalBranch6MkBalBranch4(yvy54, yvy50, yvy51, yvy67, new_gt3(new_mkBalBranch6Size_r(yvy54, yvy50, yvy51, yvy67, h, ba), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_l(yvy54, yvy50, yvy51, yvy67, h, ba))), h, ba)
new_esEs31(yvy400, yvy300, app(app(app(ty_@3, ca), cb), cc)) → new_esEs7(yvy400, yvy300, ca, cb, cc)
new_esEs12(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Double, be) → new_esEs16(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_primPlusNat0(Succ(yvy1550), yvy300100) → Succ(Succ(new_primPlusNat1(yvy1550, yvy300100)))
new_splitLT22(yvy300, yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitLT5(yvy33, h, ba)
new_esEs20(yvy49000, yvy50000, app(app(app(ty_@3, bah), bba), bbb)) → new_esEs7(yvy49000, yvy50000, bah, bba, bbb)
new_lt6(yvy49000, yvy50000, app(app(ty_Either, db), dc)) → new_lt11(yvy49000, yvy50000, db, dc)
new_ltEs19(yvy4900, yvy5000, app(ty_Maybe, cda)) → new_ltEs9(yvy4900, yvy5000, cda)
new_esEs21(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Bool) → new_lt9(yvy49000, yvy50000)
new_esEs19([], :(yvy3000, yvy3001), ce) → False
new_esEs19(:(yvy4000, yvy4001), [], ce) → False
new_esEs13(Integer(yvy4000), Integer(yvy3000)) → new_primEqInt(yvy4000, yvy3000)
new_ltEs18(GT, GT) → True
new_primCmpNat1(Succ(yvy49000), Zero) → GT
new_splitGT24(yvy31, yvy32, yvy33, yvy34, yvy400, False, h, ba) → new_splitGT14(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare32(yvy400, h), LT), h, ba)
new_esEs9(EQ, EQ) → True
new_fsEs(yvy190) → new_not(new_esEs9(yvy190, GT))
new_esEs32(yvy400, yvy300, ty_Int) → new_esEs14(yvy400, yvy300)
new_compare24(yvy49000, yvy50000, True, bah, bba, bbb) → EQ
new_primEqInt(Neg(Succ(yvy40000)), Neg(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Ordering, ced) → new_ltEs18(yvy49000, yvy50000)
new_esEs15(True, True) → True
new_addToFM_C0(Branch(Nothing, yvy51, yvy52, yvy53, yvy54), Nothing, yvy41, h, ba) → new_addToFM_C24(yvy51, yvy52, yvy53, yvy54, yvy41, new_esEs9(new_compare26(Nothing, Nothing, True, h), LT), h, ba)
new_sizeFM1(Branch(yvy2270, yvy2271, yvy2272, yvy2273, yvy2274), cf, cg) → yvy2272
new_esEs30(yvy20, yvy15, app(ty_[], dee)) → new_esEs19(yvy20, yvy15, dee)
new_ltEs18(LT, GT) → True
new_splitLT22(yvy300, yvy31, yvy32, yvy33, yvy34, False, h, ba) → new_splitLT16(yvy300, yvy31, yvy32, yvy33, yvy34, new_gt0(yvy300, h), h, ba)
new_addToFM0(yvy51, yvy41, ba) → yvy41
new_primPlusNat1(Succ(yvy15500), Zero) → Succ(yvy15500)
new_primPlusNat1(Zero, Succ(yvy3001000)) → Succ(yvy3001000)
new_esEs30(yvy20, yvy15, app(ty_Maybe, ded)) → new_esEs4(yvy20, yvy15, ded)
new_ltEs19(yvy4900, yvy5000, app(ty_Ratio, dd)) → new_ltEs17(yvy4900, yvy5000, dd)
new_esEs30(yvy20, yvy15, ty_Float) → new_esEs17(yvy20, yvy15)
new_esEs25(yvy4001, yvy3001, app(ty_Ratio, bda)) → new_esEs10(yvy4001, yvy3001, bda)
new_esEs29(yvy400, yvy500, app(app(ty_Either, bd), be)) → new_esEs5(yvy400, yvy500, bd, be)
new_ltEs8(True, True) → True
new_esEs26(yvy49000, yvy50000, app(app(app(ty_@3, dac), dad), dae)) → new_esEs7(yvy49000, yvy50000, dac, dad, dae)
new_esEs28(yvy4000, yvy3000, app(ty_Maybe, bhd)) → new_esEs4(yvy4000, yvy3000, bhd)
new_esEs31(yvy400, yvy300, ty_Char) → new_esEs8(yvy400, yvy300)
new_splitLT13(yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_mkVBalBranch0(Nothing, yvy31, yvy33, new_splitLT5(yvy34, h, ba), h, ba)
new_ltEs18(GT, LT) → False
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(app(ty_@3, bed), bee), bef), be) → new_esEs7(yvy4000, yvy3000, bed, bee, bef)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs22(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_mkBalBranch6MkBalBranch5(yvy54, yvy50, yvy51, yvy67, True, h, ba) → new_mkBranch(Zero, yvy50, yvy51, yvy67, yvy54, app(ty_Maybe, h), ba)
new_ltEs11(yvy4900, yvy5000) → new_fsEs(new_compare9(yvy4900, yvy5000))
new_lt14(yvy49000, yvy50000, bah, bba, bbb) → new_esEs9(new_compare14(yvy49000, yvy50000, bah, bba, bbb), LT)
new_esEs27(yvy49001, yvy50001, app(app(ty_Either, dba), dbb)) → new_esEs5(yvy49001, yvy50001, dba, dbb)
new_ltEs20(yvy49002, yvy50002, app(ty_Ratio, ddc)) → new_ltEs17(yvy49002, yvy50002, ddc)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, app(app(app(ty_@3, dea), deb), dec)) → new_esEs7(yvy20, yvy15, dea, deb, dec)
new_compare10(Integer(yvy49000), Integer(yvy50000)) → new_primCmpInt(yvy49000, yvy50000)
new_primEqInt(Neg(Succ(yvy40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy30000))) → False
new_esEs20(yvy49000, yvy50000, ty_Bool) → new_esEs15(yvy49000, yvy50000)
new_esEs25(yvy4001, yvy3001, ty_Ordering) → new_esEs9(yvy4001, yvy3001)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(ty_Either, cdc), cdd)) → new_ltEs10(yvy49000, yvy50000, cdc, cdd)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_[], ceb)) → new_ltEs14(yvy49000, yvy50000, ceb)
new_esEs32(yvy400, yvy300, app(ty_Ratio, bh)) → new_esEs10(yvy400, yvy300, bh)
new_esEs31(yvy400, yvy300, app(app(ty_Either, bd), be)) → new_esEs5(yvy400, yvy300, bd, be)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_compare28(yvy49000, yvy50000, ty_Int) → new_compare9(yvy49000, yvy50000)
new_esEs28(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs21(yvy4000, yvy3000, app(ty_[], ef)) → new_esEs19(yvy4000, yvy3000, ef)
new_ltEs19(yvy4900, yvy5000, ty_Double) → new_ltEs7(yvy4900, yvy5000)
new_compare15(yvy49000, yvy50000) → new_compare210(yvy49000, yvy50000, new_esEs15(yvy49000, yvy50000))
new_ltEs20(yvy49002, yvy50002, app(app(ty_@2, dce), dcf)) → new_ltEs5(yvy49002, yvy50002, dce, dcf)
new_ltEs16(yvy4900, yvy5000) → new_fsEs(new_compare16(yvy4900, yvy5000))
new_esEs5(Right(yvy4000), Right(yvy3000), bd, app(ty_[], bgb)) → new_esEs19(yvy4000, yvy3000, bgb)
new_primMinusNat0(Succ(yvy18900), Zero) → Pos(Succ(yvy18900))
new_lt20(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_splitGT24(yvy31, yvy32, yvy33, yvy34, yvy400, True, h, ba) → new_splitGT4(yvy34, yvy400, h, ba)
new_esEs22(yvy4001, yvy3001, app(ty_Maybe, fh)) → new_esEs4(yvy4001, yvy3001, fh)
new_sizeFM(EmptyFM, h, ba) → Pos(Zero)
new_esEs25(yvy4001, yvy3001, app(ty_Maybe, bde)) → new_esEs4(yvy4001, yvy3001, bde)
new_compare112(yvy49000, yvy50000, True) → LT
new_splitLT30(Nothing, yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitLT23(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), LT), h, ba)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Succ(yvy30000))) → new_primEqNat0(yvy40000, yvy30000)
new_esEs6(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bf, bg) → new_asAs(new_esEs24(yvy4000, yvy3000, bf), new_esEs25(yvy4001, yvy3001, bg))
new_lt19(yvy49001, yvy50001, app(app(ty_@2, dbc), dbd)) → new_lt12(yvy49001, yvy50001, dbc, dbd)
new_splitGT23(yvy300, yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_splitGT5(yvy34, h, ba)
new_lt9(yvy49000, yvy50000) → new_esEs9(new_compare15(yvy49000, yvy50000), LT)
new_compare12(yvy49000, yvy50000, True, db, dc) → LT
new_splitGT30(Nothing, yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitGT15(yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare30(h), LT), h, ba)
new_mkBalBranch6MkBalBranch11(yvy54, yvy50, yvy51, yvy670, yvy671, yvy672, yvy673, yvy674, True, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), yvy670, yvy671, yvy673, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), yvy50, yvy51, yvy674, yvy54, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_esEs5(Right(yvy4000), Right(yvy3000), bd, app(app(ty_Either, bfa), bfb)) → new_esEs5(yvy4000, yvy3000, bfa, bfb)
new_ltEs20(yvy49002, yvy50002, ty_@0) → new_ltEs16(yvy49002, yvy50002)
new_esEs8(Char(yvy4000), Char(yvy3000)) → new_primEqNat0(yvy4000, yvy3000)
new_primEqNat0(Succ(yvy40000), Succ(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, app(app(app(ty_@3, cge), cgf), cgg)) → new_ltEs13(yvy49000, yvy50000, cge, cgf, cgg)
new_esEs28(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs12(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_ltEs19(yvy4900, yvy5000, app(ty_[], he)) → new_ltEs14(yvy4900, yvy5000, he)
new_esEs5(Right(yvy4000), Right(yvy3000), bd, app(ty_Ratio, bfe)) → new_esEs10(yvy4000, yvy3000, bfe)
new_splitGT4(EmptyFM, yvy400, h, ba) → new_emptyFM(h, ba)
new_splitGT30(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitGT22(yvy300, yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Just(yvy300), new_esEs32(yvy400, yvy300, h), h), GT), h, ba)
new_compare111(yvy49000, yvy50000, True, bah, bba, bbb) → LT
new_gt3(yvy152, yvy151) → new_esEs9(new_compare9(yvy152, yvy151), GT)
new_esEs20(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_primCompAux00(yvy206, LT) → LT
new_esEs30(yvy20, yvy15, ty_Int) → new_esEs14(yvy20, yvy15)
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_splitGT14(yvy31, yvy32, yvy33, yvy34, yvy400, True, h, ba) → new_mkVBalBranch0(Nothing, yvy31, new_splitGT4(yvy33, yvy400, h, ba), yvy34, h, ba)
new_esEs23(yvy4002, yvy3002, ty_Bool) → new_esEs15(yvy4002, yvy3002)
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, app(app(ty_Either, cga), cgb)) → new_ltEs10(yvy49000, yvy50000, cga, cgb)
new_ltEs19(yvy4900, yvy5000, ty_Bool) → new_ltEs8(yvy4900, yvy5000)
new_addToFM_C13(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_mkBalBranch(Just(yvy500), yvy51, yvy53, new_addToFM_C0(yvy54, Just(yvy400), yvy41, h, ba), h, ba)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Int, be) → new_esEs14(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy30000))) → False
new_esEs22(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_lt20(yvy49000, yvy50000, app(ty_Ratio, dag)) → new_lt17(yvy49000, yvy50000, dag)
new_esEs21(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare13(yvy175, yvy176, True, da) → LT
new_esEs25(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_primCmpInt1(Succ(yvy6200), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_primCmpInt2(yvy6200, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, Succ(yvy6200), yvy63, yvy64, h, ba))
new_esEs23(yvy4002, yvy3002, app(ty_[], hc)) → new_esEs19(yvy4002, yvy3002, hc)
new_esEs32(yvy400, yvy300, ty_@0) → new_esEs18(yvy400, yvy300)
new_esEs23(yvy4002, yvy3002, ty_@0) → new_esEs18(yvy4002, yvy3002)
new_lt6(yvy49000, yvy50000, app(ty_Ratio, cbf)) → new_lt17(yvy49000, yvy50000, cbf)
new_lt15(yvy49000, yvy50000, cbe) → new_esEs9(new_compare0(yvy49000, yvy50000, cbe), LT)
new_splitGT16(yvy300, yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_mkVBalBranch0(Just(yvy300), yvy31, new_splitGT5(yvy33, h, ba), yvy34, h, ba)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(ty_Maybe, cdb)) → new_ltEs9(yvy49000, yvy50000, cdb)
new_addToFM_C15(yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_mkBalBranch(Nothing, yvy51, yvy53, new_addToFM_C0(yvy54, Nothing, yvy41, h, ba), h, ba)
new_compare31(yvy300, h) → new_compare26(Nothing, Just(yvy300), False, h)
new_compare14(yvy49000, yvy50000, bah, bba, bbb) → new_compare24(yvy49000, yvy50000, new_esEs7(yvy49000, yvy50000, bah, bba, bbb), bah, bba, bbb)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy5000))) → LT
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_Either, caa), cab)) → new_esEs5(yvy4000, yvy3000, caa, cab)
new_addToFM_C0(Branch(Just(yvy500), yvy51, yvy52, yvy53, yvy54), Just(yvy400), yvy41, h, ba) → new_addToFM_C26(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_esEs9(new_compare26(Just(yvy400), Just(yvy500), new_esEs29(yvy400, yvy500, h), h), LT), h, ba)
new_esEs20(yvy49000, yvy50000, app(app(ty_Either, db), dc)) → new_esEs5(yvy49000, yvy50000, db, dc)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Char) → new_esEs8(yvy4000, yvy3000)
new_mkBalBranch6MkBalBranch01(yvy540, yvy541, yvy542, Branch(yvy5430, yvy5431, yvy5432, yvy5433, yvy5434), yvy544, yvy50, yvy51, yvy67, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), yvy5430, yvy5431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), yvy50, yvy51, yvy67, yvy5433, app(ty_Maybe, h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy540, yvy541, yvy5434, yvy544, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_compare210(yvy49000, yvy50000, False) → new_compare11(yvy49000, yvy50000, new_ltEs8(yvy49000, yvy50000))
new_ltEs6(yvy49001, yvy50001, ty_Ordering) → new_ltEs18(yvy49001, yvy50001)
new_esEs5(Right(yvy4000), Right(yvy3000), bd, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_sr0(Integer(yvy490000), Integer(yvy500010)) → Integer(new_primMulInt(yvy490000, yvy500010))
new_esEs31(yvy400, yvy300, ty_Int) → new_esEs14(yvy400, yvy300)
new_primPlusNat1(Succ(yvy15500), Succ(yvy3001000)) → Succ(Succ(new_primPlusNat1(yvy15500, yvy3001000)))
new_esEs31(yvy400, yvy300, app(ty_Ratio, bh)) → new_esEs10(yvy400, yvy300, bh)
new_ps(Pos(yvy1890), Pos(yvy1880)) → Pos(new_primPlusNat1(yvy1890, yvy1880))
new_primEqInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → False
new_primEqInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → False
new_ltEs20(yvy49002, yvy50002, app(ty_[], ddb)) → new_ltEs14(yvy49002, yvy50002, ddb)
new_esEs28(yvy4000, yvy3000, app(app(ty_Either, bgd), bge)) → new_esEs5(yvy4000, yvy3000, bgd, bge)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(ty_@2, cac), cad)) → new_esEs6(yvy4000, yvy3000, cac, cad)
new_esEs32(yvy400, yvy300, app(app(ty_Either, bd), be)) → new_esEs5(yvy400, yvy300, bd, be)
new_esEs24(yvy4000, yvy3000, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_mkBalBranch6MkBalBranch3(yvy54, yvy50, yvy51, EmptyFM, True, h, ba) → error([])
new_esEs31(yvy400, yvy300, app(ty_[], ce)) → new_esEs19(yvy400, yvy300, ce)
new_compare30(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs32(yvy400, yvy300, ty_Integer) → new_esEs13(yvy400, yvy300)
new_esEs22(yvy4001, yvy3001, app(app(ty_@2, fa), fb)) → new_esEs6(yvy4001, yvy3001, fa, fb)
new_primEqInt(Pos(Zero), Neg(Succ(yvy30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy30000))) → False
new_primCmpNat2(Succ(yvy5000), yvy4900) → new_primCmpNat1(yvy5000, yvy4900)
new_lt8(yvy49000, yvy50000) → new_esEs9(new_compare7(yvy49000, yvy50000), LT)
new_compare28(yvy49000, yvy50000, app(ty_[], baf)) → new_compare0(yvy49000, yvy50000, baf)
new_ltEs9(Just(yvy49000), Nothing, cda) → False
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Bool, be) → new_esEs15(yvy4000, yvy3000)
new_primCompAux00(yvy206, EQ) → yvy206
new_compare28(yvy49000, yvy50000, ty_Ordering) → new_compare29(yvy49000, yvy50000)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_lt5(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), h, ba)), h, ba)
new_splitGT30(Just(yvy300), yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitGT23(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare26(Nothing, Just(yvy300), False, h), GT), h, ba)
new_esEs23(yvy4002, yvy3002, app(ty_Ratio, gf)) → new_esEs10(yvy4002, yvy3002, gf)
new_splitLT16(yvy300, yvy31, yvy32, yvy33, yvy34, True, h, ba) → new_mkVBalBranch0(Just(yvy300), yvy31, yvy33, new_splitLT5(yvy34, h, ba), h, ba)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Char, be) → new_esEs8(yvy4000, yvy3000)
new_ltEs6(yvy49001, yvy50001, ty_Integer) → new_ltEs12(yvy49001, yvy50001)
new_compare28(yvy49000, yvy50000, app(app(app(ty_@3, bac), bad), bae)) → new_compare14(yvy49000, yvy50000, bac, bad, bae)
new_compare26(Just(yvy4900), Just(yvy5000), False, chb) → new_compare13(yvy4900, yvy5000, new_ltEs19(yvy4900, yvy5000, chb), chb)
new_emptyFM(h, ba) → EmptyFM
new_lt6(yvy49000, yvy50000, ty_Integer) → new_lt13(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, ty_Double) → new_esEs16(yvy49001, yvy50001)
new_ltEs19(yvy4900, yvy5000, app(app(app(ty_@3, chc), chd), che)) → new_ltEs13(yvy4900, yvy5000, chc, chd, che)
new_addToFM_C13(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, False, h, ba) → Branch(Just(yvy400), new_addToFM0(yvy51, yvy41, ba), yvy52, yvy53, yvy54)
new_compare26(yvy490, yvy500, True, chb) → EQ
new_lt20(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_compare17(yvy49000, yvy50000, db, dc) → new_compare23(yvy49000, yvy50000, new_esEs5(yvy49000, yvy50000, db, dc), db, dc)
new_ltEs18(GT, EQ) → False
new_esEs30(yvy20, yvy15, app(ty_Ratio, ddh)) → new_esEs10(yvy20, yvy15, ddh)
new_addToFM_C16(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, True, h, ba) → new_mkBalBranch(Nothing, yvy51, yvy53, new_addToFM_C0(yvy54, Just(yvy400), yvy41, h, ba), h, ba)
new_ltEs8(True, False) → False
new_not(False) → True
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_@0, ced) → new_ltEs16(yvy49000, yvy50000)
new_mkBalBranch6MkBalBranch01(yvy540, yvy541, yvy542, yvy543, yvy544, yvy50, yvy51, yvy67, True, h, ba) → new_mkBranch(Succ(Succ(Zero)), yvy540, yvy541, new_mkBranch(Succ(Succ(Succ(Zero))), yvy50, yvy51, yvy67, yvy543, app(ty_Maybe, h), ba), yvy544, app(ty_Maybe, h), ba)
new_esEs29(yvy400, yvy500, ty_@0) → new_esEs18(yvy400, yvy500)
new_primCmpInt1(Zero, yvy50, yvy51, Pos(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → LT
new_esEs20(yvy49000, yvy50000, app(ty_Ratio, cbf)) → new_esEs10(yvy49000, yvy50000, cbf)
new_primPlusNat0(Zero, yvy300100) → Succ(yvy300100)
new_esEs23(yvy4002, yvy3002, app(app(ty_@2, gd), ge)) → new_esEs6(yvy4002, yvy3002, gd, ge)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Ordering) → new_ltEs18(yvy49000, yvy50000)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Float, be) → new_esEs17(yvy4000, yvy3000)
new_ltEs9(Nothing, Nothing, cda) → True
new_esEs9(GT, GT) → True
new_compare28(yvy49000, yvy50000, app(ty_Maybe, hf)) → new_compare19(yvy49000, yvy50000, hf)
new_lt6(yvy49000, yvy50000, ty_@0) → new_lt16(yvy49000, yvy50000)
new_compare8(:%(yvy49000, yvy49001), :%(yvy50000, yvy50001), ty_Int) → new_compare9(new_sr(yvy49000, yvy50001), new_sr(yvy50000, yvy49001))
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Char, ced) → new_ltEs15(yvy49000, yvy50000)
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Zero), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → EQ
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkBalBranch(yvy50, yvy51, new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), yvy53, h, ba), yvy54, h, ba)
new_ltEs18(EQ, LT) → False
new_compare0(:(yvy49000, yvy49001), [], he) → GT
new_esEs5(Right(yvy4000), Right(yvy3000), bd, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs5(Right(yvy4000), Right(yvy3000), bd, ty_Int) → new_esEs14(yvy4000, yvy3000)
new_ltEs18(LT, EQ) → True
new_mkBalBranch6MkBalBranch3(yvy54, yvy50, yvy51, yvy67, False, h, ba) → new_mkBranch(Succ(Zero), yvy50, yvy51, yvy67, yvy54, app(ty_Maybe, h), ba)
new_lt20(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_lt7(yvy49000, yvy50000) → new_esEs9(new_compare27(yvy49000, yvy50000), LT)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_esEs26(yvy49000, yvy50000, app(app(ty_Either, chg), chh)) → new_esEs5(yvy49000, yvy50000, chg, chh)
new_lt6(yvy49000, yvy50000, app(ty_[], cbe)) → new_lt15(yvy49000, yvy50000, cbe)
new_primCmpInt0(Zero, yvy50, yvy51, Neg(Succ(yvy5200)), yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → GT
new_esEs28(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_mkBalBranch6Size_r(yvy54, yvy50, yvy51, yvy67, h, ba) → new_sizeFM(yvy54, h, ba)
new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_esEs9(new_primCmpInt0(yvy620, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), LT), h, ba)
new_ltEs6(yvy49001, yvy50001, app(ty_[], ccg)) → new_ltEs14(yvy49001, yvy50001, ccg)
new_addToFM_C26(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, False, h, ba) → new_addToFM_C13(yvy500, yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_gt2(yvy400, yvy500, h), h, ba)
new_primCmpInt(Pos(Succ(yvy4900)), Neg(yvy500)) → GT
new_esEs22(yvy4001, yvy3001, app(app(app(ty_@3, fd), ff), fg)) → new_esEs7(yvy4001, yvy3001, fd, ff, fg)
new_ltEs19(yvy4900, yvy5000, ty_Integer) → new_ltEs12(yvy4900, yvy5000)
new_lt6(yvy49000, yvy50000, ty_Char) → new_lt4(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, app(ty_Maybe, bgc)) → new_lt10(yvy49000, yvy50000, bgc)
new_lt19(yvy49001, yvy50001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_lt14(yvy49001, yvy50001, dbe, dbf, dbg)
new_lt19(yvy49001, yvy50001, app(ty_[], dbh)) → new_lt15(yvy49001, yvy50001, dbh)
new_primMulInt(Pos(yvy40010), Pos(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs28(yvy4000, yvy3000, app(app(app(ty_@3, bha), bhb), bhc)) → new_esEs7(yvy4000, yvy3000, bha, bhb, bhc)
new_esEs7(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), ca, cb, cc) → new_asAs(new_esEs21(yvy4000, yvy3000, ca), new_asAs(new_esEs22(yvy4001, yvy3001, cb), new_esEs23(yvy4002, yvy3002, cc)))
new_lt6(yvy49000, yvy50000, ty_Ordering) → new_lt18(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, ty_Ordering) → new_ltEs18(yvy49002, yvy50002)
new_esEs5(Right(yvy4000), Left(yvy3000), bd, be) → False
new_esEs5(Left(yvy4000), Right(yvy3000), bd, be) → False
new_esEs23(yvy4002, yvy3002, ty_Ordering) → new_esEs9(yvy4002, yvy3002)
new_primMulInt(Neg(yvy40010), Neg(yvy30010)) → Pos(new_primMulNat0(yvy40010, yvy30010))
new_esEs27(yvy49001, yvy50001, app(app(ty_@2, dbc), dbd)) → new_esEs6(yvy49001, yvy50001, dbc, dbd)
new_esEs29(yvy400, yvy500, app(app(ty_@2, bf), bg)) → new_esEs6(yvy400, yvy500, bf, bg)
new_esEs24(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Ratio, ea)) → new_esEs10(yvy4000, yvy3000, ea)
new_esEs17(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_esEs14(new_sr(yvy4000, yvy3000), new_sr(yvy4001, yvy3001))
new_primEqNat0(Zero, Succ(yvy30000)) → False
new_primEqNat0(Succ(yvy40000), Zero) → False
new_ltEs8(False, False) → True
new_esEs22(yvy4001, yvy3001, ty_Float) → new_esEs17(yvy4001, yvy3001)
new_compare19(yvy49000, yvy50000, bgc) → new_compare26(yvy49000, yvy50000, new_esEs4(yvy49000, yvy50000, bgc), bgc)
new_splitGT15(yvy31, yvy32, yvy33, yvy34, False, h, ba) → yvy34
new_ltEs4(yvy4900, yvy5000) → new_fsEs(new_compare7(yvy4900, yvy5000))
new_lt20(yvy49000, yvy50000, app(app(ty_@2, daa), dab)) → new_lt12(yvy49000, yvy50000, daa, dab)
new_ltEs9(Just(yvy49000), Just(yvy50000), app(app(app(ty_@3, cdg), cdh), cea)) → new_ltEs13(yvy49000, yvy50000, cdg, cdh, cea)
new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, yvy62, yvy63, yvy64), EmptyFM, h, ba) → new_addToFM(Branch(yvy60, yvy61, yvy62, yvy63, yvy64), yvy40, yvy41, h, ba)
new_gt(h) → new_esEs9(new_compare30(h), GT)
new_compare25(yvy49000, yvy50000, True, bhg, bhh) → EQ
new_ltEs20(yvy49002, yvy50002, ty_Char) → new_ltEs15(yvy49002, yvy50002)
new_lt19(yvy49001, yvy50001, app(app(ty_Either, dba), dbb)) → new_lt11(yvy49001, yvy50001, dba, dbb)
new_lt20(yvy49000, yvy50000, app(ty_Maybe, chf)) → new_lt10(yvy49000, yvy50000, chf)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs4(Nothing, Nothing, cd) → True
new_primCmpInt(Pos(Succ(yvy4900)), Pos(yvy500)) → new_primCmpNat0(yvy4900, yvy500)
new_compare111(yvy49000, yvy50000, False, bah, bba, bbb) → GT
new_splitGT4(Branch(yvy340, yvy341, yvy342, yvy343, yvy344), yvy400, h, ba) → new_splitGT30(yvy340, yvy341, yvy342, yvy343, yvy344, Just(yvy400), h, ba)
new_compare210(yvy49000, yvy50000, True) → EQ
new_primCmpNat0(yvy4900, Zero) → GT
new_sizeFM(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_lt16(yvy49000, yvy50000) → new_esEs9(new_compare16(yvy49000, yvy50000), LT)
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Double, ced) → new_ltEs7(yvy49000, yvy50000)
new_esEs27(yvy49001, yvy50001, app(ty_Maybe, dah)) → new_esEs4(yvy49001, yvy50001, dah)
new_splitGT13(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, True, bb, bc) → new_mkVBalBranch0(Just(yvy15), yvy16, new_splitGT4(yvy18, yvy20, bb, bc), yvy19, bb, bc)
new_compare28(yvy49000, yvy50000, app(app(ty_Either, hg), hh)) → new_compare17(yvy49000, yvy50000, hg, hh)
new_ltEs20(yvy49002, yvy50002, ty_Float) → new_ltEs4(yvy49002, yvy50002)
new_ltEs20(yvy49002, yvy50002, app(app(ty_Either, dcc), dcd)) → new_ltEs10(yvy49002, yvy50002, dcc, dcd)
new_lt20(yvy49000, yvy50000, app(app(ty_Either, chg), chh)) → new_lt11(yvy49000, yvy50000, chg, chh)
new_compare13(yvy175, yvy176, False, da) → GT
new_esEs27(yvy49001, yvy50001, app(ty_Ratio, dca)) → new_esEs10(yvy49001, yvy50001, dca)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_mkBalBranch6MkBalBranch4(yvy54, yvy50, yvy51, yvy67, False, h, ba) → new_mkBalBranch6MkBalBranch3(yvy54, yvy50, yvy51, yvy67, new_gt3(new_mkBalBranch6Size_l(yvy54, yvy50, yvy51, yvy67, h, ba), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_r(yvy54, yvy50, yvy51, yvy67, h, ba))), h, ba)
new_compare23(yvy49000, yvy50000, True, db, dc) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(yvy5000))) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_[], cfe), ced) → new_ltEs14(yvy49000, yvy50000, cfe)
new_esEs5(Right(yvy4000), Right(yvy3000), bd, ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Char) → new_esEs8(yvy20, yvy15)
new_esEs5(Left(yvy4000), Left(yvy3000), ty_Integer, be) → new_esEs13(yvy4000, yvy3000)
new_lt17(yvy49000, yvy50000, cbf) → new_esEs9(new_compare8(yvy49000, yvy50000, cbf), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Double) → new_ltEs7(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bd, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs7(yvy4000, yvy3000, bff, bfg, bfh)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_esEs26(yvy49000, yvy50000, ty_Char) → new_esEs8(yvy49000, yvy50000)
new_ltEs20(yvy49002, yvy50002, app(app(app(ty_@3, dcg), dch), dda)) → new_ltEs13(yvy49002, yvy50002, dcg, dch, dda)
new_ltEs19(yvy4900, yvy5000, ty_Int) → new_ltEs11(yvy4900, yvy5000)
new_mkBalBranch6MkBalBranch4(EmptyFM, yvy50, yvy51, yvy67, True, h, ba) → error([])
new_addToFM_C15(yvy51, yvy52, yvy53, yvy54, yvy41, False, h, ba) → Branch(Nothing, new_addToFM0(yvy51, yvy41, ba), yvy52, yvy53, yvy54)
new_lt13(yvy49000, yvy50000) → new_esEs9(new_compare10(yvy49000, yvy50000), LT)
new_esEs28(yvy4000, yvy3000, app(app(ty_@2, bgf), bgg)) → new_esEs6(yvy4000, yvy3000, bgf, bgg)
new_gt0(yvy300, h) → new_esEs9(new_compare31(yvy300, h), GT)
new_esEs25(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_esEs30(yvy20, yvy15, ty_Ordering) → new_esEs9(yvy20, yvy15)
new_addToFM_C24(yvy51, yvy52, yvy53, yvy54, yvy41, False, h, ba) → new_addToFM_C15(yvy51, yvy52, yvy53, yvy54, yvy41, new_gt(h), h, ba)
new_esEs24(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs21(yvy4000, yvy3000, app(ty_Maybe, ee)) → new_esEs4(yvy4000, yvy3000, ee)
new_ltEs6(yvy49001, yvy50001, app(app(ty_@2, ccb), ccc)) → new_ltEs5(yvy49001, yvy50001, ccb, ccc)
new_ltEs7(yvy4900, yvy5000) → new_fsEs(new_compare27(yvy4900, yvy5000))
new_esEs27(yvy49001, yvy50001, ty_Int) → new_esEs14(yvy49001, yvy50001)
new_lt6(yvy49000, yvy50000, app(app(app(ty_@3, bah), bba), bbb)) → new_lt14(yvy49000, yvy50000, bah, bba, bbb)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Maybe, cee), ced) → new_ltEs9(yvy49000, yvy50000, cee)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs24(yvy4000, yvy3000, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs7(yvy4000, yvy3000, bbh, bca, bcb)
new_lt20(yvy49000, yvy50000, app(ty_[], daf)) → new_lt15(yvy49000, yvy50000, daf)
new_splitGT23(yvy300, yvy31, yvy32, yvy33, yvy34, False, h, ba) → new_splitGT16(yvy300, yvy31, yvy32, yvy33, yvy34, new_esEs9(new_compare31(yvy300, h), LT), h, ba)
new_lt12(yvy49000, yvy50000, bhg, bhh) → new_esEs9(new_compare18(yvy49000, yvy50000, bhg, bhh), LT)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_@0) → new_ltEs16(yvy49000, yvy50000)
new_lt6(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_esEs29(yvy400, yvy500, ty_Bool) → new_esEs15(yvy400, yvy500)
new_esEs26(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_esEs10(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), bh) → new_asAs(new_esEs11(yvy4000, yvy3000, bh), new_esEs12(yvy4001, yvy3001, bh))
new_splitLT24(yvy30, yvy31, yvy32, yvy33, yvy34, yvy35, True, hd, bhf) → new_splitLT4(yvy33, yvy35, hd, bhf)
new_asAs(False, yvy182) → False
new_primMulInt(Neg(yvy40010), Pos(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_primMulInt(Pos(yvy40010), Neg(yvy30010)) → Neg(new_primMulNat0(yvy40010, yvy30010))
new_ltEs6(yvy49001, yvy50001, ty_Float) → new_ltEs4(yvy49001, yvy50001)
new_sizeFM1(EmptyFM, cf, cg) → Pos(Zero)
new_primCmpInt(Neg(Succ(yvy4900)), Neg(yvy500)) → new_primCmpNat2(yvy500, yvy4900)
new_primMulNat0(Zero, Succ(yvy300100)) → Zero
new_primMulNat0(Succ(yvy400100), Zero) → Zero
new_gt1(yvy400, h) → new_esEs9(new_compare32(yvy400, h), GT)
new_esEs21(yvy4000, yvy3000, app(app(ty_Either, de), df)) → new_esEs5(yvy4000, yvy3000, de, df)
new_esEs26(yvy49000, yvy50000, ty_Integer) → new_esEs13(yvy49000, yvy50000)
new_esEs32(yvy400, yvy300, app(app(app(ty_@3, ca), cb), cc)) → new_esEs7(yvy400, yvy300, ca, cb, cc)
new_lt19(yvy49001, yvy50001, ty_Ordering) → new_lt18(yvy49001, yvy50001)
new_esEs32(yvy400, yvy300, ty_Bool) → new_esEs15(yvy400, yvy300)
new_ltEs6(yvy49001, yvy50001, ty_Double) → new_ltEs7(yvy49001, yvy50001)
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, ty_Bool) → new_ltEs8(yvy49000, yvy50000)
new_esEs31(yvy400, yvy300, ty_Double) → new_esEs16(yvy400, yvy300)
new_lt10(yvy49000, yvy50000, bgc) → new_esEs9(new_compare19(yvy49000, yvy50000, bgc), LT)
new_compare25(yvy49000, yvy50000, False, bhg, bhh) → new_compare110(yvy49000, yvy50000, new_ltEs5(yvy49000, yvy50000, bhg, bhh), bhg, bhh)
new_compare28(yvy49000, yvy50000, app(ty_Ratio, bag)) → new_compare8(yvy49000, yvy50000, bag)
new_lt19(yvy49001, yvy50001, ty_Float) → new_lt8(yvy49001, yvy50001)
new_esEs5(Right(yvy4000), Right(yvy3000), bd, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_lt20(yvy49000, yvy50000, ty_Float) → new_lt8(yvy49000, yvy50000)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, new_lt5(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba)), new_sizeFM(Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), h, ba)), h, ba)
new_splitGT5(Branch(yvy340, yvy341, yvy342, yvy343, yvy344), h, ba) → new_splitGT30(yvy340, yvy341, yvy342, yvy343, yvy344, Nothing, h, ba)
new_ltEs13(@3(yvy49000, yvy49001, yvy49002), @3(yvy50000, yvy50001, yvy50002), chc, chd, che) → new_pePe(new_lt20(yvy49000, yvy50000, chc), new_asAs(new_esEs26(yvy49000, yvy50000, chc), new_pePe(new_lt19(yvy49001, yvy50001, chd), new_asAs(new_esEs27(yvy49001, yvy50001, chd), new_ltEs20(yvy49002, yvy50002, che)))))
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs25(yvy4001, yvy3001, ty_Integer) → new_esEs13(yvy4001, yvy3001)
new_esEs5(Right(yvy4000), Right(yvy3000), bd, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_splitLT23(yvy31, yvy32, yvy33, yvy34, yvy400, True, h, ba) → new_splitLT4(yvy33, yvy400, h, ba)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkBalBranch(yvy50, yvy51, new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, Neg(yvy620), yvy63, yvy64), yvy53, h, ba), yvy54, h, ba)
new_esEs26(yvy49000, yvy50000, ty_@0) → new_esEs18(yvy49000, yvy50000)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy5000))) → new_primCmpNat2(Zero, yvy5000)
new_esEs28(yvy4000, yvy3000, ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy400, yvy500, app(ty_Ratio, bh)) → new_esEs10(yvy400, yvy500, bh)
new_mkBalBranch6MkBalBranch01(yvy540, yvy541, yvy542, EmptyFM, yvy544, yvy50, yvy51, yvy67, False, h, ba) → error([])
new_esEs29(yvy400, yvy500, ty_Char) → new_esEs8(yvy400, yvy500)
new_esEs24(yvy4000, yvy3000, app(ty_Ratio, bbg)) → new_esEs10(yvy4000, yvy3000, bbg)
new_esEs23(yvy4002, yvy3002, ty_Double) → new_esEs16(yvy4002, yvy3002)
new_esEs25(yvy4001, yvy3001, ty_@0) → new_esEs18(yvy4001, yvy3001)
new_splitGT14(yvy31, yvy32, yvy33, yvy34, yvy400, False, h, ba) → yvy34
new_esEs30(yvy20, yvy15, ty_@0) → new_esEs18(yvy20, yvy15)
new_esEs30(yvy20, yvy15, app(app(ty_Either, ddd), dde)) → new_esEs5(yvy20, yvy15, ddd, dde)
new_splitLT13(yvy31, yvy32, yvy33, yvy34, False, h, ba) → yvy33
new_lt19(yvy49001, yvy50001, ty_@0) → new_lt16(yvy49001, yvy50001)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Double) → new_esEs16(yvy4000, yvy3000)
new_splitGT16(yvy300, yvy31, yvy32, yvy33, yvy34, False, h, ba) → yvy34
new_ltEs6(yvy49001, yvy50001, ty_Bool) → new_ltEs8(yvy49001, yvy50001)
new_esEs32(yvy400, yvy300, app(ty_[], ce)) → new_esEs19(yvy400, yvy300, ce)
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, app(ty_Ratio, cha)) → new_ltEs17(yvy49000, yvy50000, cha)
new_esEs20(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, app(ty_Ratio, fc)) → new_esEs10(yvy4001, yvy3001, fc)
new_esEs22(yvy4001, yvy3001, ty_Bool) → new_esEs15(yvy4001, yvy3001)
new_primMinusNat0(Zero, Succ(yvy18800)) → Neg(Succ(yvy18800))
new_esEs14(yvy400, yvy300) → new_primEqInt(yvy400, yvy300)
new_esEs28(yvy4000, yvy3000, ty_Bool) → new_esEs15(yvy4000, yvy3000)
new_compare211(yvy49000, yvy50000, False) → new_compare112(yvy49000, yvy50000, new_ltEs18(yvy49000, yvy50000))
new_primCmpInt2(yvy6200, yvy140) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), yvy140)
new_esEs25(yvy4001, yvy3001, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs7(yvy4001, yvy3001, bdb, bdc, bdd)
new_ltEs6(yvy49001, yvy50001, ty_Char) → new_ltEs15(yvy49001, yvy50001)
new_lt19(yvy49001, yvy50001, ty_Integer) → new_lt13(yvy49001, yvy50001)
new_esEs20(yvy49000, yvy50000, ty_Float) → new_esEs17(yvy49000, yvy50000)
new_compare28(yvy49000, yvy50000, ty_Float) → new_compare7(yvy49000, yvy50000)
new_ps(Neg(yvy1890), Neg(yvy1880)) → Neg(new_primPlusNat1(yvy1890, yvy1880))
new_compare28(yvy49000, yvy50000, ty_@0) → new_compare16(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bd, app(ty_Maybe, bga)) → new_esEs4(yvy4000, yvy3000, bga)
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bd, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_compare11(yvy49000, yvy50000, False) → GT
new_esEs30(yvy20, yvy15, app(app(ty_@2, ddf), ddg)) → new_esEs6(yvy20, yvy15, ddf, ddg)
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_esEs21(yvy4000, yvy3000, ty_Char) → new_esEs8(yvy4000, yvy3000)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_ltEs10(Right(yvy49000), Left(yvy50000), cfg, ced) → False
new_esEs20(yvy49000, yvy50000, ty_Int) → new_esEs14(yvy49000, yvy50000)
new_mkBranch(yvy223, yvy224, yvy225, yvy226, yvy227, cf, cg) → Branch(yvy224, yvy225, new_mkBranchUnbox(yvy226, yvy224, yvy227, new_ps(new_ps(Pos(Succ(Zero)), new_sizeFM1(yvy226, cf, cg)), new_sizeFM1(yvy227, cf, cg)), cf, cg), yvy226, yvy227)
new_compare11(yvy49000, yvy50000, True) → LT
new_esEs31(yvy400, yvy300, app(ty_Maybe, cd)) → new_esEs4(yvy400, yvy300, cd)
new_esEs4(Just(yvy4000), Just(yvy3000), app(ty_[], cbb)) → new_esEs19(yvy4000, yvy3000, cbb)
new_esEs5(Left(yvy4000), Left(yvy3000), app(app(ty_Either, bdg), bdh), be) → new_esEs5(yvy4000, yvy3000, bdg, bdh)
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, app(ty_Maybe, cfh)) → new_ltEs9(yvy49000, yvy50000, cfh)
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, ty_Char) → new_ltEs15(yvy49000, yvy50000)
new_ps(Pos(yvy1890), Neg(yvy1880)) → new_primMinusNat0(yvy1890, yvy1880)
new_ps(Neg(yvy1890), Pos(yvy1880)) → new_primMinusNat0(yvy1880, yvy1890)
new_compare112(yvy49000, yvy50000, False) → GT
new_splitLT14(yvy31, yvy32, yvy33, yvy34, yvy400, False, h, ba) → yvy33
new_mkBalBranch6MkBalBranch11(yvy54, yvy50, yvy51, yvy670, yvy671, yvy672, yvy673, EmptyFM, False, h, ba) → error([])
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Float) → new_esEs17(yvy4000, yvy3000)
new_esEs24(yvy4000, yvy3000, ty_@0) → new_esEs18(yvy4000, yvy3000)
new_esEs20(yvy49000, yvy50000, app(ty_[], cbe)) → new_esEs19(yvy49000, yvy50000, cbe)
new_ltEs10(Right(yvy49000), Right(yvy50000), cfg, ty_Integer) → new_ltEs12(yvy49000, yvy50000)
new_esEs22(yvy4001, yvy3001, ty_Int) → new_esEs14(yvy4001, yvy3001)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), yvy40, yvy41, Branch(yvy60, yvy61, Pos(yvy620), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), app(ty_Maybe, h), ba)
new_esEs22(yvy4001, yvy3001, ty_Double) → new_esEs16(yvy4001, yvy3001)
new_esEs24(yvy4000, yvy3000, ty_Ordering) → new_esEs9(yvy4000, yvy3000)
new_addToFM_C24(yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_mkBalBranch(Nothing, yvy51, new_addToFM_C0(yvy53, Nothing, yvy41, h, ba), yvy54, h, ba)
new_compare7(Float(yvy49000, yvy49001), Float(yvy50000, yvy50001)) → new_compare9(new_sr(yvy49000, yvy50000), new_sr(yvy49001, yvy50001))
new_ltEs6(yvy49001, yvy50001, ty_Int) → new_ltEs11(yvy49001, yvy50001)
new_addToFM_C25(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, False, h, ba) → new_addToFM_C16(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_gt1(yvy400, h), h, ba)
new_esEs27(yvy49001, yvy50001, app(ty_[], dbh)) → new_esEs19(yvy49001, yvy50001, dbh)
new_lt4(yvy49000, yvy50000) → new_esEs9(new_compare6(yvy49000, yvy50000), LT)
new_esEs31(yvy400, yvy300, ty_@0) → new_esEs18(yvy400, yvy300)
new_compare0([], :(yvy50000, yvy50001), he) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(yvy49000, yvy50000, ty_Ordering) → new_esEs9(yvy49000, yvy50000)
new_addToFM_C0(EmptyFM, yvy40, yvy41, h, ba) → Branch(yvy40, yvy41, Pos(Succ(Zero)), new_emptyFM(h, ba), new_emptyFM(h, ba))
new_splitGT22(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, False, bb, bc) → new_splitGT13(yvy15, yvy16, yvy17, yvy18, yvy19, yvy20, new_esEs9(new_compare33(yvy20, yvy15, bb), LT), bb, bc)
new_asAs(True, yvy182) → yvy182
new_esEs27(yvy49001, yvy50001, ty_Char) → new_esEs8(yvy49001, yvy50001)
new_compare32(yvy400, h) → new_compare26(Just(yvy400), Nothing, False, h)
new_primMulNat0(Succ(yvy400100), Succ(yvy300100)) → new_primPlusNat0(new_primMulNat0(yvy400100, Succ(yvy300100)), yvy300100)
new_addToFM_C16(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, False, h, ba) → Branch(Just(yvy400), new_addToFM0(yvy51, yvy41, ba), yvy52, yvy53, yvy54)
new_ltEs19(yvy4900, yvy5000, ty_Ordering) → new_ltEs18(yvy4900, yvy5000)
new_esEs32(yvy400, yvy300, ty_Double) → new_esEs16(yvy400, yvy300)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Int) → new_esEs14(yvy4000, yvy3000)
new_esEs27(yvy49001, yvy50001, ty_Bool) → new_esEs15(yvy49001, yvy50001)
new_esEs18(@0, @0) → True
new_compare211(yvy49000, yvy50000, True) → EQ
new_ltEs9(Just(yvy49000), Just(yvy50000), ty_Int) → new_ltEs11(yvy49000, yvy50000)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkBalBranch(yvy60, yvy61, yvy63, new_mkVBalBranch0(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba), h, ba)
new_esEs26(yvy49000, yvy50000, app(app(ty_@2, daa), dab)) → new_esEs6(yvy49000, yvy50000, daa, dab)
new_esEs32(yvy400, yvy300, ty_Char) → new_esEs8(yvy400, yvy300)
new_esEs26(yvy49000, yvy50000, ty_Double) → new_esEs16(yvy49000, yvy50000)
new_esEs5(Right(yvy4000), Right(yvy3000), bd, ty_Double) → new_esEs16(yvy4000, yvy3000)
new_esEs30(yvy20, yvy15, ty_Double) → new_esEs16(yvy20, yvy15)
new_mkBalBranch(yvy50, yvy51, yvy67, yvy54, h, ba) → new_mkBalBranch6MkBalBranch5(yvy54, yvy50, yvy51, yvy67, new_lt5(new_ps(new_mkBalBranch6Size_l(yvy54, yvy50, yvy51, yvy67, h, ba), new_mkBalBranch6Size_r(yvy54, yvy50, yvy51, yvy67, h, ba)), Pos(Succ(Succ(Zero)))), h, ba)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_Integer) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy400, yvy500, ty_Float) → new_esEs17(yvy400, yvy500)
new_esEs4(Just(yvy4000), Just(yvy3000), app(app(app(ty_@3, caf), cag), cah)) → new_esEs7(yvy4000, yvy3000, caf, cag, cah)
new_esEs5(Left(yvy4000), Left(yvy3000), app(ty_Ratio, bec), be) → new_esEs10(yvy4000, yvy3000, bec)
new_splitGT30(Nothing, yvy31, yvy32, yvy33, yvy34, Just(yvy400), h, ba) → new_splitGT24(yvy31, yvy32, yvy33, yvy34, yvy400, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), GT), h, ba)
new_esEs29(yvy400, yvy500, app(ty_Maybe, cd)) → new_esEs4(yvy400, yvy500, cd)
new_splitLT30(Nothing, yvy31, yvy32, yvy33, yvy34, Nothing, h, ba) → new_splitLT13(yvy31, yvy32, yvy33, yvy34, new_gt(h), h, ba)
new_splitLT16(yvy300, yvy31, yvy32, yvy33, yvy34, False, h, ba) → yvy33
new_compare28(yvy49000, yvy50000, ty_Integer) → new_compare10(yvy49000, yvy50000)
new_ltEs10(Left(yvy49000), Left(yvy50000), app(ty_Ratio, cff), ced) → new_ltEs17(yvy49000, yvy50000, cff)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkBalBranch(yvy60, yvy61, yvy63, new_mkVBalBranch0(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba), h, ba)
new_lt11(yvy49000, yvy50000, db, dc) → new_esEs9(new_compare17(yvy49000, yvy50000, db, dc), LT)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy620, yvy63, yvy64, h, ba) → new_sizeFM0(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_esEs9(LT, LT) → True
new_esEs19(:(yvy4000, yvy4001), :(yvy3000, yvy3001), ce) → new_asAs(new_esEs28(yvy4000, yvy3000, ce), new_esEs19(yvy4001, yvy3001, ce))
new_esEs22(yvy4001, yvy3001, app(app(ty_Either, eg), eh)) → new_esEs5(yvy4001, yvy3001, eg, eh)
new_primCompAux00(yvy206, GT) → GT
new_ltEs10(Left(yvy49000), Left(yvy50000), ty_Bool, ced) → new_ltEs8(yvy49000, yvy50000)
new_addToFM_C0(Branch(Just(yvy500), yvy51, yvy52, yvy53, yvy54), Nothing, yvy41, h, ba) → new_addToFM_C23(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, new_esEs9(new_compare26(Nothing, Just(yvy500), False, h), LT), h, ba)
new_esEs31(yvy400, yvy300, app(app(ty_@2, bf), bg)) → new_esEs6(yvy400, yvy300, bf, bg)
new_splitGT5(EmptyFM, h, ba) → new_emptyFM(h, ba)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(yvy49000, yvy50000, app(app(ty_@2, bhg), bhh)) → new_lt12(yvy49000, yvy50000, bhg, bhh)
new_esEs29(yvy400, yvy500, ty_Ordering) → new_esEs9(yvy400, yvy500)
new_ltEs19(yvy4900, yvy5000, ty_@0) → new_ltEs16(yvy4900, yvy5000)
new_compare28(yvy49000, yvy50000, app(app(ty_@2, baa), bab)) → new_compare18(yvy49000, yvy50000, baa, bab)
new_esEs4(Just(yvy4000), Just(yvy3000), ty_@0) → new_esEs18(yvy4000, yvy3000)
new_primCmpNat0(yvy4900, Succ(yvy5000)) → new_primCmpNat1(yvy4900, yvy5000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primCmpInt(Neg(Succ(yvy4900)), Pos(yvy500)) → LT
new_ltEs17(yvy4900, yvy5000, dd) → new_fsEs(new_compare8(yvy4900, yvy5000, dd))
new_addToFM_C0(Branch(Nothing, yvy51, yvy52, yvy53, yvy54), Just(yvy400), yvy41, h, ba) → new_addToFM_C25(yvy51, yvy52, yvy53, yvy54, yvy400, yvy41, new_esEs9(new_compare26(Just(yvy400), Nothing, False, h), LT), h, ba)
new_not(True) → False
new_esEs15(False, False) → True
new_primMinusNat0(Succ(yvy18900), Succ(yvy18800)) → new_primMinusNat0(yvy18900, yvy18800)
new_addToFM_C14(yvy500, yvy51, yvy52, yvy53, yvy54, yvy41, True, h, ba) → new_mkBalBranch(Just(yvy500), yvy51, yvy53, new_addToFM_C0(yvy54, Nothing, yvy41, h, ba), h, ba)

The set Q consists of the following terms:

new_ltEs20(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_@0)
new_compare110(x0, x1, True, x2, x3)
new_esEs18(@0, @0)
new_gt2(x0, x1, x2)
new_primMinusNat0(Zero, Succ(x0))
new_esEs32(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Left(x1), ty_Double, x2)
new_splitGT23(x0, x1, x2, x3, x4, True, x5, x6)
new_primMinusNat0(Zero, Zero)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_primMinusNat0(Succ(x0), Zero)
new_splitLT15(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_esEs11(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Bool)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_compare210(x0, x1, False)
new_asAs(True, x0)
new_lt20(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_ltEs9(Just(x0), Just(x1), ty_@0)
new_esEs32(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs10(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_esEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs4(Just(x0), Just(x1), ty_Int)
new_esEs31(x0, x1, ty_Float)
new_compare25(x0, x1, False, x2, x3)
new_compare9(x0, x1)
new_splitGT4(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_esEs26(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Float)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_compare25(x0, x1, True, x2, x3)
new_compare15(x0, x1)
new_mkVBalBranch3MkVBalBranch22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs19(:(x0, x1), [], x2)
new_lt11(x0, x1, x2, x3)
new_ltEs10(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs6(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs15(True, True)
new_primCmpNat0(x0, Zero)
new_splitGT24(x0, x1, x2, x3, x4, True, x5, x6)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt6(x0, x1, ty_@0)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_@0)
new_splitGT5(EmptyFM, x0, x1)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, ty_Bool)
new_compare28(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Int)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Float)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs15(False, False)
new_ltEs9(Just(x0), Just(x1), ty_Int)
new_lt13(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat2(Succ(x0), x1)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9)
new_esEs23(x0, x1, ty_Bool)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Nothing, Just(x0), x1)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Bool)
new_primCompAux00(x0, EQ)
new_lt6(x0, x1, ty_Double)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_ltEs10(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_sizeFM(EmptyFM, x0, x1)
new_ltEs6(x0, x1, ty_Float)
new_esEs31(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Int)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_compare0([], [], x0)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs8(True, True)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(Char(x0), Char(x1))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs15(x0, x1)
new_compare28(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs11(x0, x1, ty_Integer)
new_addToFM_C24(x0, x1, x2, x3, x4, True, x5, x6)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Int)
new_splitLT23(x0, x1, x2, x3, x4, False, x5, x6)
new_esEs21(x0, x1, ty_Bool)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_esEs25(x0, x1, ty_Int)
new_ltEs9(Just(x0), Just(x1), ty_Float)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(True, x0)
new_esEs20(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1, False, x2, x3)
new_addToFM_C0(Branch(Just(x0), x1, x2, x3, x4), Just(x5), x6, x7, x8)
new_splitLT16(x0, x1, x2, x3, x4, False, x5, x6)
new_lt20(x0, x1, ty_Ordering)
new_primCompAux00(x0, GT)
new_ltEs10(Right(x0), Right(x1), x2, ty_Int)
new_lt10(x0, x1, x2)
new_primCmpNat1(Zero, Zero)
new_ltEs6(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1, ty_Char)
new_lt14(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs9(Just(x0), Nothing, x1)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_@0)
new_compare111(x0, x1, True, x2, x3, x4)
new_splitLT16(x0, x1, x2, x3, x4, True, x5, x6)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs18(LT, GT)
new_ltEs18(GT, LT)
new_esEs19([], [], x0)
new_lt6(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs19(:(x0, x1), :(x2, x3), x4)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1, x2, x3)
new_compare11(x0, x1, False)
new_esEs22(x0, x1, ty_Float)
new_ltEs9(Nothing, Just(x0), x1)
new_ltEs19(x0, x1, ty_Double)
new_compare33(x0, x1, x2)
new_splitLT30(Nothing, x0, x1, x2, x3, Nothing, x4, x5)
new_compare29(x0, x1)
new_esEs26(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs9(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs4(Just(x0), Just(x1), ty_Char)
new_compare28(x0, x1, ty_@0)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_ltEs4(x0, x1)
new_addToFM_C16(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_primMulNat0(Zero, Zero)
new_esEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare23(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_@0)
new_ltEs18(LT, EQ)
new_ltEs18(EQ, LT)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_mkBalBranch6MkBalBranch4(x0, x1, x2, x3, False, x4, x5)
new_ltEs10(Left(x0), Left(x1), ty_Char, x2)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_gt3(x0, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_compare0([], :(x0, x1), x2)
new_lt20(x0, x1, ty_Double)
new_esEs4(Just(x0), Nothing, x1)
new_ltEs10(Left(x0), Left(x1), ty_@0, x2)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Float)
new_ps(Pos(x0), Neg(x1))
new_ps(Neg(x0), Pos(x1))
new_ltEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), False, x12, x13)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_splitLT30(Just(x0), x1, x2, x3, x4, Just(x5), x6, x7)
new_lt20(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Bool)
new_ltEs10(Right(x0), Right(x1), x2, ty_Integer)
new_sIZE_RATIO
new_addToFM_C25(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_esEs25(x0, x1, ty_Double)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_esEs29(x0, x1, ty_@0)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch12(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_mkVBalBranch3MkVBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13)
new_esEs27(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Double)
new_splitGT23(x0, x1, x2, x3, x4, False, x5, x6)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Float)
new_splitLT22(x0, x1, x2, x3, x4, True, x5, x6)
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs19([], :(x0, x1), x2)
new_esEs12(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_splitGT4(EmptyFM, x0, x1, x2)
new_ltEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare26(Nothing, Just(x0), False, x1)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs31(x0, x1, ty_Double)
new_ltEs7(x0, x1)
new_esEs28(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Char)
new_splitGT30(Just(x0), x1, x2, x3, x4, Nothing, x5, x6)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare7(Float(x0, x1), Float(x2, x3))
new_emptyFM(x0, x1)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Bool)
new_splitLT13(x0, x1, x2, x3, True, x4, x5)
new_compare16(@0, @0)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Ordering)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_sizeFM1(Branch(x0, x1, x2, x3, x4), x5, x6)
new_compare17(x0, x1, x2, x3)
new_splitLT5(EmptyFM, x0, x1)
new_ltEs16(x0, x1)
new_splitLT24(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_esEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt5(x0, x1)
new_ltEs11(x0, x1)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_lt19(x0, x1, ty_Float)
new_esEs30(x0, x1, ty_Integer)
new_compare28(x0, x1, ty_Char)
new_esEs4(Nothing, Nothing, x0)
new_mkVBalBranch3MkVBalBranch12(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13)
new_mkVBalBranch3MkVBalBranch22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13)
new_ltEs19(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_splitLT30(Just(x0), x1, x2, x3, x4, Nothing, x5, x6)
new_lt6(x0, x1, ty_Integer)
new_addToFM_C15(x0, x1, x2, x3, x4, False, x5, x6)
new_ltEs10(Right(x0), Right(x1), x2, ty_Double)
new_compare28(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs25(x0, x1, ty_Char)
new_ltEs10(Right(x0), Right(x1), x2, ty_Bool)
new_compare110(x0, x1, False, x2, x3)
new_mkVBalBranch0(x0, x1, Branch(x2, x3, Neg(x4), x5, x6), Branch(x7, x8, x9, x10, x11), x12, x13)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9, x10, x11, False, x12, x13)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs4(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare28(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_splitGT22(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_splitGT16(x0, x1, x2, x3, x4, False, x5, x6)
new_splitLT15(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_splitGT14(x0, x1, x2, x3, x4, True, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, app(ty_[], x2))
new_addToFM_C0(EmptyFM, x0, x1, x2, x3)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_primPlusNat1(Zero, Succ(x0))
new_addToFM_C0(Branch(Nothing, x0, x1, x2, x3), Nothing, x4, x5, x6)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_splitLT13(x0, x1, x2, x3, False, x4, x5)
new_splitGT13(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs30(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, True, x4, x5)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_gt(x0)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Double)
new_primMinusNat0(Succ(x0), Succ(x1))
new_compare19(x0, x1, x2)
new_compare13(x0, x1, True, x2)
new_esEs9(GT, GT)
new_ltEs9(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs8(False, False)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, EmptyFM, False, x7, x8)
new_splitGT15(x0, x1, x2, x3, False, x4, x5)
new_addToFM0(x0, x1, x2)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_compare32(x0, x1)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_addToFM_C25(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primCompAux00(x0, LT)
new_ltEs8(True, False)
new_ltEs8(False, True)
new_primCmpInt0(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM_C26(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_splitLT30(Nothing, x0, x1, x2, x3, Just(x4), x5, x6)
new_pePe(False, x0)
new_addToFM_C26(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_esEs21(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare111(x0, x1, False, x2, x3, x4)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9)
new_lt15(x0, x1, x2)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ps(Pos(x0), Pos(x1))
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs30(x0, x1, ty_Ordering)
new_esEs4(Just(x0), Just(x1), ty_Double)
new_sizeFM0(x0, x1, x2, x3, x4, x5, x6)
new_esEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare26(Nothing, Nothing, False, x0)
new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs15(False, True)
new_esEs15(True, False)
new_esEs23(x0, x1, ty_Double)
new_esEs9(EQ, EQ)
new_gt0(x0, x1)
new_esEs32(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare211(x0, x1, True)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch4(EmptyFM, x0, x1, x2, True, x3, x4)
new_esEs28(x0, x1, ty_Ordering)
new_ps(Neg(x0), Neg(x1))
new_lt19(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, x3, False, x4, x5)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare18(x0, x1, x2, x3)
new_splitGT24(x0, x1, x2, x3, x4, False, x5, x6)
new_ltEs18(LT, LT)
new_ltEs6(x0, x1, ty_Integer)
new_ltEs9(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Bool)
new_ltEs14(x0, x1, x2)
new_esEs4(Just(x0), Just(x1), ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare211(x0, x1, False)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat2(Zero, x0)
new_esEs14(x0, x1)
new_esEs29(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, ty_Int)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_splitLT14(x0, x1, x2, x3, x4, True, x5, x6)
new_splitLT22(x0, x1, x2, x3, x4, False, x5, x6)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs12(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_addToFM_C0(Branch(Nothing, x0, x1, x2, x3), Just(x4), x5, x6, x7)
new_esEs28(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Ordering)
new_splitLT14(x0, x1, x2, x3, x4, False, x5, x6)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Bool)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_splitGT13(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_compare26(x0, x1, True, x2)
new_esEs22(x0, x1, ty_Bool)
new_ltEs10(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Just(x0), Just(x1), ty_Integer)
new_compare12(x0, x1, True, x2, x3)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(GT, EQ)
new_ltEs18(EQ, GT)
new_esEs29(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Double)
new_esEs4(Just(x0), Just(x1), ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_ltEs10(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Bool)
new_mkBranchUnbox(x0, x1, x2, x3, x4, x5)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Ordering)
new_sr(x0, x1)
new_addToFM_C14(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_ltEs9(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs24(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_compare210(x0, x1, True)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_compare28(x0, x1, ty_Ordering)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, False, x4, x5)
new_lt19(x0, x1, ty_@0)
new_ltEs6(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Just(x0), Just(x1), ty_Char)
new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_splitGT15(x0, x1, x2, x3, True, x4, x5)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Integer)
new_ltEs10(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt17(x0, x1, x2)
new_addToFM_C0(Branch(Just(x0), x1, x2, x3, x4), Nothing, x5, x6, x7)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_splitLT4(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_ltEs10(Right(x0), Left(x1), x2, x3)
new_esEs28(x0, x1, ty_Int)
new_ltEs10(Left(x0), Right(x1), x2, x3)
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs9(Just(x0), Just(x1), ty_Bool)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_compare112(x0, x1, False)
new_ltEs10(Right(x0), Right(x1), x2, ty_@0)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(:(x0, x1), [], x2)
new_primPlusNat1(Succ(x0), Zero)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, ty_Double)
new_compare31(x0, x1)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, EmptyFM, True, x3, x4)
new_primMulNat0(Zero, Succ(x0))
new_lt6(x0, x1, ty_Ordering)
new_ltEs18(EQ, EQ)
new_lt19(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Ordering)
new_compare26(Just(x0), Just(x1), False, x2)
new_primCmpInt2(x0, x1)
new_addToFM(x0, x1, x2, x3, x4)
new_esEs30(x0, x1, ty_Bool)
new_primCompAux0(x0, x1, x2, x3)
new_splitLT23(x0, x1, x2, x3, x4, True, x5, x6)
new_mkVBalBranch0(x0, x1, Branch(x2, x3, Pos(x4), x5, x6), Branch(x7, x8, x9, x10, x11), x12, x13)
new_esEs28(x0, x1, ty_Integer)
new_not(True)
new_esEs20(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(ty_[], x2))
new_sizeFM1(EmptyFM, x0, x1)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare14(x0, x1, x2, x3, x4)
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_lt8(x0, x1)
new_esEs4(Just(x0), Just(x1), ty_@0)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_lt20(x0, x1, ty_Int)
new_lt7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_ltEs20(x0, x1, ty_Bool)
new_splitGT30(Just(x0), x1, x2, x3, x4, Just(x5), x6, x7)
new_addToFM_C14(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, ty_@0)
new_not(False)
new_addToFM_C24(x0, x1, x2, x3, x4, False, x5, x6)
new_lt9(x0, x1)
new_ltEs19(x0, x1, ty_Int)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, Branch(x3, x4, x5, x6, x7), True, x8, x9)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs8(Char(x0), Char(x1))
new_esEs29(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Int)
new_compare28(x0, x1, app(ty_[], x2))
new_compare13(x0, x1, False, x2)
new_splitGT14(x0, x1, x2, x3, x4, False, x5, x6)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primEqNat0(Succ(x0), Zero)
new_esEs12(x0, x1, ty_Int)
new_compare10(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Float)
new_lt16(x0, x1)
new_esEs31(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_mkBalBranch6MkBalBranch4(Branch(x0, x1, x2, x3, x4), x5, x6, x7, True, x8, x9)
new_splitLT24(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_esEs27(x0, x1, ty_Int)
new_splitLT4(EmptyFM, x0, x1, x2)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_splitLT5(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs10(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs18(GT, GT)
new_sr0(Integer(x0), Integer(x1))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_primCmpInt0(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13)
new_esEs23(x0, x1, ty_@0)
new_esEs13(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Integer)
new_ltEs10(Right(x0), Right(x1), x2, ty_Float)
new_fsEs(x0)
new_ltEs10(Left(x0), Left(x1), ty_Integer, x2)
new_compare26(Just(x0), Nothing, False, x1)
new_ltEs20(x0, x1, ty_Double)
new_ltEs10(Left(x0), Left(x1), ty_Ordering, x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare28(x0, x1, ty_Integer)
new_compare30(x0)
new_ltEs9(Just(x0), Just(x1), ty_Ordering)
new_addToFM_C16(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, EmptyFM, x3, x4, x5, x6, False, x7, x8)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs10(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs19(x0, x1, ty_Integer)
new_splitGT16(x0, x1, x2, x3, x4, True, x5, x6)
new_lt18(x0, x1)
new_compare27(Double(x0, x1), Double(x2, x3))
new_ltEs10(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs10(Left(x0), Left(x1), ty_Int, x2)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt3(x0, x1)
new_esEs23(x0, x1, ty_Ordering)
new_addToFM_C15(x0, x1, x2, x3, x4, True, x5, x6)
new_compare112(x0, x1, True)
new_splitGT30(Nothing, x0, x1, x2, x3, Nothing, x4, x5)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Zero)
new_compare23(x0, x1, True, x2, x3)
new_compare28(x0, x1, ty_Float)
new_lt6(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Just(x0), Just(x1), app(ty_[], x2))
new_esEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt0(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_gt1(x0, x1)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Left(x0), Left(x1), ty_Float, x2)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(x0, x1, x2)
new_ltEs10(Right(x0), Right(x1), x2, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare28(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt0(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT22(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_compare11(x0, x1, True)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_splitGT30(Nothing, x0, x1, x2, x3, Just(x4), x5, x6)
new_ltEs10(Left(x0), Left(x1), ty_Bool, x2)
new_mkVBalBranch0(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7, x8)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primCmpInt0(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_ltEs10(Right(x0), Right(x1), x2, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Just(x0), Just(x1), ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(LT, LT)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs10(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_splitGT5(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkVBalBranch0(x0, x1, EmptyFM, x2, x3, x4)
new_esEs22(x0, x1, ty_Integer)

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: